CA1127749A - Echo location system transmitting and receiving component signals of known initial time interval for determination of angular information - Google Patents
Echo location system transmitting and receiving component signals of known initial time interval for determination of angular informationInfo
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- CA1127749A CA1127749A CA303,851A CA303851A CA1127749A CA 1127749 A CA1127749 A CA 1127749A CA 303851 A CA303851 A CA 303851A CA 1127749 A CA1127749 A CA 1127749A
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Abstract
ABSTRACT
This invention relates to a method for ascertaining for one or more targets information about the positions and velocities of the targets by using at least one transmitter and at least one receiver stationed at known relative positions in a medium having a known signal propagation velocity. Each transmitter transmits concurrently at least one component signal of known initial time consisting of at least two member signals, the time intervals between member signals being initially known. The concurrent component signals are separable. Each target reflects each component signal to each receiver. From each received signal the component signals are separated. From the component signals member signals reflected by each target are identified. For each identified member signal its transit time between transmitter and receiver, and the interval time, between member signals of each component signal reflected by each target are measured. Target velocity components from each measured time interval are produced using the known initial time interval value. Each measured transit time in each component signal is corrected for determined relative motions between the transmitter, receiver and targets. The corr-ected transit time measurements in the component signals and the known signal propagation velocity are used to make target range determinations.
This invention relates to a method for ascertaining for one or more targets information about the positions and velocities of the targets by using at least one transmitter and at least one receiver stationed at known relative positions in a medium having a known signal propagation velocity. Each transmitter transmits concurrently at least one component signal of known initial time consisting of at least two member signals, the time intervals between member signals being initially known. The concurrent component signals are separable. Each target reflects each component signal to each receiver. From each received signal the component signals are separated. From the component signals member signals reflected by each target are identified. For each identified member signal its transit time between transmitter and receiver, and the interval time, between member signals of each component signal reflected by each target are measured. Target velocity components from each measured time interval are produced using the known initial time interval value. Each measured transit time in each component signal is corrected for determined relative motions between the transmitter, receiver and targets. The corr-ected transit time measurements in the component signals and the known signal propagation velocity are used to make target range determinations.
Description
~ ' ~127~
Echo location systems are designed to identify some subset of individual reflector or target parameters.
These parameters include the target position in terms like bearing and elevation angle, the range, target relative velocity and the impedance contrast which causes the echo and is also a measure of target quality. Individual targets distributed within a propagation medium make up a target :field. The propagation medium can be attenuative and preferentially cause the loss of the higher frequency components of a propagating signal according to some physical law. Additionally, the propagation medium can be dispersive causing the different frequency components of a signal to travel with different velocities hence, introducing distortations of phase and equivalently of form into the propagating signal as a function of its travel.
Such known echo systems emit a signal or signals into the propagation medium; the identification process involves detecting the echo train and performing a variety ~0 of appropriate analyses. While this procedure is conceptually straight forward, there are a number of practical difficulties which act to complicate, degrade and make ambiguous such identifications.
First, there is a noise background to consider which is almost always a problem in systems where signals are --1-- ~
transmitted and detected. Noise is defined in this instance as any contribution which is not a part of the particular identification process and has as its sources such elements as incoherent scattering by the propagation medium or even the targets themselves. There are a variety of techniques for the detection and enhancement of signals in the presence of noise.
Next, there is the inherent ambiguity between the , range and the relative velocity of a target. A moving ~o target can not only stretch or shrink a returning,echo æignature depending on the sense of its motion, but will also delay or speed up the time of its detection, hence affecting the range calculation. Once again, there are a variety of known techniques which can resolve this ambiguity. It is widely recognized that continuous wave signals, for example, a persistent sinusoid at a single frequency can provide good resolution of the target's relative velocity by means of the Doppler frequency shift.
The companion range resolution of such a signal is necessarily poor since its character is indistinguishable from cycle to cycle. Very short duration signals are affected only slightly by tar,get motion and while they provide good resolution in detection time, they convey little or no information about relative velocities. The chirp signal described by Klauder, Price, Darlington and Albersheim in the Bell System Technical - 112 774~
Journal, Vol. 39, pp 745-808, July 1960, represents a compromise having ambiguity in both velocity and range.
Its advantages lie rather in effectiveness of equipment utilization and the noise suppression of its companion correlation detection.
Lastly, there is the problem of resolving target angular parameters such as elevation and/or bearing. Cur-rently, definition of angles is achieved by the use of arrays of broad-beam source or receiver elements, or else 19 by means of narrow-beam source or receiver elements. In both cases, the space in which the target field is dis-tributed must be scanned or viewed only one small part at a time. Scanning is accomplished either electronically be steering array beams or sequencing the operation of large numbers of elements, or even mechanically by rotating ~perational narrow-beam elements to new positions.
The energy requirements of a scanned system are usually favorable since the entire field of potential targets need not be illuminated at once. On the negative side, however, the individual targets are then not being continuously monitored.
This invention employs encoded signals followed by the correlation of the received echo train with known ~ignal signatures. A relatively long signal train made up of essentially short signals is used, thereby encompassing ,, ~ .
, , , ' ' .
_3_ ~ . :
~lZ77~9 both continuous wave and impulse-like properties. The correlation step achieves a measure of noise suppression.
Simultaneous high resolution information about range and relative velocity is achieved essentially by means of simultaneous solutions involving use of all of the obser-vables embodied in the signal train after detection by correlation.
Both the sources and receivers operate as broad-beam elements with simultaneous illumination of all targets.
Angular resolution is achieved by appropriately interposing phase distorting lenses between the sources and echo receiv-ers. Information about the angles is encoded into the phase character of the propagating signal train. Energy require-ments are modest despite the simultaneous illumination of the entire field of targets because the high repetition rate of the system allows that a rather low echo signal level be tolerated. Also, since range and velocity resolution are not directly dependent on the use of high frequency signal components, lower frequency band signals 2Q may be used with correspondingly less energy loss through attenuation.
Even if the propagating medium does modify the traveling signals by altering their amplitude and phase spectral properties, the system described by the invention will be able to function nevertheless. Some empirical llZ7749 corrections would then have to be made to compensate for the propagation effects, but these could be easily determined by calibration studies using targets of known parameters.
STAq~EMENT OF THE INVENTION
According to one aspect of the present invention there is provided a method of determining angular information concerning the direction of a signal reflecting object relative to a signal transmitter and a signal receiver, comprising the steps of: aj transmitting a signal from the transmitter, such signal having a continuous amplitude spectrum between low and high frequency limits, for reflection from the object; b) receiving the reflected signal with the receiver; c) changing the phase of the signal in dependence upon the direction of its travel while propagating between the transmitter and the receiver, 8uch phase change characterized other than by a simple time delay; d) measuring the phase of the received reflected signal; and e) determining the angular information concerning direction of the ob~ect based on the measured phase.
, - 4a -sb/J~
llZ7749 In accordance with a second aspect of the present invention there is provided a system for determining angular information concerning the direction of a signal reflecting object, comprising: a) transmitter means for transmitting a sign~l having a continuous amplitude spectrum between low and high frequency limits, for reflection from the object; b) receiver means for receiving the reflected signal; c) means for changing the phase of the signal in dependence upon the direction of its travel while propagating between the transmitter means and the receiver means, such phase change characterized other than by a simple time delay; d) means for measuring the phase of the received reflected signal;
and e) means for determining angular information concerning the direction of the object based on the - measured phase.
- 4b -sb/~ 4 - llZ7~49 ~ better understanding of the principles of the present invention will be gained -from the following description when taken in conjunction with the accompany-ing drawings, in which:
Fig. 1 shows an embodiment of the invention with a single transmitter, receiver and target;
Fig. 2 shows a processing sequence for the embodiment shown in Fig. 1 with a single transmitter, receiver and target; -Fig. 3 shows another embodiment in which a single phase lens encodes angular information about targets;
Fig. 4 shows a processing sequence for theembodiment of Fig. 3;
Fig. 5 shows another embodiment utilizing a number of mutually exclusive signal trains from the - transmitter, one phase lens being interposed for each signal train;
Fig. 6 shows a processing sequence for the embodiment shown in Fig. 5;
jb/ - 5 -C~
llZ~ 9 Fig. 7 shows another embodiment having different phase encodings of angular information for each member signal of a single outgoing signal train;
Fig. 8 shows a processing sequence for the embodi-ment of Fig. 7;
Fig. 9 shows another embodiment where the propaga-tion phase distortion and/or the reflecting phase distor-tion are treated as an additional lens;-Fig. 10 shows another embodiment with a single trans-mitter, a single receiver and a multiplicity of reflecting targets;
Fig. 11 sh0ws the derivation of angles resolution by triangulation for an embodiment with a single transmitter, two receivers and a multiplicity of reflecting targets;
Fig~ 12 shows the time and Fourier frequency domain properties of a design base signal pair having respectively - oad and even symmetry;
Fig. 13 shows a typical outgoing signal connection of two members;
Fig. 14 shows the graphical evaluation of the ampli-tude spectrum of a cross-correlation in the Fourier frequency domain between a detection signal pair and a propagating sig-nal which has been Doppler distorted;
Fig. 15 shows a computer simulation of the phase encoding of angular information in a two member signal train;
Fig. 16 shows a simulated develop~ent of a correla-tion amplitude function for the signal train with phase encoded angular information;
Fig. 17 shows a sequence of cross-correlations of a sine chirp with Doppler distortions of its original forms;
Fig~ 18 shows the computation of phase and ampli-tude spectra of me~ber signals carrying phase-encoded angular information; and Fig. 19 shows a computer simulation of the invention utilizing three moving targets in the presence of random noise.
llZ'~ 9 .
Figures 1 and 2 show an elementary echo location system of the invention. ' A suitable transmitter 1 emits a signal train lA
having at least two members into a propagation medium 2 in which is embedded a reflecting target 3. An echo 3~ from the target propagates to a receiver 4 where it is detected and sent on to the processing sequencer 5. The outputs of the processing sequencer are directly interpreta~le as the target parameter estimator 6, which gives the relative velocities between the source or transmitter 1, receiver 4,and reflecting target 3, and the range to the reflecting target 3 as a sum of the distances to the transmitter 1 and the receiver 4.
It should be understood that transmitter 1 and receiver 4 may be coincident.
The system shown in Figure 1 embodies components which are essentially standard for the particular application.
For example, in the case of a sonar system, transmitter 1 might be a transducer capable of introducing pressure waves into the water of a form and sequence prescribed by a control signal. Receiver 4 might be a hydrophone while a submarine can serve as reflecting target 3. In this instance the sea water would be the propagation medium 2 and processing sequencer 5 could be,simple electronic network or alter~atively digitai logic accomplishing equivalent operations.
At least two signals are needed in the outgoing train to provide a calibration standard to separate the contribution of the relative velocity to the echo arrival time from the effect of target range. By such means, the echo location system described is capable of simultaneously 112~749 making quite simple, highly resolved estimates of both the target relative velocity and range.
Each member signal of the outgoing train has like polarization characteristics if these are applicable and a common amplitude spectrum as aefinea by the modulus of the exponential Fourier transform. Further, the common amplitude spectrum F(w) is essentially flat or smoothly unimodal over the ranges of positive and negative angular frequencies wO < ¦w¦ c Wf and zero for practical purposes outsidé the band as defined by these constant limiting fre-quencies wO, Wf.
Additionally, each member signal will be a linear combination of a pair of ~ase signals fott)~ fl(t) which have the follo.wing properties to the practical approximation required by the system:
I. fo(t)~ fl(t) share the common.amplitude spectrum F(w) as described.
II. There is a finite time interval of duration , before and after which both fo(t) and fl(t) may be con-sidered to be zero.
i III. fo(t) and fl(t) are in quadrature. Every Fourier frequency component necessary for the description of fo(t) is displaced in phase as measured from any origin in time by 90 from its counterpart in the description of fl(t). Property I above implies that all Fourier frequency -components are present in approximately equal amounts in folt) and fl(t).
As a mathematical formalism, Property III states that fo(t) and fl(t) are a Hilbert transform pair at least to the accuracy of the system and !
112~79~9 fl(t) = I ~fo(u) du ~J t - u By way of illustration, several pairs of signals which satisfy the above specified properties are:
I. "Chirpn Signals slt~, c(t) s(t) = A si~ (wot + wf - Wo t2) 2 . 2 c(t) = A cos (wot + wf - w . 2 A = constant, s(t) = c(t) = 0 for ~ -II. "Klauder" Signals ko(t), kl(t) t < o 10ko(t) = A cos wft - c05 wot 2B
(wf - wo)t kl(t) = A sin wft - sin wot (wf - wo)t A = constant; ko(t) = kl(t? 0 f _ III. "Gabor" Signals go(tj~ gl(t) (t) = A (t/to) . 2C
gl(t) = A
1 ~ (t/to)2 A = constant; gO(t) = gl(t) - 0 for t.~ ¦a¦
to = constant Figure 12 shows the time and frequency domain pro-perties of the Xlauder Signals depicted as fo(t)~ fl(t), the base signal pair.
If fk(t) is a member signal of the outgoing train and there are no distortions introduced by the propagation ~lZ77~9 medium 2, then the received echo 3A for a moving reflecting target 3 will have the mathematical form fktst - T) T is a time delay associated with the target range at the time of detection while s is a scale factor which arises from the target relative velocity. For a reflecting target fleeing detection, s ~ 1 and a stretched signal signature will result. We have assumed a positive impedance contrast between the propagation medium 2 and the reflecting target 3.
A "soft" target having a smaller impedance than the medium for signal travel would cause a sign reversal (or equivalently a 180 phase shift) in the echo signal 3A.
The stretching or compression of the propagating signal is the familiar Doppler effect and gives rise to the ambiguity in resolution between target relative velocity and target range. Suppose one could recognize some signal charac-teristic which occurred at t = to~ In the echo 3A it would occur at t = sto ~ T. If it were assumed, never~heless, that it occurred at t z to + T, one would make an error in deter-nining the echo arrival time of (1 - s)tO which would cor-respondingly cause an error in the estimation of target range.
Signals designed as described, however, have a companion processing sequencer 5 which allows a signal charac-teristic to be unambiguously identified despite stretching or compression.
One embodiment of this sequencer is shown in Figure
Echo location systems are designed to identify some subset of individual reflector or target parameters.
These parameters include the target position in terms like bearing and elevation angle, the range, target relative velocity and the impedance contrast which causes the echo and is also a measure of target quality. Individual targets distributed within a propagation medium make up a target :field. The propagation medium can be attenuative and preferentially cause the loss of the higher frequency components of a propagating signal according to some physical law. Additionally, the propagation medium can be dispersive causing the different frequency components of a signal to travel with different velocities hence, introducing distortations of phase and equivalently of form into the propagating signal as a function of its travel.
Such known echo systems emit a signal or signals into the propagation medium; the identification process involves detecting the echo train and performing a variety ~0 of appropriate analyses. While this procedure is conceptually straight forward, there are a number of practical difficulties which act to complicate, degrade and make ambiguous such identifications.
First, there is a noise background to consider which is almost always a problem in systems where signals are --1-- ~
transmitted and detected. Noise is defined in this instance as any contribution which is not a part of the particular identification process and has as its sources such elements as incoherent scattering by the propagation medium or even the targets themselves. There are a variety of techniques for the detection and enhancement of signals in the presence of noise.
Next, there is the inherent ambiguity between the , range and the relative velocity of a target. A moving ~o target can not only stretch or shrink a returning,echo æignature depending on the sense of its motion, but will also delay or speed up the time of its detection, hence affecting the range calculation. Once again, there are a variety of known techniques which can resolve this ambiguity. It is widely recognized that continuous wave signals, for example, a persistent sinusoid at a single frequency can provide good resolution of the target's relative velocity by means of the Doppler frequency shift.
The companion range resolution of such a signal is necessarily poor since its character is indistinguishable from cycle to cycle. Very short duration signals are affected only slightly by tar,get motion and while they provide good resolution in detection time, they convey little or no information about relative velocities. The chirp signal described by Klauder, Price, Darlington and Albersheim in the Bell System Technical - 112 774~
Journal, Vol. 39, pp 745-808, July 1960, represents a compromise having ambiguity in both velocity and range.
Its advantages lie rather in effectiveness of equipment utilization and the noise suppression of its companion correlation detection.
Lastly, there is the problem of resolving target angular parameters such as elevation and/or bearing. Cur-rently, definition of angles is achieved by the use of arrays of broad-beam source or receiver elements, or else 19 by means of narrow-beam source or receiver elements. In both cases, the space in which the target field is dis-tributed must be scanned or viewed only one small part at a time. Scanning is accomplished either electronically be steering array beams or sequencing the operation of large numbers of elements, or even mechanically by rotating ~perational narrow-beam elements to new positions.
The energy requirements of a scanned system are usually favorable since the entire field of potential targets need not be illuminated at once. On the negative side, however, the individual targets are then not being continuously monitored.
This invention employs encoded signals followed by the correlation of the received echo train with known ~ignal signatures. A relatively long signal train made up of essentially short signals is used, thereby encompassing ,, ~ .
, , , ' ' .
_3_ ~ . :
~lZ77~9 both continuous wave and impulse-like properties. The correlation step achieves a measure of noise suppression.
Simultaneous high resolution information about range and relative velocity is achieved essentially by means of simultaneous solutions involving use of all of the obser-vables embodied in the signal train after detection by correlation.
Both the sources and receivers operate as broad-beam elements with simultaneous illumination of all targets.
Angular resolution is achieved by appropriately interposing phase distorting lenses between the sources and echo receiv-ers. Information about the angles is encoded into the phase character of the propagating signal train. Energy require-ments are modest despite the simultaneous illumination of the entire field of targets because the high repetition rate of the system allows that a rather low echo signal level be tolerated. Also, since range and velocity resolution are not directly dependent on the use of high frequency signal components, lower frequency band signals 2Q may be used with correspondingly less energy loss through attenuation.
Even if the propagating medium does modify the traveling signals by altering their amplitude and phase spectral properties, the system described by the invention will be able to function nevertheless. Some empirical llZ7749 corrections would then have to be made to compensate for the propagation effects, but these could be easily determined by calibration studies using targets of known parameters.
STAq~EMENT OF THE INVENTION
According to one aspect of the present invention there is provided a method of determining angular information concerning the direction of a signal reflecting object relative to a signal transmitter and a signal receiver, comprising the steps of: aj transmitting a signal from the transmitter, such signal having a continuous amplitude spectrum between low and high frequency limits, for reflection from the object; b) receiving the reflected signal with the receiver; c) changing the phase of the signal in dependence upon the direction of its travel while propagating between the transmitter and the receiver, 8uch phase change characterized other than by a simple time delay; d) measuring the phase of the received reflected signal; and e) determining the angular information concerning direction of the ob~ect based on the measured phase.
, - 4a -sb/J~
llZ7749 In accordance with a second aspect of the present invention there is provided a system for determining angular information concerning the direction of a signal reflecting object, comprising: a) transmitter means for transmitting a sign~l having a continuous amplitude spectrum between low and high frequency limits, for reflection from the object; b) receiver means for receiving the reflected signal; c) means for changing the phase of the signal in dependence upon the direction of its travel while propagating between the transmitter means and the receiver means, such phase change characterized other than by a simple time delay; d) means for measuring the phase of the received reflected signal;
and e) means for determining angular information concerning the direction of the object based on the - measured phase.
- 4b -sb/~ 4 - llZ7~49 ~ better understanding of the principles of the present invention will be gained -from the following description when taken in conjunction with the accompany-ing drawings, in which:
Fig. 1 shows an embodiment of the invention with a single transmitter, receiver and target;
Fig. 2 shows a processing sequence for the embodiment shown in Fig. 1 with a single transmitter, receiver and target; -Fig. 3 shows another embodiment in which a single phase lens encodes angular information about targets;
Fig. 4 shows a processing sequence for theembodiment of Fig. 3;
Fig. 5 shows another embodiment utilizing a number of mutually exclusive signal trains from the - transmitter, one phase lens being interposed for each signal train;
Fig. 6 shows a processing sequence for the embodiment shown in Fig. 5;
jb/ - 5 -C~
llZ~ 9 Fig. 7 shows another embodiment having different phase encodings of angular information for each member signal of a single outgoing signal train;
Fig. 8 shows a processing sequence for the embodi-ment of Fig. 7;
Fig. 9 shows another embodiment where the propaga-tion phase distortion and/or the reflecting phase distor-tion are treated as an additional lens;-Fig. 10 shows another embodiment with a single trans-mitter, a single receiver and a multiplicity of reflecting targets;
Fig. 11 sh0ws the derivation of angles resolution by triangulation for an embodiment with a single transmitter, two receivers and a multiplicity of reflecting targets;
Fig~ 12 shows the time and Fourier frequency domain properties of a design base signal pair having respectively - oad and even symmetry;
Fig. 13 shows a typical outgoing signal connection of two members;
Fig. 14 shows the graphical evaluation of the ampli-tude spectrum of a cross-correlation in the Fourier frequency domain between a detection signal pair and a propagating sig-nal which has been Doppler distorted;
Fig. 15 shows a computer simulation of the phase encoding of angular information in a two member signal train;
Fig. 16 shows a simulated develop~ent of a correla-tion amplitude function for the signal train with phase encoded angular information;
Fig. 17 shows a sequence of cross-correlations of a sine chirp with Doppler distortions of its original forms;
Fig~ 18 shows the computation of phase and ampli-tude spectra of me~ber signals carrying phase-encoded angular information; and Fig. 19 shows a computer simulation of the invention utilizing three moving targets in the presence of random noise.
llZ'~ 9 .
Figures 1 and 2 show an elementary echo location system of the invention. ' A suitable transmitter 1 emits a signal train lA
having at least two members into a propagation medium 2 in which is embedded a reflecting target 3. An echo 3~ from the target propagates to a receiver 4 where it is detected and sent on to the processing sequencer 5. The outputs of the processing sequencer are directly interpreta~le as the target parameter estimator 6, which gives the relative velocities between the source or transmitter 1, receiver 4,and reflecting target 3, and the range to the reflecting target 3 as a sum of the distances to the transmitter 1 and the receiver 4.
It should be understood that transmitter 1 and receiver 4 may be coincident.
The system shown in Figure 1 embodies components which are essentially standard for the particular application.
For example, in the case of a sonar system, transmitter 1 might be a transducer capable of introducing pressure waves into the water of a form and sequence prescribed by a control signal. Receiver 4 might be a hydrophone while a submarine can serve as reflecting target 3. In this instance the sea water would be the propagation medium 2 and processing sequencer 5 could be,simple electronic network or alter~atively digitai logic accomplishing equivalent operations.
At least two signals are needed in the outgoing train to provide a calibration standard to separate the contribution of the relative velocity to the echo arrival time from the effect of target range. By such means, the echo location system described is capable of simultaneously 112~749 making quite simple, highly resolved estimates of both the target relative velocity and range.
Each member signal of the outgoing train has like polarization characteristics if these are applicable and a common amplitude spectrum as aefinea by the modulus of the exponential Fourier transform. Further, the common amplitude spectrum F(w) is essentially flat or smoothly unimodal over the ranges of positive and negative angular frequencies wO < ¦w¦ c Wf and zero for practical purposes outsidé the band as defined by these constant limiting fre-quencies wO, Wf.
Additionally, each member signal will be a linear combination of a pair of ~ase signals fott)~ fl(t) which have the follo.wing properties to the practical approximation required by the system:
I. fo(t)~ fl(t) share the common.amplitude spectrum F(w) as described.
II. There is a finite time interval of duration , before and after which both fo(t) and fl(t) may be con-sidered to be zero.
i III. fo(t) and fl(t) are in quadrature. Every Fourier frequency component necessary for the description of fo(t) is displaced in phase as measured from any origin in time by 90 from its counterpart in the description of fl(t). Property I above implies that all Fourier frequency -components are present in approximately equal amounts in folt) and fl(t).
As a mathematical formalism, Property III states that fo(t) and fl(t) are a Hilbert transform pair at least to the accuracy of the system and !
112~79~9 fl(t) = I ~fo(u) du ~J t - u By way of illustration, several pairs of signals which satisfy the above specified properties are:
I. "Chirpn Signals slt~, c(t) s(t) = A si~ (wot + wf - Wo t2) 2 . 2 c(t) = A cos (wot + wf - w . 2 A = constant, s(t) = c(t) = 0 for ~ -II. "Klauder" Signals ko(t), kl(t) t < o 10ko(t) = A cos wft - c05 wot 2B
(wf - wo)t kl(t) = A sin wft - sin wot (wf - wo)t A = constant; ko(t) = kl(t? 0 f _ III. "Gabor" Signals go(tj~ gl(t) (t) = A (t/to) . 2C
gl(t) = A
1 ~ (t/to)2 A = constant; gO(t) = gl(t) - 0 for t.~ ¦a¦
to = constant Figure 12 shows the time and frequency domain pro-perties of the Xlauder Signals depicted as fo(t)~ fl(t), the base signal pair.
If fk(t) is a member signal of the outgoing train and there are no distortions introduced by the propagation ~lZ77~9 medium 2, then the received echo 3A for a moving reflecting target 3 will have the mathematical form fktst - T) T is a time delay associated with the target range at the time of detection while s is a scale factor which arises from the target relative velocity. For a reflecting target fleeing detection, s ~ 1 and a stretched signal signature will result. We have assumed a positive impedance contrast between the propagation medium 2 and the reflecting target 3.
A "soft" target having a smaller impedance than the medium for signal travel would cause a sign reversal (or equivalently a 180 phase shift) in the echo signal 3A.
The stretching or compression of the propagating signal is the familiar Doppler effect and gives rise to the ambiguity in resolution between target relative velocity and target range. Suppose one could recognize some signal charac-teristic which occurred at t = to~ In the echo 3A it would occur at t = sto ~ T. If it were assumed, never~heless, that it occurred at t z to + T, one would make an error in deter-nining the echo arrival time of (1 - s)tO which would cor-respondingly cause an error in the estimation of target range.
Signals designed as described, however, have a companion processing sequencer 5 which allows a signal charac-teristic to be unambiguously identified despite stretching or compression.
One embodiment of this sequencer is shown in Figure
2. The use of a train of signals of known intervals of separation then allows that s be computed from the changes of such intervals in the echo train 3A. Once s is known, llZ~9 the echo arrival ti~es may be compensated for the target relative velocity effects so that accurate estimates of the taxget range can be obtained.
To illustrate the principle, there is shown in Figure 13 an outgoing signal train of two members, these being respectively ko(t) and kl(t), the Klauder Signals with their origins of definition shifted. In mathematical language, the outgoing train shown is simply given by ko(t -- a/2) ~ kl(t - /2 - 1). 4 Further generality can be added by defining fk(t) = cko(t) + dkl(t) fj(t) = akO(t) ~ bkl(t) where a, b, c, d are constants. Let us also introduce a scaling such that Jc~ + d~ z ~a2 + b2 = 1 6 The outgoing signal train now will be taken to have the more general form fk(t - ~/2) + fj(t - ~/2 - ~) 7 The returning echo 3A will then have the following mathematical form fk(s(t - ~/2) - T) + fj(s(t - a/2 - ~) - T). 8 The processing sequencer 5 is shown in Figure 2.
The received signal is divided into two parts by signal splitter 5B. The correlation in parallel of the two parts with fo(t) and fltt), ko(t) and kl(t) in this case is effected by cross-correlators 5Cl and 5C2.
One can evaluate the correlation functions A(t), , B(t) and their squared functions A2(t), B2(t) very simply by ; considering only the first mem~er signal of the returning écho as given by equation 8. If we relocate the origin of the first member signal of the echo for convenience, the indicated chain of operations gives the following A2(t) = 1/4[(cko(st) + dkl(st)) * ko(--t)]2 B2(t) = 1/4t(ckO(st) + dkl(st)) * klt-t)]2 where * denotes a convolution operation (standard signal proces-.sing usage) and -t denotes rèversal of the signal in the time variable t.
Owing to the symmetry properties of kltt) and anti-symmetry ~ ko(t) it is evident that k (-t) = -k (t) 10 kl(-t) = kl(t) and one can writé
A2(t) + B2(t) = 1/41-cko(st) * ko(t) - dkl(st) * ko(t)]2 1/41cko(st) * kl(t) + dkl(st) * kl(t)~2 = 1/4{c2(1ko(st) * ko(t)]2 + lko(st) * kl(t)]2) ~ d !rkl~St) * ~o(t)]2 + lkl(st) * kl(t)~2)}
= 1/4{lko(st) * ko(t)]2 + [ko(st) * kl(t)]2}
or = 1/4{tkl(st) * ko(t)]2 + lkl(st) * kl(t)]2} 11 which follows along the processing sequence through 5E and which has made use of a number of unstated assumptions and extended properties of ko(t), kl(t). These latter points will now be briefly discussed.
. ~he result of the convolution of two functions both having either a point of symmetry or antisymmetry is a function which has a point of symmetry. Similarly, if one function has a point of symmetry while the other has a point of antisymmetry, the result will have a point of antisymmetry.
4~
If we perform Fourier analyses, using as a coordinate origin these points of symmetry and antisymmetry, the phase spectrum of the resulting transform must eit,her be identically zero, +
or else equal to ~/2 sgn(w).
From the well-known convolution theorem, three results can be ~erivea. First, if we scale a time variable by a constant s, we scale the frequency domain variable by l/s. In mathematical terms, ' g(stj ; G(w/s) 12 are time and frequency domain equivalents. Convolution in the ti~e domain is equivalent to multiplication in the frequency domain. Hence, - f~t) * g~t) ; F(w)G(w) 13 are time and frequency aomain equivalents. In polar form, the product F(w)G(w) is equivalent to a multiplication of th- respective amplitude spectra and a simple ordered differ-enc~ of the phase spectra. Finally, the time an~ ~re~uency domain equivalents of reversal in time are as follows:
,, g(-t) ; G+(w) ' 14 where + denotes complex conjugation or simply the reversal in sign of the Phase Spectrum.
, With the three results 12, 13 and 14, we return to Equation 11 where we note that they have been used to elimi-nate,cross-product terms having the coefficient cd. Also ,we recognize that - ' ' ' ko(st) * ko(t) = kl(st) * kl(t) 15 which is in fact yet another Klauder Signal of slightly different frequency content with a point of even symmetry, which we shall call ki(t). We can readily appreciate the make-up of ki(t) by examining Figure 14 which is a graphical , -lA-evaluation of the convolution of Equation 15 for an approach-ing target performed in the Fourier frequency domain. i Using analogous reasoning we find also that ko(st) * kl(t~ = -kl(st) * ko(t) 16 which is the antisymmetric counterpart of ki(t) and shall herein be called ko(t). We shall now state as a general principle that any signal base pair having Properties I, II and III, supra, and further exhibiting respectively anti-symmetry and a symmetry characteristic will have a sum of squares which is sharply peaked about the respective point of symmetry and coincident point of antisymmetry. This property holds for all Xlauder Signals 2B including ko(t), kl(t) ko(st) , kl(st) 17 ko(t) , ki(t) and all Gabor Signals 2C. Befoxe presenting some analysis whi~h suggests the validity of this general principle, we should note that equation 11 nay be rewritten as A2(t) + B2(t) = 1/4{lko(t)]2 + t~l(t)]2} 18 ko~t) and k;(t) as functions with coincident points of antisymmetry and symmetry must have Fourier serieg repre-sentations of the form ko(t) ~i~0hi sin wi 19 k'(t) ~ ~ h. cos w t i=O 1 e sum of the squares of equation 18 is then simply O 1 l(t)l i~ ~ hihj sin wit sin wjt i-o j~ohih~ cos wit cos wjt = ~ I hihj cos (wi j 20 Since the common amplitude spectrum F(w) of ko(t) and ki(t) is smooth and unimodal, we can take all the hi which are non-zero to ~e approximately equal. This allows us to recognize that equation 20 has a maximum at t=0 where all the cosine harmonics are in phase. We also recognize that equation 20 is symmetrical about t=0.
- An analysis of fj(s(t - aj2 - ~) - T), the second member signal of the echo train described by equation 8 through the processing sequencè of Figure 2 would parallel the considerations of equations 9 through 20. Hence the net effect of the processing sequency of Figure 2 on the echo 3A
described mathematically for the particular example by equation 8 is to identify two well-defined correlation peaks of mathematical form of equation 18 which occur at times st = T ~ s~/2 21 st = T + s~/2 + Sl ~n the correlated varia~le time scale.
The interval between the peaks is simply s~ and since T is known, s can be determined thus providing the estimate of the target relative velocity. Once s is known, the target range may be computed from T and a knowledge of the velocity V of the signal lA in the propagation medium 2 (Figure l).
Figures 15 and 16 further illustrate the technique through the results of a digital computer simulation. In Figure 15 we o~serve seven returning two-member Rlauder echo signal trains of the mathematical form of equation 8. ~he various trains correspond to differing choices of the constants c, d, ~, b as they are defined ~y eguations 5 and 6. For the particular illustration ~, . , I
w - 800 ~ wf = 20,000 ~ -s = 1.005 , -~ = 0.0015 sec. 22 note that the signal echo train identified by "Return Azimuth" 0 is in fact of the form illustrated by Figure 13.
Results of the processing sequencer of Figure 2 are shown in Figure 16. The interval between the peaks is simply s~
, in all cases and it can easily be determined as described, ~ Application of the technique using signals like the chirps of equation 2A are similar, but require somewhat more subtlety in their explanation. It is well-known,that the cross- and auto-correlation signatures of the chirp signals 2A in the absence of any stretching or compression are in fact to a good approximation the Rlauder Signals 2B.
While this is well-known, we illustrate this point again by computer simulation. The bottom curve of Figure 17 is in fact the auto-correlation of a sinusoidal chirp or sweep where 20 ~ ~f = 80 ~
a = 7 sec. Sample Interval = 0.004 sec. 23 The,cross-correlations of the undeformed sweep with stretched versions of itself are also shown.
,, It is believed that the processing sequence of Figure 2 when applied to the deformed echo chirps wi~l never-theless produce a result as in Figure 17 with easily identi-fiable,ma~or peaks. ~s before, the two peaks would have similar form and be separated by an intervai s~. There now will be, however, a correction to be made to the peaX arrival times which depends on the computed value of s prior to any estimation of the target range. The nature of the correction and its variation with s may be determined by calibrati;on ,studies using correlations as illustrated in Figure 17.
.
llZ7'749 As a final note, we emphasize that additional member signals in the outgoing train will provide redundant informa-tion about the target relative velocity and range which will enable the echo location technique to function even in noisy environments.
Figure 3 shows another embodiment of the invention.
The major difference between the embodiments of Figures 1 and
To illustrate the principle, there is shown in Figure 13 an outgoing signal train of two members, these being respectively ko(t) and kl(t), the Klauder Signals with their origins of definition shifted. In mathematical language, the outgoing train shown is simply given by ko(t -- a/2) ~ kl(t - /2 - 1). 4 Further generality can be added by defining fk(t) = cko(t) + dkl(t) fj(t) = akO(t) ~ bkl(t) where a, b, c, d are constants. Let us also introduce a scaling such that Jc~ + d~ z ~a2 + b2 = 1 6 The outgoing signal train now will be taken to have the more general form fk(t - ~/2) + fj(t - ~/2 - ~) 7 The returning echo 3A will then have the following mathematical form fk(s(t - ~/2) - T) + fj(s(t - a/2 - ~) - T). 8 The processing sequencer 5 is shown in Figure 2.
The received signal is divided into two parts by signal splitter 5B. The correlation in parallel of the two parts with fo(t) and fltt), ko(t) and kl(t) in this case is effected by cross-correlators 5Cl and 5C2.
One can evaluate the correlation functions A(t), , B(t) and their squared functions A2(t), B2(t) very simply by ; considering only the first mem~er signal of the returning écho as given by equation 8. If we relocate the origin of the first member signal of the echo for convenience, the indicated chain of operations gives the following A2(t) = 1/4[(cko(st) + dkl(st)) * ko(--t)]2 B2(t) = 1/4t(ckO(st) + dkl(st)) * klt-t)]2 where * denotes a convolution operation (standard signal proces-.sing usage) and -t denotes rèversal of the signal in the time variable t.
Owing to the symmetry properties of kltt) and anti-symmetry ~ ko(t) it is evident that k (-t) = -k (t) 10 kl(-t) = kl(t) and one can writé
A2(t) + B2(t) = 1/41-cko(st) * ko(t) - dkl(st) * ko(t)]2 1/41cko(st) * kl(t) + dkl(st) * kl(t)~2 = 1/4{c2(1ko(st) * ko(t)]2 + lko(st) * kl(t)]2) ~ d !rkl~St) * ~o(t)]2 + lkl(st) * kl(t)~2)}
= 1/4{lko(st) * ko(t)]2 + [ko(st) * kl(t)]2}
or = 1/4{tkl(st) * ko(t)]2 + lkl(st) * kl(t)]2} 11 which follows along the processing sequence through 5E and which has made use of a number of unstated assumptions and extended properties of ko(t), kl(t). These latter points will now be briefly discussed.
. ~he result of the convolution of two functions both having either a point of symmetry or antisymmetry is a function which has a point of symmetry. Similarly, if one function has a point of symmetry while the other has a point of antisymmetry, the result will have a point of antisymmetry.
4~
If we perform Fourier analyses, using as a coordinate origin these points of symmetry and antisymmetry, the phase spectrum of the resulting transform must eit,her be identically zero, +
or else equal to ~/2 sgn(w).
From the well-known convolution theorem, three results can be ~erivea. First, if we scale a time variable by a constant s, we scale the frequency domain variable by l/s. In mathematical terms, ' g(stj ; G(w/s) 12 are time and frequency domain equivalents. Convolution in the ti~e domain is equivalent to multiplication in the frequency domain. Hence, - f~t) * g~t) ; F(w)G(w) 13 are time and frequency aomain equivalents. In polar form, the product F(w)G(w) is equivalent to a multiplication of th- respective amplitude spectra and a simple ordered differ-enc~ of the phase spectra. Finally, the time an~ ~re~uency domain equivalents of reversal in time are as follows:
,, g(-t) ; G+(w) ' 14 where + denotes complex conjugation or simply the reversal in sign of the Phase Spectrum.
, With the three results 12, 13 and 14, we return to Equation 11 where we note that they have been used to elimi-nate,cross-product terms having the coefficient cd. Also ,we recognize that - ' ' ' ko(st) * ko(t) = kl(st) * kl(t) 15 which is in fact yet another Klauder Signal of slightly different frequency content with a point of even symmetry, which we shall call ki(t). We can readily appreciate the make-up of ki(t) by examining Figure 14 which is a graphical , -lA-evaluation of the convolution of Equation 15 for an approach-ing target performed in the Fourier frequency domain. i Using analogous reasoning we find also that ko(st) * kl(t~ = -kl(st) * ko(t) 16 which is the antisymmetric counterpart of ki(t) and shall herein be called ko(t). We shall now state as a general principle that any signal base pair having Properties I, II and III, supra, and further exhibiting respectively anti-symmetry and a symmetry characteristic will have a sum of squares which is sharply peaked about the respective point of symmetry and coincident point of antisymmetry. This property holds for all Xlauder Signals 2B including ko(t), kl(t) ko(st) , kl(st) 17 ko(t) , ki(t) and all Gabor Signals 2C. Befoxe presenting some analysis whi~h suggests the validity of this general principle, we should note that equation 11 nay be rewritten as A2(t) + B2(t) = 1/4{lko(t)]2 + t~l(t)]2} 18 ko~t) and k;(t) as functions with coincident points of antisymmetry and symmetry must have Fourier serieg repre-sentations of the form ko(t) ~i~0hi sin wi 19 k'(t) ~ ~ h. cos w t i=O 1 e sum of the squares of equation 18 is then simply O 1 l(t)l i~ ~ hihj sin wit sin wjt i-o j~ohih~ cos wit cos wjt = ~ I hihj cos (wi j 20 Since the common amplitude spectrum F(w) of ko(t) and ki(t) is smooth and unimodal, we can take all the hi which are non-zero to ~e approximately equal. This allows us to recognize that equation 20 has a maximum at t=0 where all the cosine harmonics are in phase. We also recognize that equation 20 is symmetrical about t=0.
- An analysis of fj(s(t - aj2 - ~) - T), the second member signal of the echo train described by equation 8 through the processing sequencè of Figure 2 would parallel the considerations of equations 9 through 20. Hence the net effect of the processing sequency of Figure 2 on the echo 3A
described mathematically for the particular example by equation 8 is to identify two well-defined correlation peaks of mathematical form of equation 18 which occur at times st = T ~ s~/2 21 st = T + s~/2 + Sl ~n the correlated varia~le time scale.
The interval between the peaks is simply s~ and since T is known, s can be determined thus providing the estimate of the target relative velocity. Once s is known, the target range may be computed from T and a knowledge of the velocity V of the signal lA in the propagation medium 2 (Figure l).
Figures 15 and 16 further illustrate the technique through the results of a digital computer simulation. In Figure 15 we o~serve seven returning two-member Rlauder echo signal trains of the mathematical form of equation 8. ~he various trains correspond to differing choices of the constants c, d, ~, b as they are defined ~y eguations 5 and 6. For the particular illustration ~, . , I
w - 800 ~ wf = 20,000 ~ -s = 1.005 , -~ = 0.0015 sec. 22 note that the signal echo train identified by "Return Azimuth" 0 is in fact of the form illustrated by Figure 13.
Results of the processing sequencer of Figure 2 are shown in Figure 16. The interval between the peaks is simply s~
, in all cases and it can easily be determined as described, ~ Application of the technique using signals like the chirps of equation 2A are similar, but require somewhat more subtlety in their explanation. It is well-known,that the cross- and auto-correlation signatures of the chirp signals 2A in the absence of any stretching or compression are in fact to a good approximation the Rlauder Signals 2B.
While this is well-known, we illustrate this point again by computer simulation. The bottom curve of Figure 17 is in fact the auto-correlation of a sinusoidal chirp or sweep where 20 ~ ~f = 80 ~
a = 7 sec. Sample Interval = 0.004 sec. 23 The,cross-correlations of the undeformed sweep with stretched versions of itself are also shown.
,, It is believed that the processing sequence of Figure 2 when applied to the deformed echo chirps wi~l never-theless produce a result as in Figure 17 with easily identi-fiable,ma~or peaks. ~s before, the two peaks would have similar form and be separated by an intervai s~. There now will be, however, a correction to be made to the peaX arrival times which depends on the computed value of s prior to any estimation of the target range. The nature of the correction and its variation with s may be determined by calibrati;on ,studies using correlations as illustrated in Figure 17.
.
llZ7'749 As a final note, we emphasize that additional member signals in the outgoing train will provide redundant informa-tion about the target relative velocity and range which will enable the echo location technique to function even in noisy environments.
Figure 3 shows another embodiment of the invention.
The major difference between the embodiments of Figures 1 and
3 in terms of physical elements is the interposition of a phase lens 7 somewhere in the signal path from the transmitter 1 to the reflecting target 3 to the receiver 4. We term the lens a "phase lens" since its primary purpose is to intro-duce into the propagating signal train a phase distortion which varies in a known and single valued manner with cértain desired angular information. The outgoing signal lA will now be designed in such a manner that after the received echo 3A passes through the processing sequencer 5, outlined in some detail in Figure 4, recoverable target par~meters will include range and relative velocity as in the embodiment of Figure 1, as well as the angular information which may, for example, relate to the target azimuth or bearing.
Again the transmitter 1 emits a signal train lA
with at?east two members. The signal may encounter the phase lens 7 at this time or else intercept it prior to detection by the receiver 4. A reflecting target 3 as before is imbedded in the propagation medium. The principal difference in aesign of members of the signal train for the application in Figure 3 and the one in Figure 1 is that we now require a fourth property in that fo(t)~ fl(t) must have properties of anti-symmetry and symmetry respectively or be "odd" or "even"
respectively about the points of antisymmetry ar symmetry.
Formally stated, the fourth property is IV. fo(t) and fl(t) must be odd (or antisymmetric) and even (symmetric) respectively about the central coordinate value in their interval of definition of duration .
Let us for the moment assume that the phase lens 7 introduces a constant phase shift ~ independent of w which varies only as described with the desired angular information.
We shall describe the operation of the processing sequencer 5 of Figure 3 for this circumstance and then indicate those modifications which would be required for more complex phase shifts. Recall the signal train 7 and its manner of defini-tion from ~lauder signals 2B and the constants c, d, a, b according to equations 5 and 6. We shall use such a signal train or one designed analogously from Gabor signals 2C with the following modification a = sin ~ -= cos ~
c = cos fl , d = - sin ~
~ = constant 24 Note that owing to property IV, the chirp signals 2A are dis,qualified from direct use'in this techniqu,e.
Let us consider fk(t) and fj(t) ~equation 5) indi-vidually for the moment and their Fourier freque~cy domain equivalents. In the-Fourier frequency domain:
Fk(w) - Jfk(t)e iwt dt - b ~ f (t)e~iwt dt - a J fl(t)e~iWt dt _ oo = bFo(w) - aFl(w) = (~ib - a)F(w) --1~--11277~
= +i (b + ai) F (w) = F (w) e ( / ) Fj(w) = aFO(w) ~ bFl(w) = (+ia + b) F(w) = F(w)e+i9 25 In equation 25, F(w) is the common amplitude spectrum (Property I), + is a shorthand notation for -sgn(w), and equations 24 have been applied. The properties of fk(t) and fj(t) in the complex Fourier frequency domain are much like those of fo(t)~
fl(t) except that a constant phase angle ~ has been introduced into each frequency component.
In fact, a phase lens 7 able to introduce phase distortions independent-of w would convert the wave train 4 into the form of the wave train 7. If now this phase distor-tion were diagnostic of the desired angular information, then recovery of it would be tantamount to recovery of the angular information. Assuming such a phase lens 7, we now change our - notation for the propagating signal train 7 to fk(t - ~/2 ~) ~ fj(t - ~/2 - ~) 26 to give expression to the variation of the train with the desired angular information. The received echo (3A and 4) can correspondingly be expressed as fk(s(t - a/2) - T,~) + fj(s(t - a/2 - T) - T,~) 27 - refer to equation 8. It is important to recognize that ~ is unaffected by the Doppler effects owing to the special properties of our signals.
For an understanding of the essentials of processing of Figure 4, it will be more convenient to look at the math-ematical analyses entirely in terms of their Fourier frequency domain equivalents. To facilitate comprehension, we refer to the results of equations 12, 13, 14, 25 and Figure 14.
In the Fourier frequency domain, the received signal 5A is simply F~w/s)e+i~ e+i w/s T/S {e+i(w/s ~/2 + ~/2~
+ e+i(w/s[a/2 + ~])} 28 The signal splitting operation 5B simply requires division of - e~uation 28 by 2. The cross-correlations 5Cl and 5C2 simply require that the halved components of equation 28 be multiplied respectively by F+o(w) and Fl(w). Evaluation of the amplitude portion of the convolutions proceeds analogously to the.
illustration of Figure 14 and we are again led to define the signals fo(t) and f1(t) analogously to ko(t) and ki(t) as described in the discussions surrounding equations 15 and 16.
Recall that f'(t), fi(t) are much like fo(t)~ fl(t), but span a slightly diffe~ent frequency range.
. In detail, and in the frequency domain, the two convolution products are simply . +i~ +i w/s T/s . ~i(w/s a/2~ .
A(w) z F(w)F(w/s)e e {e +
e~i(w/sla/2 + ~] - ~/2)} .
B~w) = F(w)F(w/s)e+i~ e+i w/s T/S {e+i(w/s a/2 + ~/2) ~i (w js 1a/2 + ~])} - 29 Now making use of the signal pair fo(t)~ fi(t) we can write explicitly the time domain equivalents of the expressions of equation 29 or A(t) = 1/2 T 1 {F(W)F(w/s)e~i w/s T/Slcos 3 e+i(w/s a/2) i ~ e~i(w/s a/2 + ~/2) + cos ~ e+i(W/ 1 /
+ sin ~ e+i(W~S[a/2 + ~l) .
-2i-= 1/2(bfl(s(t - a/2) - T) + afO(s(t - a/2) - T) - bfo(s(* - a/2 - T) - T) + af;(s(t - /2 - T) - T~
= lJ2~f~(s(t - /2) - T ~) - fk(s(t - ~/2 - T) - T ~)) B(t) = 1/2 T ~F(w)F~w/s)e~i w/s T/s t +i(w/ /2 +i(w/s a/2) ~i(w/sla/2 ~ T] ) - sin ~ e + cos ~ e +i(w/s¦~/2 + T] + ~/2) + sin ~ e ]}
= 1/2 (fk(s(t -- a/2) -- T,~) + f~s(t - a/2 - r) - T,~)).
In deriving the results of equation 30 we have defined (an~ employed) the signal pair fk(t ~) f~(t ~) in a manner analogous to the definitions implied by equations 26 and 27. Also the notation T-l{ } denotes the operation of an inverse Fourier transform.
At this point following the sequence of ~igure 4 we must take A~t) and B(t) the two expressions of Equation square them (SDl and 5D2) and add them (SE). Note that owing to a sign difference no "cross-terms" of the form fk~t ~) f~t ~) appear. We are left simply with the quantity . .
A2(t) ~ B ~t) = 1/4{fk (s(t - aj2) - T ~) + f~ ~s(t - a/2) - T ~) ~ fk ~s(t - a/2 - T) - T ~) + f; ~s~t - a/2 - T) - T ~)} 31 Before interpreting the significance of equation 31 it is desirable to comment on the nature of the expression which has the form f 2~t ~) ~ fj ~t ~) 32 Recalling all of the arguments of similar nature surrounding the understanding of equation 11, and in specific the results developed through equations 18, 19 and 20, we recognize that equation 31 will have well defined maxima at times.
st = T + sa/2 st = T ~ sa/2 + s T - 33 We can now determine the target relative velocity and range precisely as in the application of Figure 1. Before we consider some alternate methods of recovery of the target angular information SGl and SG2, it is instructive to refer -back to Figure 15 where we now recognize a family of two member signal trains with encoded values of ~ ranging from 90 to -90 in 30 increments. Note that the computer simula-tion of the sequence of Figure 4 through 5F (Eguation 33) shows that the detected peak interval is for practical purposes independent of the encoded phase information.
We shall now consider some methods of recovery of ~ or equivalently the target angular information by the alternate SGl of Figure 4. On the stretched time scale of equati~n 31 consider the arctangent of the ratio of ordinate values of the return signal (equation 27) at the two parti-cular time values corresponding to the correlation maxima.
In detail, ; Phase Angle = arctan Z
where z = {cos9 fo(s(t - a/2) - T) - sin~ fl(s (t - /2) - T) } /2 {sin~ fo(s(t - 3/2 - T) - T) + cos~ fl(s(t-/2-T) ~ T)}st=T~sa/2~S
Phase Angle - arctan {-sin~/cos~}= arctan {-tan~} = -e 34 ~1~77~
To derive the result of equation 34 we have used the definitions of equation S and property IV or fO(0) = 0 and fl(0) = 1.
Analogous reasoning allows additional computations of ~ using the correlation components A(t), B(t) certain of which are illustrated in Figure 4 as SGl.
The alternate SG2 of Figure 4 for determining ~
or the target angular information is also readily accomplished.
Using the peak positions determined by SF (equation 33) as coordinate origins, Fourier transforms of the correlated member signals of the trains A(t), B(t), or the returning echo train itself may be computed and the phase spectra computed. Over the band of frequencies encompassed by f(w) (property I), the phase spectrum will be constant and equal to ~ or ~ /2. We illustrate this point again by computer simulation.
Figure 18 illustrates a nine member returning signal train in wh-ch ~ is succesEively encoded at 10 increments from -90 to 0. Note that sign convention used here is the opposite of the one used in Figure 15. An amplitude and phase speCtrum was computed for each mem~er signal using as the coordinate origin the peak indicated by processing according to Figure 4 up through élement 5F. ~he train is denoted by Seguence B and it is readily observed that the amplitude spectra are identical as they should be. For the meaningful frequency band defined by the amplitude spectrum we see that the phase spectrum is in fact constant and equal in value to ~.
We now address the question of the introduction by the phase lens 7 of Figure 3, phase variations which vary with the target angular information but which are not independent of the frequency. It should be noted, however, that for -~ llZ~49 restricted frequency bands the approximation ~ (w) = ~O ~ ~lw where ~O~ ~1 are constants 35 may be expected to reasonably represent phase effects. The linear variation of phase with frequency inherent in equation 35 and governed by ~1 necessarily implies that some timing adjustment depending on ~1 will be needed which will change the target range computation. Target relative velocity will be unchanged as all member signals undergo the same phase distortion for any given value of the target angular informa-tion hence suffering also the same delays.
To illustrate the previous discussion we note that substituting ~(w) for ~ in equation 25 would give in the tïme domain in place of equation 26 fk(t - ~/2 - T - al, ~O) ~ f~ (t - ~/2 - T ~ 91~ ~o) The received echot3A and 4)would be correspondingly modified.
If the desired angular information is functionally related to ~(wj then it is similarly related to ~O~ ~1 through equation 35.
Referring to Figure 4 in this circumstance, it is evident that the alternate computation for ~, 5Gl will yield a single characteristic eO value which can uniquely be relaied to the desired target angular information for reasonably behaved phase lenses 7 as described by empirical procedures which make use of reflecting targets of known parameters. The same calibration procedures can be used to relate ~1 to the measured ~O so that the echo timing correction can be made.
Of course, alternate 5G2 will similarly allow a direct esti-mation of ~O~ and ~1 may then be related to ~O by empirical calibrations. 91 is again directly interpretable as the timing correction needed for determining the target range, 11~7~
and ~O and ~1 are now both available to define the approxima-tion to ~(w) thus allowing as before determination of the target angular information.
Yet another emboaiment of the invention similar to that illustrated in Figure 3 is indicated in Figure 5. Here a reflecting target 3 is identified in terms of its relative velocity, range and angular information in more than one angle as perhaps the bearing and elevation angle. The technique uses a number of the embodiments of the type of Figure 3 in concert, each realization of the former technique occupying different but non-o~erlapping bands of frequency or polariza-tion (if applicable). The signal bands are selected to retain their exclusion in polarization and/or frequency despite all Doppler ef~ects and effects introduced by the propagation medium 2 or reflecting target 3. Angular information is encoded in each signal band or polarization direction by an appropriate phase lens as in Figure 3 exce~t that the ~enses may affect -only certain of the signal bands or polarizations, and different angular information may be encoded in the different bands.
Figure 5 illustrates the technique in terms of a number of different frequency bands, but it should be under-stood that mutual exclusion may still be achieved within a single band if differing directions of polarization are employed. In this case, separation of the signal bands is accomplished by filtering according to polarization first.
The transmitter 1 of Figure ~ emits the coincident signal trains as described which may have any relative align-ment in time including simultaneity. Prior to encountering the receiver 4 a ~eries of phase lenses 7A, 7B, 7C, etc. are interposed or some other meChanism employed which encodes desired angular information as a phase distortion in the manner previously described. The lenses 7A, 7B, 7C, etc. or equiva-lent mechanisms act independently upon the differing signal bands so that differing angular information may be encodea in each of them. Encoding o~ the same information in differing bands would, of course, provide redundancy and improved recovery of such information in noisy environments.
The propagation medium 2 and reflecting target 3 function analogously to ~heir respective roles in Figure 3.
The processing sequence 5 functions much as in Figure 3, but in parallel for each signal band. Figure 6 diagramatically illustrates the parallel processing for the configuration outlined by Figure 5. The target parameter estimator 6 might encompass certain added features to allow for the effective use of redundant infoxmation about target range and relative velocity.
We can readily appreciate that pol~r~zztion filtering (if applicable) or the cross-correlation operations SCA, 5CB, SCC, etc. of Figure 6 do in fact achieve a separation of the signal bands. For example, each such operation develops cor-relation components analogous to A~t), Blt)- of Figure ~ (also Eguation 30). Equation 29 shows the counterpart Fourier trans-forms A(w3, B~w) in polar form. If the amplitude spectrum of the received return signal does not overlap that of the base function pair of the cross-correlation 5CA, 5CB, 5CC, etc., no ~utput whatsoever will result. Hence the coincident signal bands do not interfere and may be treated quite independently.
Figure 7 illustrates another embodiment of the invention which is like the embodiment of Figure S in that the reflecting target 3 is again identified in terms of its relative velocity, range, and angular information in more than one angle as perhaps the bearing and elevation angle.
Unlike the embodiment of Figure 5 which utilizes simultaneously many signal bands, the angular information in this approach is phase encoded differently in the various member signals of the outgoing signal train lA. The transmitter in this instance functions as in Figure 3 utilizing only a single signal band defined as having uniform polarization (if appli-cable) with impulsive member signals of four properties as described having a frequency content limited to wO ~¦ w ~ < Wf.
One possible mechanism for accomplishing the diverse phase encodings is shown in Figure 7 where differing phase lenses 7 are interposed in turn between the transmitter 1 and the reflecting target 3 such that each member signal of the outgoing signal train lA encounters a different lens. If information is desired about two angles, at least two such -lenses are required. Additional anales would reyuire additional lenses and at least an equivalent n~mber of member signals in the outgoing train.
Let each phase encoding be characterized by a single phase value ~i recognizing that as in preceding aiscussions the characterization can be generalized to accommodate more realistic encodings of general linear form. We shall now assume that the desired angular information ~j is related to ei by the known or empirically determined relation ~i = gi(~j) 36 where i denotes the member signal of the train and j denotes the particular angular information in a plane j containing the transmitter 1 and referred to a line in this plane.
For a more concrete discussion, we shall consider the specific case in which there are only two outgoing member signals, i = 1,2 and one value of ~j or ~1 91 and g2 shall be aefined as implied by the equations 02 = ~~ 37 We may now similarly interpose other phase lenses 8 between echo 3A from reflecting target 3 and receiver 4. One such lens is depicted in Figure 7. As before, the single value of phase ~i will characterize the encoding, where i again refers to the member signals, but now of the echo train 3A. The ~i are related to the desired angular information referred to a specified line in a plane k through the receiver
Again the transmitter 1 emits a signal train lA
with at?east two members. The signal may encounter the phase lens 7 at this time or else intercept it prior to detection by the receiver 4. A reflecting target 3 as before is imbedded in the propagation medium. The principal difference in aesign of members of the signal train for the application in Figure 3 and the one in Figure 1 is that we now require a fourth property in that fo(t)~ fl(t) must have properties of anti-symmetry and symmetry respectively or be "odd" or "even"
respectively about the points of antisymmetry ar symmetry.
Formally stated, the fourth property is IV. fo(t) and fl(t) must be odd (or antisymmetric) and even (symmetric) respectively about the central coordinate value in their interval of definition of duration .
Let us for the moment assume that the phase lens 7 introduces a constant phase shift ~ independent of w which varies only as described with the desired angular information.
We shall describe the operation of the processing sequencer 5 of Figure 3 for this circumstance and then indicate those modifications which would be required for more complex phase shifts. Recall the signal train 7 and its manner of defini-tion from ~lauder signals 2B and the constants c, d, a, b according to equations 5 and 6. We shall use such a signal train or one designed analogously from Gabor signals 2C with the following modification a = sin ~ -= cos ~
c = cos fl , d = - sin ~
~ = constant 24 Note that owing to property IV, the chirp signals 2A are dis,qualified from direct use'in this techniqu,e.
Let us consider fk(t) and fj(t) ~equation 5) indi-vidually for the moment and their Fourier freque~cy domain equivalents. In the-Fourier frequency domain:
Fk(w) - Jfk(t)e iwt dt - b ~ f (t)e~iwt dt - a J fl(t)e~iWt dt _ oo = bFo(w) - aFl(w) = (~ib - a)F(w) --1~--11277~
= +i (b + ai) F (w) = F (w) e ( / ) Fj(w) = aFO(w) ~ bFl(w) = (+ia + b) F(w) = F(w)e+i9 25 In equation 25, F(w) is the common amplitude spectrum (Property I), + is a shorthand notation for -sgn(w), and equations 24 have been applied. The properties of fk(t) and fj(t) in the complex Fourier frequency domain are much like those of fo(t)~
fl(t) except that a constant phase angle ~ has been introduced into each frequency component.
In fact, a phase lens 7 able to introduce phase distortions independent-of w would convert the wave train 4 into the form of the wave train 7. If now this phase distor-tion were diagnostic of the desired angular information, then recovery of it would be tantamount to recovery of the angular information. Assuming such a phase lens 7, we now change our - notation for the propagating signal train 7 to fk(t - ~/2 ~) ~ fj(t - ~/2 - ~) 26 to give expression to the variation of the train with the desired angular information. The received echo (3A and 4) can correspondingly be expressed as fk(s(t - a/2) - T,~) + fj(s(t - a/2 - T) - T,~) 27 - refer to equation 8. It is important to recognize that ~ is unaffected by the Doppler effects owing to the special properties of our signals.
For an understanding of the essentials of processing of Figure 4, it will be more convenient to look at the math-ematical analyses entirely in terms of their Fourier frequency domain equivalents. To facilitate comprehension, we refer to the results of equations 12, 13, 14, 25 and Figure 14.
In the Fourier frequency domain, the received signal 5A is simply F~w/s)e+i~ e+i w/s T/S {e+i(w/s ~/2 + ~/2~
+ e+i(w/s[a/2 + ~])} 28 The signal splitting operation 5B simply requires division of - e~uation 28 by 2. The cross-correlations 5Cl and 5C2 simply require that the halved components of equation 28 be multiplied respectively by F+o(w) and Fl(w). Evaluation of the amplitude portion of the convolutions proceeds analogously to the.
illustration of Figure 14 and we are again led to define the signals fo(t) and f1(t) analogously to ko(t) and ki(t) as described in the discussions surrounding equations 15 and 16.
Recall that f'(t), fi(t) are much like fo(t)~ fl(t), but span a slightly diffe~ent frequency range.
. In detail, and in the frequency domain, the two convolution products are simply . +i~ +i w/s T/s . ~i(w/s a/2~ .
A(w) z F(w)F(w/s)e e {e +
e~i(w/sla/2 + ~] - ~/2)} .
B~w) = F(w)F(w/s)e+i~ e+i w/s T/S {e+i(w/s a/2 + ~/2) ~i (w js 1a/2 + ~])} - 29 Now making use of the signal pair fo(t)~ fi(t) we can write explicitly the time domain equivalents of the expressions of equation 29 or A(t) = 1/2 T 1 {F(W)F(w/s)e~i w/s T/Slcos 3 e+i(w/s a/2) i ~ e~i(w/s a/2 + ~/2) + cos ~ e+i(W/ 1 /
+ sin ~ e+i(W~S[a/2 + ~l) .
-2i-= 1/2(bfl(s(t - a/2) - T) + afO(s(t - a/2) - T) - bfo(s(* - a/2 - T) - T) + af;(s(t - /2 - T) - T~
= lJ2~f~(s(t - /2) - T ~) - fk(s(t - ~/2 - T) - T ~)) B(t) = 1/2 T ~F(w)F~w/s)e~i w/s T/s t +i(w/ /2 +i(w/s a/2) ~i(w/sla/2 ~ T] ) - sin ~ e + cos ~ e +i(w/s¦~/2 + T] + ~/2) + sin ~ e ]}
= 1/2 (fk(s(t -- a/2) -- T,~) + f~s(t - a/2 - r) - T,~)).
In deriving the results of equation 30 we have defined (an~ employed) the signal pair fk(t ~) f~(t ~) in a manner analogous to the definitions implied by equations 26 and 27. Also the notation T-l{ } denotes the operation of an inverse Fourier transform.
At this point following the sequence of ~igure 4 we must take A~t) and B(t) the two expressions of Equation square them (SDl and 5D2) and add them (SE). Note that owing to a sign difference no "cross-terms" of the form fk~t ~) f~t ~) appear. We are left simply with the quantity . .
A2(t) ~ B ~t) = 1/4{fk (s(t - aj2) - T ~) + f~ ~s(t - a/2) - T ~) ~ fk ~s(t - a/2 - T) - T ~) + f; ~s~t - a/2 - T) - T ~)} 31 Before interpreting the significance of equation 31 it is desirable to comment on the nature of the expression which has the form f 2~t ~) ~ fj ~t ~) 32 Recalling all of the arguments of similar nature surrounding the understanding of equation 11, and in specific the results developed through equations 18, 19 and 20, we recognize that equation 31 will have well defined maxima at times.
st = T + sa/2 st = T ~ sa/2 + s T - 33 We can now determine the target relative velocity and range precisely as in the application of Figure 1. Before we consider some alternate methods of recovery of the target angular information SGl and SG2, it is instructive to refer -back to Figure 15 where we now recognize a family of two member signal trains with encoded values of ~ ranging from 90 to -90 in 30 increments. Note that the computer simula-tion of the sequence of Figure 4 through 5F (Eguation 33) shows that the detected peak interval is for practical purposes independent of the encoded phase information.
We shall now consider some methods of recovery of ~ or equivalently the target angular information by the alternate SGl of Figure 4. On the stretched time scale of equati~n 31 consider the arctangent of the ratio of ordinate values of the return signal (equation 27) at the two parti-cular time values corresponding to the correlation maxima.
In detail, ; Phase Angle = arctan Z
where z = {cos9 fo(s(t - a/2) - T) - sin~ fl(s (t - /2) - T) } /2 {sin~ fo(s(t - 3/2 - T) - T) + cos~ fl(s(t-/2-T) ~ T)}st=T~sa/2~S
Phase Angle - arctan {-sin~/cos~}= arctan {-tan~} = -e 34 ~1~77~
To derive the result of equation 34 we have used the definitions of equation S and property IV or fO(0) = 0 and fl(0) = 1.
Analogous reasoning allows additional computations of ~ using the correlation components A(t), B(t) certain of which are illustrated in Figure 4 as SGl.
The alternate SG2 of Figure 4 for determining ~
or the target angular information is also readily accomplished.
Using the peak positions determined by SF (equation 33) as coordinate origins, Fourier transforms of the correlated member signals of the trains A(t), B(t), or the returning echo train itself may be computed and the phase spectra computed. Over the band of frequencies encompassed by f(w) (property I), the phase spectrum will be constant and equal to ~ or ~ /2. We illustrate this point again by computer simulation.
Figure 18 illustrates a nine member returning signal train in wh-ch ~ is succesEively encoded at 10 increments from -90 to 0. Note that sign convention used here is the opposite of the one used in Figure 15. An amplitude and phase speCtrum was computed for each mem~er signal using as the coordinate origin the peak indicated by processing according to Figure 4 up through élement 5F. ~he train is denoted by Seguence B and it is readily observed that the amplitude spectra are identical as they should be. For the meaningful frequency band defined by the amplitude spectrum we see that the phase spectrum is in fact constant and equal in value to ~.
We now address the question of the introduction by the phase lens 7 of Figure 3, phase variations which vary with the target angular information but which are not independent of the frequency. It should be noted, however, that for -~ llZ~49 restricted frequency bands the approximation ~ (w) = ~O ~ ~lw where ~O~ ~1 are constants 35 may be expected to reasonably represent phase effects. The linear variation of phase with frequency inherent in equation 35 and governed by ~1 necessarily implies that some timing adjustment depending on ~1 will be needed which will change the target range computation. Target relative velocity will be unchanged as all member signals undergo the same phase distortion for any given value of the target angular informa-tion hence suffering also the same delays.
To illustrate the previous discussion we note that substituting ~(w) for ~ in equation 25 would give in the tïme domain in place of equation 26 fk(t - ~/2 - T - al, ~O) ~ f~ (t - ~/2 - T ~ 91~ ~o) The received echot3A and 4)would be correspondingly modified.
If the desired angular information is functionally related to ~(wj then it is similarly related to ~O~ ~1 through equation 35.
Referring to Figure 4 in this circumstance, it is evident that the alternate computation for ~, 5Gl will yield a single characteristic eO value which can uniquely be relaied to the desired target angular information for reasonably behaved phase lenses 7 as described by empirical procedures which make use of reflecting targets of known parameters. The same calibration procedures can be used to relate ~1 to the measured ~O so that the echo timing correction can be made.
Of course, alternate 5G2 will similarly allow a direct esti-mation of ~O~ and ~1 may then be related to ~O by empirical calibrations. 91 is again directly interpretable as the timing correction needed for determining the target range, 11~7~
and ~O and ~1 are now both available to define the approxima-tion to ~(w) thus allowing as before determination of the target angular information.
Yet another emboaiment of the invention similar to that illustrated in Figure 3 is indicated in Figure 5. Here a reflecting target 3 is identified in terms of its relative velocity, range and angular information in more than one angle as perhaps the bearing and elevation angle. The technique uses a number of the embodiments of the type of Figure 3 in concert, each realization of the former technique occupying different but non-o~erlapping bands of frequency or polariza-tion (if applicable). The signal bands are selected to retain their exclusion in polarization and/or frequency despite all Doppler ef~ects and effects introduced by the propagation medium 2 or reflecting target 3. Angular information is encoded in each signal band or polarization direction by an appropriate phase lens as in Figure 3 exce~t that the ~enses may affect -only certain of the signal bands or polarizations, and different angular information may be encoded in the different bands.
Figure 5 illustrates the technique in terms of a number of different frequency bands, but it should be under-stood that mutual exclusion may still be achieved within a single band if differing directions of polarization are employed. In this case, separation of the signal bands is accomplished by filtering according to polarization first.
The transmitter 1 of Figure ~ emits the coincident signal trains as described which may have any relative align-ment in time including simultaneity. Prior to encountering the receiver 4 a ~eries of phase lenses 7A, 7B, 7C, etc. are interposed or some other meChanism employed which encodes desired angular information as a phase distortion in the manner previously described. The lenses 7A, 7B, 7C, etc. or equiva-lent mechanisms act independently upon the differing signal bands so that differing angular information may be encodea in each of them. Encoding o~ the same information in differing bands would, of course, provide redundancy and improved recovery of such information in noisy environments.
The propagation medium 2 and reflecting target 3 function analogously to ~heir respective roles in Figure 3.
The processing sequence 5 functions much as in Figure 3, but in parallel for each signal band. Figure 6 diagramatically illustrates the parallel processing for the configuration outlined by Figure 5. The target parameter estimator 6 might encompass certain added features to allow for the effective use of redundant infoxmation about target range and relative velocity.
We can readily appreciate that pol~r~zztion filtering (if applicable) or the cross-correlation operations SCA, 5CB, SCC, etc. of Figure 6 do in fact achieve a separation of the signal bands. For example, each such operation develops cor-relation components analogous to A~t), Blt)- of Figure ~ (also Eguation 30). Equation 29 shows the counterpart Fourier trans-forms A(w3, B~w) in polar form. If the amplitude spectrum of the received return signal does not overlap that of the base function pair of the cross-correlation 5CA, 5CB, 5CC, etc., no ~utput whatsoever will result. Hence the coincident signal bands do not interfere and may be treated quite independently.
Figure 7 illustrates another embodiment of the invention which is like the embodiment of Figure S in that the reflecting target 3 is again identified in terms of its relative velocity, range, and angular information in more than one angle as perhaps the bearing and elevation angle.
Unlike the embodiment of Figure 5 which utilizes simultaneously many signal bands, the angular information in this approach is phase encoded differently in the various member signals of the outgoing signal train lA. The transmitter in this instance functions as in Figure 3 utilizing only a single signal band defined as having uniform polarization (if appli-cable) with impulsive member signals of four properties as described having a frequency content limited to wO ~¦ w ~ < Wf.
One possible mechanism for accomplishing the diverse phase encodings is shown in Figure 7 where differing phase lenses 7 are interposed in turn between the transmitter 1 and the reflecting target 3 such that each member signal of the outgoing signal train lA encounters a different lens. If information is desired about two angles, at least two such -lenses are required. Additional anales would reyuire additional lenses and at least an equivalent n~mber of member signals in the outgoing train.
Let each phase encoding be characterized by a single phase value ~i recognizing that as in preceding aiscussions the characterization can be generalized to accommodate more realistic encodings of general linear form. We shall now assume that the desired angular information ~j is related to ei by the known or empirically determined relation ~i = gi(~j) 36 where i denotes the member signal of the train and j denotes the particular angular information in a plane j containing the transmitter 1 and referred to a line in this plane.
For a more concrete discussion, we shall consider the specific case in which there are only two outgoing member signals, i = 1,2 and one value of ~j or ~1 91 and g2 shall be aefined as implied by the equations 02 = ~~ 37 We may now similarly interpose other phase lenses 8 between echo 3A from reflecting target 3 and receiver 4. One such lens is depicted in Figure 7. As before, the single value of phase ~i will characterize the encoding, where i again refers to the member signals, but now of the echo train 3A. The ~i are related to the desired angular information referred to a specified line in a plane k through the receiver
4 by the known or empirically determined relation ~i hi(Yk) 38 Again, for illustrative purposes and with no loss of generality, we shall assume a single lens 8, a single desired angle Yl such that for.the two returning member signals, the phase encoding by the lens 8 would be = Yl ~2 = Yl where hl, h2 have implicit definition in equations 39. It i8 important to add that for each desired angle beyond the first, either g~ or hi(yk) for member signal i must have a single valued form more general than the simple addition of a constant value.
The processing sequence 5 described in greater detail in Figure 8 is analogous to the sequence of Figure 4 through element 5F of that Figure where the timing of peaks in the correlation component square sum leads to estimates - ~ ~127~49 of the target relative velocity and range. Figure B illustrates alternate 5Gl of Figure 4 being employed to estimate the phase characteristic for each member signal. Referring to equations 36 and 37 these are given generally by ~ i = gi(~ hi(Yk) 40 which are a set of i simultaneous equations for-j + k unknowns.
The unknown ~j and Yk constitute the desired angular informa-tion and may be determined when i > j + k.
In the simplified case cited for illustration in eguations 37 and 39, the counterparts to equations 40 are ~1 + ~1 ~1 + ~1 - 41 ~2 + ~2 = ~ Yl whose solution can be directly obtained as a simple sum and difference of observed phases or Yl = ~ 2 + ~2 ~1 = 1 + ~1 - Q2 - ~2 Note that the successive phase encodings imposed on the propa-gating signal by the cascaded phase lenses 7 and 8 are simply ~dditive.
Where the phase distortion imparted by any lens requires a more general description such as a linear approxi-mation as described by equation 35, the procedure is similar except that after determining the desired angular information from member signal i, a timing correction is needed leading once again to a correction to the target range and in this embodiment also to the target relative velocity. Note that in other embodiments of the invention where all member signals passed through common phase lenses, no correction was needed , ' "' .
~ -30-~12~
for the target relative velocity. The timing correction apper-taining to each lens may be detenmined empirically as a function of phase as before using targets of known parameters. These same calibration techniques would define the relations ~.i = gi(~j) ~ i = hi ~Yk) (equations 37 and 38) unless they were determined theoretically or on some other basis.
It should also be recognized that alternate SG2 of Figure 4 for each mem~er signal would again provide values of i which could be similarly employed to derive the desired angular information and to correct the target relative velocity and range should such corrections be needed.
Another embodiment of the invention which follows from the previous discussions is one which incorporates the elements exemplified by both Figures 5 and 7 and their complem_ntary processing sequences illustrated by Figures , 6 and 8. Here again, a reflecting target 3 (of Figure 5 or i 7) would be identified in terms of its relative velocity, range and angular information in more than one angle as perhaps the bearing and elevation angle. However, the phase encoding of the desired angular information would not be the same for all member signals of the outgoing train as in Figure 7, and, more than a single band would also be utilized, such bands being mutually exclusive even after Doppler effects, by virtue of polarization and/or frequency differences, with each band having encoded differing angular information.
One practical objective in combining the approaches of Figures 5 and 7 as described is to achieve even greater redundancy of all the reflecting target parameters yet without increasing the period of time which is needed to make such identifications. Details of accomplishing the processing for such identification follows precisely from both Figures 6 and 8.
Figure 9 depicts an embodiment of the invention much as described by Figure 7, where again a reflecting target 3 is identified in terms of its parameters as target range, rela-tive velocity and angular information in many angles, but now an accommodation is made also for a phase distortion 2A which is-a function of the target range introduced by the propagation medium 2 and/or the reflecting target 3 as a function of the angle of signal incidence. For illustrative purposes in this discussion the phase distortion will be assumed attributable in its entirety to the propagation medium 2, with no loss of generality of the technique implied by such assumption.
For practical materials or propagation media 2, the phase distortion 2A will be smoothly varying and repre-sented well by an analytic ex~ession like equation 35. Such a phase distortion was specifically discussed and treated in all of the previous embodiments of the invention where angular information was to be determined. As a consequence of a distortion of this form a target range correction will result, however, no relative velocity error would be introduced since all of the member signals see the same phase distortion 2A. The constants which approximate the phase distortion in the form of equation 35 will also be estimated.
In Figure 9, the role of the propagation medium 2 with regard to phase is analogous to the interposition of one additional phase lens 7 or 8. Unlike the phase lenses 7 or 8, the phase effects to be introduced are not designed as a part of the invention and vary with the target range or better the travel distance of the signal rather than any angular information. ~et us designate the phase distortions 2A for a given value of target range R as O ~lw ~O = l(R) Since phase effects-are additive, and if the phase distortion introduced by the phase lenses 7 and 8 have form analogous to equation 43, then for the ith member signal of the echo train 3A after being received 4 and processed according to the processing sequence 5 of Figure 8, the detected phase would be -i ~i o gi(~j) + hi(Yk) + ~(R) 44 ~here gi and hi are defined as in equations 36 and 38 and where A(R) is a function of the target range.
In this case gi, hi and ~(R) are all determined theoretically or else by empirical studies using a reflect-ing target 3 of known parameters. The equations 44 may be solved simultaneously or by least squares for a sufficient number of member signals (i > j + k + 1) to give ~ k and R which in ~urn can give values for ~ O as distinct from their sum. For phase characterization of the general form specified it should be recognized that a timing correc-tion would be needed for each member signal which would modify the determinations both of target relative velocity and target range.
The timing correction as described in certain of the previous embodiments can be computed theoretically or else can be determined by some empirical method using a known reflecting target 3 so that for values of ~ o or ~, Yk, R an appropriate sum of corrections may be applied.
Of course, once ~O and the timing correction for the propagation medium 2 are known, the phase distortion 2A of the medium is known according to equation 43 as is all other desired information. Note that the timing correction associated with ~O or R gives rise to no change in the computation for target relative velocity since, as was ~entioned, all member signals are subjected to the same timing adjustment.
Figure 9 represents the most general embodiment of the invention up to this point in a single signal band as defined by frequency range and polarization direction, if the latter is applicable. Figure 5, on the other hand, depicts an embodiment in which the phase encoding of target parameters and propagation material properties (if applicable) would utilize a number of signal bands. It follows then that a more comprehensive embodiment may yet be envisaged in which a number of signal bands are employed, the technique in each single signal band being represented as in Figure 9.
An embodiment as described would provide the great-est redundancy yet for the identification parameters of the reflecting target and would also allow the characterization of the phase distortion of the propagation medium and/or the reflecting target in a number of frequency bands and polariza-tion di,rections.
Another embodiment of the invention complementing all other variations described up to this point would include the use of amplitude spectral information determined either collectively from the received return signal or else computed from individual member signals as one additional target identi-fication parameter describing its "qualityn. Referring to Figure 4 in alternate 5G2 we first noted the use of Fourier analysis in the processing sequence for the received return signal 5A.
-3~-~lZ~
Throughout preceding discussions, the only modifi-cation admitted for the amplitude spectrum of the base signal pairs had been a Doppler induced effect. We shall now want to give cognizance to variations in the amplitude spectrum caused by freguency dependent alternative mechanisms of the propaga-tion medium and also the frequency dependent reflective pro-perties of the target.
A preferential loss of higher frequency components as a function of the length of propagation path is a common characteristic of most propagation media. Particular media can exhibit "window" effects where for certain frequencies or polarizations (if applicable) anomalous attenuation or lack of attenuation will occur. For all of the permissible base signals having either three or four fundamental properties, these effects should not alter in most circumstances the basic smooth and unimodal character of the amplitude spectrum and so the mathematical approximations presented would retain their validity. No effects would be induced on phase as it is measured here, since the base signals share a common ampli-tude spectrum.
Empirical studies have been cited in a number of pr,eviou~ discussions as a means for establishing standards or functional relationships necessary of the determination of certain of the target identification parameters. Clearly, by empirical studies it is possible to determine the absolute amplitudes and changes in form of the amplitude spectrum of mem~er signals caused by a propagation medium so that these effects might be removed from consideration. Other differences o~ magnitude and form must then be diagnostic in some sense of the target, describing its quality.
Peculiarities of the target figure or shape, as well as perhaps a transitional character in reflective pro-perties can cause modifications to the amplitude spectrum which might be unique to certain targets hence facilitating positive identifications, or else simply assisting in their categorization. We must also note in the context of target quality determination that phase plays some role, since it is a 180 phase shift or reversal of arithmetic sign of the echo which allows distinction between "hard" and "soft" targets 1~ where the magnitudes of the reflective contrasts between the target and the propagation medium are equal. The terminology "hard" is being applied to targets of materials in which the signal propagation velocity exceeds its velocity in the propa-gation medium.
Target quality information is contained in the member signals of the signal train as well as in the entire train itself. Hence as in the case of most of the other para-meters describing the target, a measure of redundancy is again present.
Figure 1 illustrates the most elementary embodiment of the invention described, but can be used to help explain the most encompassing embodiment of the invention yet to be described. All variations of the invention discussed so far have included a single transmitter 1, a single receiver 4, and single reflecting target 3. In fact, any number of any of these elements can be used, yet allowing all other essen-tials of the invention so that the plurality of reflecting targets can each be identified individually according to their parameters with whatever degree of redundancy the particular embodiment allows. Figure 10 exemplifies such an embodiment based on the variation shown in Figure 1.
112~q9 In Figure 10, three distinct reflecting targets 3, two distinct receivers 4A, 4B and a single transmitter 1 are shown. The propagating signal lA is taken as in Figure 1 and the propagation medium 2 is also as in Figure 1. Each reflect-îng target returns an echo to each of the receivers 4A, 4B.
The processing sequences 5 are essentially as depicted in greater detail in Figure 2 except that each of the reflecting targets 3 now corresponds to a sequence of peaks in the step 5E of Figure 2 which may have any arbitrary relation in time, one sequence to another, hence necessitating also the inclusion of some logic to separate the member peaks in each sequence so that target parameter estimates 6 can be made for each -reflecting target. Since there are two receivers, the target parameter estimator 6 may now include angular information, even though the embodiment of Figure l upon which we based this illustrative case made no provision for the inclusion o~ such information.
Figure 11 suggests a familiar analytic basis by which the use of information from the two receivers 4A, 4B
may be handled to yield angular information. The transmitter T and receivers Rl, R2 of Figure 11 occupy known relative positions which are either fixed or changing in a known manner in time. The processing sequence 5 as described by Figure 2 is capable of estimating for each reflecting target only a ~ange and relative velocity. For any estimated range, the permissible target locus is an ellipse with the transmitter and recei~er which detected the particular echo at its focii.
The intersection of the elliptical locii will define the target position and thus pro~ide the angular information about ; ¦
the target expressed in the coordinate network of the trans-mitter ana two receivers. Ambiguity of position can be eliminated as indicated again in Figure 11 by designing the configuration so that cextain positions are disallowed, as for example those to the left of the dashed line AA'.
It is important to mention that the logic by which the sequences corresponding to the differing targets are isolated can include clues about the consistency of relative velocity of the targets and even amplitude spectral information which in fact was not mentioned in the embodiment of Figure 1, but was described in a later, re sophisticated technique.
To further illustrate the technique in which a plura-lity of elements is permissible, we address now the embodiment of Figure 3, where angular information in one angle is one of the target identification parameters, and appeal also to a computer simulation. For illustrative purposes we adopt the configuration shown in Fisu~e 3 but declare only a plurality of reflecting targets, specifically three. The signal lA from transmitter 1 is taken to be made of a Klauaer base signal pair as described by equation 4 and depicted in Figure 13.
Amplitudes of the three reflecting targets are taken to be in the ratio 4, 3, 2 while their initial ranges, angular information and relative velocities tabulate as:
Range Angular Relative Amplitude (Arbitrary Information Velocity (Ratio) Units) (Ratio) Target 1 150 0 1 4 Target 2 300 -45 1.05* 3 Target 3 450 90 .g5~ 2 approaching ~ fleeinq Note that we are using the same convention for encoding the angular information as indicated in Figure 15. We are assum-ing constant phase distortions imparted by the phase lens llZ77 ~9 .7 of Figure 3. Also, the target r~lative velocities are expressed .as 1 ~ their rations with the speed~at which echo.location signal lA travels.
Since target 2 is approaching the detection system centroid while target 3..is fleeing, the expected targe$ ranges for the assigned target relative velocities are 280 and 475 units respectively. Also, if all other parameters can be oorrectly identified, then a reconstruction.of the received return signal 4 may be accomplished for comparison with the observed one. Such a sequence is~shown by the computer simu-lations of Figure 19 where the noise-free and noisy case are examined.
In Figure 19, curve A is the observed received return signal 4. The reconstruction from detected parameters is denoted curve D. Curve B shows the sum of the squares of the correlation components, curves Cl and C2. Referring to Figure ~ which describes the particular processing se~uence 5, -we secognize curve Cl as 5Dl, curve C2 as SD2 and curve B as 5E. The family of curves with primes represent results from the circumstance where background noise is present. For this case note that there is little difficulty in distinguishing among the reflecting targets.
.Hence these illustrations make clear certain of the advantages of the e~bodiments which function in environments with a plurality of reflecting targets and utilize where bene-ficial, pluralities of transmitters and receivers.
A more general variation of the invention, encom-passing all other variations described and which can be developed starting with any of thse techniques, employs a base signal pair in the processing sequence which can differ from the base signal pair of the outgoing signal design., The two distinct base signal pairs shall be designated as the design signal pair ' ~ ,. .
llZ77~9 and the processing signal pair respectively. For any given design signal pair, the admissible processing signal pairs must represent only rotations of the-design signal pair phase spectra by a constant angle, and all differences in amplitude spectrum must be constrained such that the product of the design signal pair common amplitude spectrum and the processing signal pair common amplitude spectrum in itself has a form appropriate to a base signal pair.
All embodiments described heretofore employed a common base signal pair for the design of the outgoing signal train and the processing sequence. In fact, this restriction need not exist and we may with appropriate planning use an-out-going signal train developed with Rlauder signals, yet select a processing base signal pair constructed with Gabor signals to extract desired target parameters (refer to equations 2B and , 2C which specifically define Klauder and Gabor signals.~
Should the particular application of the invention not make use of phase encoding of information as the variation ¦ described in Figures 1 and 2, the~ both the design signal pair and processing signal pair would each have to satisfy only the first three fundamental properties which were outlined in that discussion. Where angular resolution via phase encoding is called upon, the fourth fundamental property introduced in the discussion of the application depicted in Figures 3 and 4 is needed. A modified form of this property may now be taken for both the design signal pair and the processing signal pair.
Calling such a signal pair fk(t), fj(t) the revised statement , of Property IV reads:
IV. fk(t) and fj(t) must be transformable to respect-1 ive odd and even form about the central coordlnate value in ; their interval of definition of duration a, by a constant -~12~
shift of phase at all frequencies where the coordinate origin of definition of such phase is again taken at the same central coordinate value.
In reviewing the m~thematical discussions of the simpler techniques it becomes clear that the processing sequences as described can progress up to determinations of phase using differing design and processing signal pairs having three or four fundamental properties as the application requires, and having permissible departures in amplitude spectra. Specifi-cally, in the embodiment shown in Figure 1, any appropriate processing signal pair allows completion of the entire proces-sing sequence shown in Figure 2 in its entirety with no modifi-cation. Alternatively, in the embodiment shown in Figure 3 where phase encoding is employed to achieve angular resolution, the processing sequence of Figure 4 would be unmodified through element 5F. Thereafter, an adjustment in phase related-to the constant shift of the processing base pair relative t~ the design base pair described by the revised Property IV would be required.
For purposes of having a more concrete illustration, consider an outgoing signal train developed using as the design signal pair fk(t), fj(t) defined by equation 5 with the con-straint of equation 6 and subject to equation 24. In the Fourier frequency domain following equation 25, we have the counterparts ~ /2) Fj(w) = F(w) e 45 If we envisage a phase encoding mechanism as in the technique described by Figures 3 and 4, the recei~ed return signal 5A
having undergone a constant phase shift now termed B for the particular angular resolution, would have a form similar to equation 27 but specifically fk(s(t - /2) - T,~ ~.B) + fj(s(t - a/2 - ~) - T,fl + B) 46 In the Fourier frequency domain the received return signal SA
(also equation 46) is now ' F(w/s)e~ B) e~i w/s T/s {+i(w/s a/2~2)+ e+i(w/st~/2+l~)}
(Compare with eguation 28).
Let us select a processing signal pair gk(t), gj(t) defined analogously to fk(t), fj(t) having as Fourier frequency domain count,erparts Gk ~w) = G (w) e+i ( Y + ~/2 ) Gj (w) = G(w) e+iY . 48 A(t), B(t) or 5Dl, 5D2 of the processing seguence of Figure 4 would then have as frequehcy domain equivalents +i(~+B--y) +i w/s T/s +(w/s c~/2) A (w) = G (w~ F (w/s ) e e {e ~i (w/s [~/2 ~ ~ r/2) e }
-y) +i w/s T/s ~i (w/s a/2 + ~/2) 8(w) ~ G(w)F(w/s)e e {e +i (w/s la/2 ~ r 3 ) + e } 49 ;(Co,mpare with equation 29).
From equation 49 onward this illustrative analysis may proceed in parallel with the development based on Figures 3 and 4 with two provisions. First, the product G(w)F(w/s) must define an amplitude spectrum which is essentially smooth and unim~dal so that a signal pair analogous to fk.(t,~), fj(t,~) of equation 30 may be defined., Second, the phase encoded angular information relating to B can be determined only after compensating for the phase rotation of the design signal pair by ~ and the processing signal pair rotation by y. Note that the relative rotation between these two pairs is again constant and equal to ~ - y. In particular, alter-nates 5Gl and 5G2 of Figure 4 would both yield phase determi-nations in this case of ~ y) which would give a value for ~ when corrected as necessary for the known phase rotations and ~. (See for example equation 34).
The nature of the amplitude spectral differences permitted between the design signal pair and the processing signal pair is now greatly clarified. G(w) and F(w/s) must for all realistic Doppler variations governed by s overlap sufficiently ;n frequency w so that the product G(w)F(w/s) has a band width sufficiently broad to correspond to a signal of finite duration and impulsive character when transformed to the time domain with a constant zero phase spectrum. (This re-quir2ment is analogous in some measure to fundamental Property II). Also, the product G(w) F(w/s) must have a character essentially as demanded in fundamental Property I.
It should ~e apparent to anyone with some background in signal processing that the permissible differences in the amplitude spectra of the design signal pair and the processing pair can often be used to great advantage. Techniques utiliz-ing some "conditioning" of amplitude spectra in association with a correlation or convolution process are widely used and even standard in the treatment of signals for detection and other applications (see for example Phillip E. Panter, ~odulation, Noise and SPectral AnalYsis, McGraw Hill, 759 P, 1965). By analogy, similar enhancement techniques can be designed to function in the context of this invention.
112,7~49 As a most elementary example of such a method, one may consider a practical environment which is attenuative in nature and preferentially removes the high frequency content of F(w/s) as the propagation distance to the target increases.
For some approximation to the expected target range, Gtw) might con~ersely give appropriate emphasis to the high frequencies so that the product F(w/s)G(w) is again almost flat. Such a method would improve both the resolution obtain-able in the relative velocity determination and range calcu-lation.
Hence this embodiment of the invention endows great flexibility in all the alternative variations making possible a numbér of advantages which can arise from a judicious manipu-lation of the amplitude and phase spectral character of the design signal pair and the processing signal pair. Introduc-tion of a time variation in the definition of the processing signa~ pair might enhance detectability through amplitude spectral "whitening" whilé also compensating for the changing constant phase characteristic introduced by a propagation medium. The scope and significance of such possibilities can be appreciable.
, WHA~ IS CLAIMED IS:
The processing sequence 5 described in greater detail in Figure 8 is analogous to the sequence of Figure 4 through element 5F of that Figure where the timing of peaks in the correlation component square sum leads to estimates - ~ ~127~49 of the target relative velocity and range. Figure B illustrates alternate 5Gl of Figure 4 being employed to estimate the phase characteristic for each member signal. Referring to equations 36 and 37 these are given generally by ~ i = gi(~ hi(Yk) 40 which are a set of i simultaneous equations for-j + k unknowns.
The unknown ~j and Yk constitute the desired angular informa-tion and may be determined when i > j + k.
In the simplified case cited for illustration in eguations 37 and 39, the counterparts to equations 40 are ~1 + ~1 ~1 + ~1 - 41 ~2 + ~2 = ~ Yl whose solution can be directly obtained as a simple sum and difference of observed phases or Yl = ~ 2 + ~2 ~1 = 1 + ~1 - Q2 - ~2 Note that the successive phase encodings imposed on the propa-gating signal by the cascaded phase lenses 7 and 8 are simply ~dditive.
Where the phase distortion imparted by any lens requires a more general description such as a linear approxi-mation as described by equation 35, the procedure is similar except that after determining the desired angular information from member signal i, a timing correction is needed leading once again to a correction to the target range and in this embodiment also to the target relative velocity. Note that in other embodiments of the invention where all member signals passed through common phase lenses, no correction was needed , ' "' .
~ -30-~12~
for the target relative velocity. The timing correction apper-taining to each lens may be detenmined empirically as a function of phase as before using targets of known parameters. These same calibration techniques would define the relations ~.i = gi(~j) ~ i = hi ~Yk) (equations 37 and 38) unless they were determined theoretically or on some other basis.
It should also be recognized that alternate SG2 of Figure 4 for each mem~er signal would again provide values of i which could be similarly employed to derive the desired angular information and to correct the target relative velocity and range should such corrections be needed.
Another embodiment of the invention which follows from the previous discussions is one which incorporates the elements exemplified by both Figures 5 and 7 and their complem_ntary processing sequences illustrated by Figures , 6 and 8. Here again, a reflecting target 3 (of Figure 5 or i 7) would be identified in terms of its relative velocity, range and angular information in more than one angle as perhaps the bearing and elevation angle. However, the phase encoding of the desired angular information would not be the same for all member signals of the outgoing train as in Figure 7, and, more than a single band would also be utilized, such bands being mutually exclusive even after Doppler effects, by virtue of polarization and/or frequency differences, with each band having encoded differing angular information.
One practical objective in combining the approaches of Figures 5 and 7 as described is to achieve even greater redundancy of all the reflecting target parameters yet without increasing the period of time which is needed to make such identifications. Details of accomplishing the processing for such identification follows precisely from both Figures 6 and 8.
Figure 9 depicts an embodiment of the invention much as described by Figure 7, where again a reflecting target 3 is identified in terms of its parameters as target range, rela-tive velocity and angular information in many angles, but now an accommodation is made also for a phase distortion 2A which is-a function of the target range introduced by the propagation medium 2 and/or the reflecting target 3 as a function of the angle of signal incidence. For illustrative purposes in this discussion the phase distortion will be assumed attributable in its entirety to the propagation medium 2, with no loss of generality of the technique implied by such assumption.
For practical materials or propagation media 2, the phase distortion 2A will be smoothly varying and repre-sented well by an analytic ex~ession like equation 35. Such a phase distortion was specifically discussed and treated in all of the previous embodiments of the invention where angular information was to be determined. As a consequence of a distortion of this form a target range correction will result, however, no relative velocity error would be introduced since all of the member signals see the same phase distortion 2A. The constants which approximate the phase distortion in the form of equation 35 will also be estimated.
In Figure 9, the role of the propagation medium 2 with regard to phase is analogous to the interposition of one additional phase lens 7 or 8. Unlike the phase lenses 7 or 8, the phase effects to be introduced are not designed as a part of the invention and vary with the target range or better the travel distance of the signal rather than any angular information. ~et us designate the phase distortions 2A for a given value of target range R as O ~lw ~O = l(R) Since phase effects-are additive, and if the phase distortion introduced by the phase lenses 7 and 8 have form analogous to equation 43, then for the ith member signal of the echo train 3A after being received 4 and processed according to the processing sequence 5 of Figure 8, the detected phase would be -i ~i o gi(~j) + hi(Yk) + ~(R) 44 ~here gi and hi are defined as in equations 36 and 38 and where A(R) is a function of the target range.
In this case gi, hi and ~(R) are all determined theoretically or else by empirical studies using a reflect-ing target 3 of known parameters. The equations 44 may be solved simultaneously or by least squares for a sufficient number of member signals (i > j + k + 1) to give ~ k and R which in ~urn can give values for ~ O as distinct from their sum. For phase characterization of the general form specified it should be recognized that a timing correc-tion would be needed for each member signal which would modify the determinations both of target relative velocity and target range.
The timing correction as described in certain of the previous embodiments can be computed theoretically or else can be determined by some empirical method using a known reflecting target 3 so that for values of ~ o or ~, Yk, R an appropriate sum of corrections may be applied.
Of course, once ~O and the timing correction for the propagation medium 2 are known, the phase distortion 2A of the medium is known according to equation 43 as is all other desired information. Note that the timing correction associated with ~O or R gives rise to no change in the computation for target relative velocity since, as was ~entioned, all member signals are subjected to the same timing adjustment.
Figure 9 represents the most general embodiment of the invention up to this point in a single signal band as defined by frequency range and polarization direction, if the latter is applicable. Figure 5, on the other hand, depicts an embodiment in which the phase encoding of target parameters and propagation material properties (if applicable) would utilize a number of signal bands. It follows then that a more comprehensive embodiment may yet be envisaged in which a number of signal bands are employed, the technique in each single signal band being represented as in Figure 9.
An embodiment as described would provide the great-est redundancy yet for the identification parameters of the reflecting target and would also allow the characterization of the phase distortion of the propagation medium and/or the reflecting target in a number of frequency bands and polariza-tion di,rections.
Another embodiment of the invention complementing all other variations described up to this point would include the use of amplitude spectral information determined either collectively from the received return signal or else computed from individual member signals as one additional target identi-fication parameter describing its "qualityn. Referring to Figure 4 in alternate 5G2 we first noted the use of Fourier analysis in the processing sequence for the received return signal 5A.
-3~-~lZ~
Throughout preceding discussions, the only modifi-cation admitted for the amplitude spectrum of the base signal pairs had been a Doppler induced effect. We shall now want to give cognizance to variations in the amplitude spectrum caused by freguency dependent alternative mechanisms of the propaga-tion medium and also the frequency dependent reflective pro-perties of the target.
A preferential loss of higher frequency components as a function of the length of propagation path is a common characteristic of most propagation media. Particular media can exhibit "window" effects where for certain frequencies or polarizations (if applicable) anomalous attenuation or lack of attenuation will occur. For all of the permissible base signals having either three or four fundamental properties, these effects should not alter in most circumstances the basic smooth and unimodal character of the amplitude spectrum and so the mathematical approximations presented would retain their validity. No effects would be induced on phase as it is measured here, since the base signals share a common ampli-tude spectrum.
Empirical studies have been cited in a number of pr,eviou~ discussions as a means for establishing standards or functional relationships necessary of the determination of certain of the target identification parameters. Clearly, by empirical studies it is possible to determine the absolute amplitudes and changes in form of the amplitude spectrum of mem~er signals caused by a propagation medium so that these effects might be removed from consideration. Other differences o~ magnitude and form must then be diagnostic in some sense of the target, describing its quality.
Peculiarities of the target figure or shape, as well as perhaps a transitional character in reflective pro-perties can cause modifications to the amplitude spectrum which might be unique to certain targets hence facilitating positive identifications, or else simply assisting in their categorization. We must also note in the context of target quality determination that phase plays some role, since it is a 180 phase shift or reversal of arithmetic sign of the echo which allows distinction between "hard" and "soft" targets 1~ where the magnitudes of the reflective contrasts between the target and the propagation medium are equal. The terminology "hard" is being applied to targets of materials in which the signal propagation velocity exceeds its velocity in the propa-gation medium.
Target quality information is contained in the member signals of the signal train as well as in the entire train itself. Hence as in the case of most of the other para-meters describing the target, a measure of redundancy is again present.
Figure 1 illustrates the most elementary embodiment of the invention described, but can be used to help explain the most encompassing embodiment of the invention yet to be described. All variations of the invention discussed so far have included a single transmitter 1, a single receiver 4, and single reflecting target 3. In fact, any number of any of these elements can be used, yet allowing all other essen-tials of the invention so that the plurality of reflecting targets can each be identified individually according to their parameters with whatever degree of redundancy the particular embodiment allows. Figure 10 exemplifies such an embodiment based on the variation shown in Figure 1.
112~q9 In Figure 10, three distinct reflecting targets 3, two distinct receivers 4A, 4B and a single transmitter 1 are shown. The propagating signal lA is taken as in Figure 1 and the propagation medium 2 is also as in Figure 1. Each reflect-îng target returns an echo to each of the receivers 4A, 4B.
The processing sequences 5 are essentially as depicted in greater detail in Figure 2 except that each of the reflecting targets 3 now corresponds to a sequence of peaks in the step 5E of Figure 2 which may have any arbitrary relation in time, one sequence to another, hence necessitating also the inclusion of some logic to separate the member peaks in each sequence so that target parameter estimates 6 can be made for each -reflecting target. Since there are two receivers, the target parameter estimator 6 may now include angular information, even though the embodiment of Figure l upon which we based this illustrative case made no provision for the inclusion o~ such information.
Figure 11 suggests a familiar analytic basis by which the use of information from the two receivers 4A, 4B
may be handled to yield angular information. The transmitter T and receivers Rl, R2 of Figure 11 occupy known relative positions which are either fixed or changing in a known manner in time. The processing sequence 5 as described by Figure 2 is capable of estimating for each reflecting target only a ~ange and relative velocity. For any estimated range, the permissible target locus is an ellipse with the transmitter and recei~er which detected the particular echo at its focii.
The intersection of the elliptical locii will define the target position and thus pro~ide the angular information about ; ¦
the target expressed in the coordinate network of the trans-mitter ana two receivers. Ambiguity of position can be eliminated as indicated again in Figure 11 by designing the configuration so that cextain positions are disallowed, as for example those to the left of the dashed line AA'.
It is important to mention that the logic by which the sequences corresponding to the differing targets are isolated can include clues about the consistency of relative velocity of the targets and even amplitude spectral information which in fact was not mentioned in the embodiment of Figure 1, but was described in a later, re sophisticated technique.
To further illustrate the technique in which a plura-lity of elements is permissible, we address now the embodiment of Figure 3, where angular information in one angle is one of the target identification parameters, and appeal also to a computer simulation. For illustrative purposes we adopt the configuration shown in Fisu~e 3 but declare only a plurality of reflecting targets, specifically three. The signal lA from transmitter 1 is taken to be made of a Klauaer base signal pair as described by equation 4 and depicted in Figure 13.
Amplitudes of the three reflecting targets are taken to be in the ratio 4, 3, 2 while their initial ranges, angular information and relative velocities tabulate as:
Range Angular Relative Amplitude (Arbitrary Information Velocity (Ratio) Units) (Ratio) Target 1 150 0 1 4 Target 2 300 -45 1.05* 3 Target 3 450 90 .g5~ 2 approaching ~ fleeinq Note that we are using the same convention for encoding the angular information as indicated in Figure 15. We are assum-ing constant phase distortions imparted by the phase lens llZ77 ~9 .7 of Figure 3. Also, the target r~lative velocities are expressed .as 1 ~ their rations with the speed~at which echo.location signal lA travels.
Since target 2 is approaching the detection system centroid while target 3..is fleeing, the expected targe$ ranges for the assigned target relative velocities are 280 and 475 units respectively. Also, if all other parameters can be oorrectly identified, then a reconstruction.of the received return signal 4 may be accomplished for comparison with the observed one. Such a sequence is~shown by the computer simu-lations of Figure 19 where the noise-free and noisy case are examined.
In Figure 19, curve A is the observed received return signal 4. The reconstruction from detected parameters is denoted curve D. Curve B shows the sum of the squares of the correlation components, curves Cl and C2. Referring to Figure ~ which describes the particular processing se~uence 5, -we secognize curve Cl as 5Dl, curve C2 as SD2 and curve B as 5E. The family of curves with primes represent results from the circumstance where background noise is present. For this case note that there is little difficulty in distinguishing among the reflecting targets.
.Hence these illustrations make clear certain of the advantages of the e~bodiments which function in environments with a plurality of reflecting targets and utilize where bene-ficial, pluralities of transmitters and receivers.
A more general variation of the invention, encom-passing all other variations described and which can be developed starting with any of thse techniques, employs a base signal pair in the processing sequence which can differ from the base signal pair of the outgoing signal design., The two distinct base signal pairs shall be designated as the design signal pair ' ~ ,. .
llZ77~9 and the processing signal pair respectively. For any given design signal pair, the admissible processing signal pairs must represent only rotations of the-design signal pair phase spectra by a constant angle, and all differences in amplitude spectrum must be constrained such that the product of the design signal pair common amplitude spectrum and the processing signal pair common amplitude spectrum in itself has a form appropriate to a base signal pair.
All embodiments described heretofore employed a common base signal pair for the design of the outgoing signal train and the processing sequence. In fact, this restriction need not exist and we may with appropriate planning use an-out-going signal train developed with Rlauder signals, yet select a processing base signal pair constructed with Gabor signals to extract desired target parameters (refer to equations 2B and , 2C which specifically define Klauder and Gabor signals.~
Should the particular application of the invention not make use of phase encoding of information as the variation ¦ described in Figures 1 and 2, the~ both the design signal pair and processing signal pair would each have to satisfy only the first three fundamental properties which were outlined in that discussion. Where angular resolution via phase encoding is called upon, the fourth fundamental property introduced in the discussion of the application depicted in Figures 3 and 4 is needed. A modified form of this property may now be taken for both the design signal pair and the processing signal pair.
Calling such a signal pair fk(t), fj(t) the revised statement , of Property IV reads:
IV. fk(t) and fj(t) must be transformable to respect-1 ive odd and even form about the central coordlnate value in ; their interval of definition of duration a, by a constant -~12~
shift of phase at all frequencies where the coordinate origin of definition of such phase is again taken at the same central coordinate value.
In reviewing the m~thematical discussions of the simpler techniques it becomes clear that the processing sequences as described can progress up to determinations of phase using differing design and processing signal pairs having three or four fundamental properties as the application requires, and having permissible departures in amplitude spectra. Specifi-cally, in the embodiment shown in Figure 1, any appropriate processing signal pair allows completion of the entire proces-sing sequence shown in Figure 2 in its entirety with no modifi-cation. Alternatively, in the embodiment shown in Figure 3 where phase encoding is employed to achieve angular resolution, the processing sequence of Figure 4 would be unmodified through element 5F. Thereafter, an adjustment in phase related-to the constant shift of the processing base pair relative t~ the design base pair described by the revised Property IV would be required.
For purposes of having a more concrete illustration, consider an outgoing signal train developed using as the design signal pair fk(t), fj(t) defined by equation 5 with the con-straint of equation 6 and subject to equation 24. In the Fourier frequency domain following equation 25, we have the counterparts ~ /2) Fj(w) = F(w) e 45 If we envisage a phase encoding mechanism as in the technique described by Figures 3 and 4, the recei~ed return signal 5A
having undergone a constant phase shift now termed B for the particular angular resolution, would have a form similar to equation 27 but specifically fk(s(t - /2) - T,~ ~.B) + fj(s(t - a/2 - ~) - T,fl + B) 46 In the Fourier frequency domain the received return signal SA
(also equation 46) is now ' F(w/s)e~ B) e~i w/s T/s {+i(w/s a/2~2)+ e+i(w/st~/2+l~)}
(Compare with eguation 28).
Let us select a processing signal pair gk(t), gj(t) defined analogously to fk(t), fj(t) having as Fourier frequency domain count,erparts Gk ~w) = G (w) e+i ( Y + ~/2 ) Gj (w) = G(w) e+iY . 48 A(t), B(t) or 5Dl, 5D2 of the processing seguence of Figure 4 would then have as frequehcy domain equivalents +i(~+B--y) +i w/s T/s +(w/s c~/2) A (w) = G (w~ F (w/s ) e e {e ~i (w/s [~/2 ~ ~ r/2) e }
-y) +i w/s T/s ~i (w/s a/2 + ~/2) 8(w) ~ G(w)F(w/s)e e {e +i (w/s la/2 ~ r 3 ) + e } 49 ;(Co,mpare with equation 29).
From equation 49 onward this illustrative analysis may proceed in parallel with the development based on Figures 3 and 4 with two provisions. First, the product G(w)F(w/s) must define an amplitude spectrum which is essentially smooth and unim~dal so that a signal pair analogous to fk.(t,~), fj(t,~) of equation 30 may be defined., Second, the phase encoded angular information relating to B can be determined only after compensating for the phase rotation of the design signal pair by ~ and the processing signal pair rotation by y. Note that the relative rotation between these two pairs is again constant and equal to ~ - y. In particular, alter-nates 5Gl and 5G2 of Figure 4 would both yield phase determi-nations in this case of ~ y) which would give a value for ~ when corrected as necessary for the known phase rotations and ~. (See for example equation 34).
The nature of the amplitude spectral differences permitted between the design signal pair and the processing signal pair is now greatly clarified. G(w) and F(w/s) must for all realistic Doppler variations governed by s overlap sufficiently ;n frequency w so that the product G(w)F(w/s) has a band width sufficiently broad to correspond to a signal of finite duration and impulsive character when transformed to the time domain with a constant zero phase spectrum. (This re-quir2ment is analogous in some measure to fundamental Property II). Also, the product G(w) F(w/s) must have a character essentially as demanded in fundamental Property I.
It should ~e apparent to anyone with some background in signal processing that the permissible differences in the amplitude spectra of the design signal pair and the processing pair can often be used to great advantage. Techniques utiliz-ing some "conditioning" of amplitude spectra in association with a correlation or convolution process are widely used and even standard in the treatment of signals for detection and other applications (see for example Phillip E. Panter, ~odulation, Noise and SPectral AnalYsis, McGraw Hill, 759 P, 1965). By analogy, similar enhancement techniques can be designed to function in the context of this invention.
112,7~49 As a most elementary example of such a method, one may consider a practical environment which is attenuative in nature and preferentially removes the high frequency content of F(w/s) as the propagation distance to the target increases.
For some approximation to the expected target range, Gtw) might con~ersely give appropriate emphasis to the high frequencies so that the product F(w/s)G(w) is again almost flat. Such a method would improve both the resolution obtain-able in the relative velocity determination and range calcu-lation.
Hence this embodiment of the invention endows great flexibility in all the alternative variations making possible a numbér of advantages which can arise from a judicious manipu-lation of the amplitude and phase spectral character of the design signal pair and the processing signal pair. Introduc-tion of a time variation in the definition of the processing signa~ pair might enhance detectability through amplitude spectral "whitening" whilé also compensating for the changing constant phase characteristic introduced by a propagation medium. The scope and significance of such possibilities can be appreciable.
, WHA~ IS CLAIMED IS:
Claims (20)
PROPERTY OF PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:
1. A method of determining angular information con-cerning the direction of a signal reflecting object relative to a signal transmitter and a signal receiver, comprising the steps of:
a) transmitting a signal from the transmitter, such signal having a continuous amplitude spectrum between low and high frequency limits, for reflection from the object;
b) receiving the reflected signal with the receiver;
c) changing the phase of the signal in dependence upon the direction of its travel while propagating between the transmitter and the receiver, such phase change char-acterized other than by a simple time delay;
d) measuring the phase of the received reflected signal; and e) determining the angular information concerning direction of the object based on the measured phase.
a) transmitting a signal from the transmitter, such signal having a continuous amplitude spectrum between low and high frequency limits, for reflection from the object;
b) receiving the reflected signal with the receiver;
c) changing the phase of the signal in dependence upon the direction of its travel while propagating between the transmitter and the receiver, such phase change char-acterized other than by a simple time delay;
d) measuring the phase of the received reflected signal; and e) determining the angular information concerning direction of the object based on the measured phase.
2. The method of claim 1 wherein the phase change is a constant for each direction independent of frequency.
3. The method of claim 2 wherein said step of changing the phase of the signal comprises:
propagating the signal through a medium having a dimension which varies in dependence upon the direction of travel of the signal.
propagating the signal through a medium having a dimension which varies in dependence upon the direction of travel of the signal.
4. The method of claim 1 wherein said step of changing the phase of the signal comprises:
propogating the signal through a medium having a dimension which varies in dependence upon the direction of travel of the signal.
propogating the signal through a medium having a dimension which varies in dependence upon the direction of travel of the signal.
5. A method of ascertaining the angular information of one or more reflecting targets in a target field referred to a coordinate system, comprising the steps of:
a) producing a signal being a linear combination of a pair of base signals such signals having the properties of:
(1) sharing a common amplitude spectrum which is essentially flat or smoothly unimodal occupying a contiguous band of frequencies (2) having a finite time interval before and after which each signal of said pair of base signals is zero;
(3) each base signal of such a pair being in phase quadrature to the other member of the pair; and (4) each of such pair of base signals being transformable to a symmetric signal relative to a time reference by adding a constant phase angle to the phase at each frequency;
b) transmitting the signal pattern;
c) introducing a phase distortion, characterized by other than a simple time delay and having a component independent of frequency, which varies in a known and single valued manner according to desired angular information into the signal propagation path;
d) receiving reflections of the transmitted signal pattern from the target field; and e) processing the received reflections to ascertain the angular information for at least one of such targets in the target field.
a) producing a signal being a linear combination of a pair of base signals such signals having the properties of:
(1) sharing a common amplitude spectrum which is essentially flat or smoothly unimodal occupying a contiguous band of frequencies (2) having a finite time interval before and after which each signal of said pair of base signals is zero;
(3) each base signal of such a pair being in phase quadrature to the other member of the pair; and (4) each of such pair of base signals being transformable to a symmetric signal relative to a time reference by adding a constant phase angle to the phase at each frequency;
b) transmitting the signal pattern;
c) introducing a phase distortion, characterized by other than a simple time delay and having a component independent of frequency, which varies in a known and single valued manner according to desired angular information into the signal propagation path;
d) receiving reflections of the transmitted signal pattern from the target field; and e) processing the received reflections to ascertain the angular information for at least one of such targets in the target field.
6. The method of claim 5, further including the step of determining the range of at least one of the targets, comprising the step of:
processing the received reflections to ascertain the range of at least one of such targets in the target field.
processing the received reflections to ascertain the range of at least one of such targets in the target field.
7. The method of claim 5, further including the step of determining the range and velocity of at least one of the targets, comprising the step of:
producing a signal pattern comprising of at least two said signals, transmitting the signal pattern into the target field during at least partially different time intervals for each signal of the signal pattern, and processing the received reflections to ascertain the range and velocity of at least one of such targets in the target field.
producing a signal pattern comprising of at least two said signals, transmitting the signal pattern into the target field during at least partially different time intervals for each signal of the signal pattern, and processing the received reflections to ascertain the range and velocity of at least one of such targets in the target field.
8. The method of claim 5, wherein the pair of base signals have the property of:
one of each such pair of base signals being odd about a central coordinate value in its finite time interval and the other of each such pair being even with respect to its central coordinate value.
one of each such pair of base signals being odd about a central coordinate value in its finite time interval and the other of each such pair being even with respect to its central coordinate value.
9. The method of claim 5, further including the step of ascertaining angular information regarding more than one angle of at least one of the targets, comprising the steps of:
a) producing a signal pattern comprising at least two signals each said signal being a linear pair combination of base signals each having the properties of:
(1) sharing a common amplitude spectrum which is essentially flat or smoothly unimodal occupying a contiguous band of frequencies;
(2) having a finite time interval before and after which each signal of each said pair of base signals is zero;
(3) each base signal of such a pair being in phase quadrature to the other member of the pair;
(4) each of such pair of base signals being transformable to a symmetric signal relative to a time reference by adding a constant phase angle to the phase at each frequency; and (5) each pair of such base signals occupying at least partially non-overlapping band of frequency from the other pairs;
b) transmitting such signal pattern;
c) introducing phase distortions, characterized by other than a simple time delay and having a component independent of frequency which vary in a known and single valued manner according to desired angular information into the signal propagation path, differing angular information being introduced in differing frequency bands;
d) receiving reflections of the transmitted signal pattern from the target field; and e) processing the received reflections to ascertain the angular information for at least one of such targets in the target field.
a) producing a signal pattern comprising at least two signals each said signal being a linear pair combination of base signals each having the properties of:
(1) sharing a common amplitude spectrum which is essentially flat or smoothly unimodal occupying a contiguous band of frequencies;
(2) having a finite time interval before and after which each signal of each said pair of base signals is zero;
(3) each base signal of such a pair being in phase quadrature to the other member of the pair;
(4) each of such pair of base signals being transformable to a symmetric signal relative to a time reference by adding a constant phase angle to the phase at each frequency; and (5) each pair of such base signals occupying at least partially non-overlapping band of frequency from the other pairs;
b) transmitting such signal pattern;
c) introducing phase distortions, characterized by other than a simple time delay and having a component independent of frequency which vary in a known and single valued manner according to desired angular information into the signal propagation path, differing angular information being introduced in differing frequency bands;
d) receiving reflections of the transmitted signal pattern from the target field; and e) processing the received reflections to ascertain the angular information for at least one of such targets in the target field.
10. The method of claim 5, further including the step of ascertaining angular information regarding more than one angle of at least one of the targets, comprising the steps of:
a) producing a signal pattern comprising at least two signals each said signal being a linear pair combination of base signals each having the properties of:
(1) sharing a common amplitude spectrum which is essentially flat or smoothly unimodal occupying a contiguous band of frequencies;
(2) having a finite time interval before and after which each signal of each said pair of base signals is zero;
(3) each base signal of such a pair being in phase quadrature to the other member of the pair;
(4) each of such pair of base signals being transformable to a symmetric signal relative to a time reference by adding a constant phase angle to the phase at each frequency; and (5) each pair of such base signals occupying at least partially overlapping band of frequency from the other pairs;
b) transmitting such signal pattern;
c) phase encoding positional information about plural angles in each signal;
d) receiving reflections of the transmitted signal pattern from the target field; and e) processing the received reflections to ascertain the angular information for at least one of such targets in the target field.
a) producing a signal pattern comprising at least two signals each said signal being a linear pair combination of base signals each having the properties of:
(1) sharing a common amplitude spectrum which is essentially flat or smoothly unimodal occupying a contiguous band of frequencies;
(2) having a finite time interval before and after which each signal of each said pair of base signals is zero;
(3) each base signal of such a pair being in phase quadrature to the other member of the pair;
(4) each of such pair of base signals being transformable to a symmetric signal relative to a time reference by adding a constant phase angle to the phase at each frequency; and (5) each pair of such base signals occupying at least partially overlapping band of frequency from the other pairs;
b) transmitting such signal pattern;
c) phase encoding positional information about plural angles in each signal;
d) receiving reflections of the transmitted signal pattern from the target field; and e) processing the received reflections to ascertain the angular information for at least one of such targets in the target field.
11. The method of claim 10, wherein said step of phase encoding comprises the step of:
introducing phase distortions, characterized by other than a simple time delay and having a component independent of frequency which vary in a known and single valued manner according to desired angular information into the signal propagation path, differing angular information being introduced into member signals of the signal pattern with independent phase encoding.
introducing phase distortions, characterized by other than a simple time delay and having a component independent of frequency which vary in a known and single valued manner according to desired angular information into the signal propagation path, differing angular information being introduced into member signals of the signal pattern with independent phase encoding.
12. A system for determining angular information concerning the direction of a signal reflecting object, comprising:
a) transmitter means for transmitting a signal having a continuous amplitude spectrum between low and high fre-quency limits, for reflection from the object;
b) receiver means for receiving the reflected signal;
c) means for changing the phase of the signal in dependence upon the direction of its travel while propa-gating between said transmitter means and said receiver means, such phase change characterized other than by a simple time delay;
d) means for measuring the phase of the received reflected signal; and e) means for determining angular information concerning the direction of the object based on the measured phase.
a) transmitter means for transmitting a signal having a continuous amplitude spectrum between low and high fre-quency limits, for reflection from the object;
b) receiver means for receiving the reflected signal;
c) means for changing the phase of the signal in dependence upon the direction of its travel while propa-gating between said transmitter means and said receiver means, such phase change characterized other than by a simple time delay;
d) means for measuring the phase of the received reflected signal; and e) means for determining angular information concerning the direction of the object based on the measured phase.
13. The system of claim 12 wherein said means for changing the phase comprises means for changing the phase by a constant for each direction independent of frequency.
14. The system of claim 13 wherein said means for changing the phase of the signal comprises:
a medium having a dimension which varies in dependence upon the direction of travel of the signal.
a medium having a dimension which varies in dependence upon the direction of travel of the signal.
15. The system of claim 12 wherein said means for changing the phase of the signal comprises:
a medium having a dimension which varies in dependence upon the direction of travel of the signal.
a medium having a dimension which varies in dependence upon the direction of travel of the signal.
16. A system for ascertaining the angular information of one or more reflecting targets in a target field referred to a coordinate system, comprising:
a) means for producing a signal being a linear combination of a pair of base signals such signals having the properties of:
(1) sharing a common amplitude spectrum which is essentially flat or smoothly unimodal occupying a contiguous band of frequencies (2) having a finite time interval before and after which each signal of said pair of base signals is zero (3) each base signal of such a pair being in phase quadrature to the other member of the pair; and (4) each of such pair of base signals being transformable to a symmetric signal relative to a time reference by adding a constant phase angle to the phase at each frequency;
b) means for transmitting the signal pattern into the target field;
c) means for introducing a phase distortion, charac-terized by other than a simple time delay and having a component independent of frequency, which varies in a known and single valued manner according to desired angular information into the signal propagation path;
d) means for receiving reflections of the transmitted signal pattern from the target field; and e) means for processing the received reflections to ascertain the angular information for at least one of such targets in the target field.
a) means for producing a signal being a linear combination of a pair of base signals such signals having the properties of:
(1) sharing a common amplitude spectrum which is essentially flat or smoothly unimodal occupying a contiguous band of frequencies (2) having a finite time interval before and after which each signal of said pair of base signals is zero (3) each base signal of such a pair being in phase quadrature to the other member of the pair; and (4) each of such pair of base signals being transformable to a symmetric signal relative to a time reference by adding a constant phase angle to the phase at each frequency;
b) means for transmitting the signal pattern into the target field;
c) means for introducing a phase distortion, charac-terized by other than a simple time delay and having a component independent of frequency, which varies in a known and single valued manner according to desired angular information into the signal propagation path;
d) means for receiving reflections of the transmitted signal pattern from the target field; and e) means for processing the received reflections to ascertain the angular information for at least one of such targets in the target field.
17. The system of claim 16, wherein said means for processing further includes:
means for processing the received reflections to ascertain the range of at least one of such targets in the target field.
means for processing the received reflections to ascertain the range of at least one of such targets in the target field.
18. The system of claim 16, wherein:
said means for producing comprises means for producing a signal pattern comprising at least two said signals, and said means for transmitting comprising means for transmitting the signal pattern into the target field during at least partially different time intervals for each signal of the signal pattern;
said means for processing comprises means for processing the received reflections to ascertain the range and velocity of at least one of such targets in the target field.
said means for producing comprises means for producing a signal pattern comprising at least two said signals, and said means for transmitting comprising means for transmitting the signal pattern into the target field during at least partially different time intervals for each signal of the signal pattern;
said means for processing comprises means for processing the received reflections to ascertain the range and velocity of at least one of such targets in the target field.
19. The system of claim 16, wherein:
a) said means for producing comprises means for producing a signal pattern comprising at least two signals each said signal being a linear pair combination of base signals each having the properties of:
(1) sharing a common amplitude spectrum which is essentially flat or smoothly unimodal occupying a contiguous band of frequencies;
(2) having a finite time interval before and after which each signal of each said pair of base signals is zero;
(3) each base signal of such a pair being in phase quadrature to the other member of the pair;
(4) each of such pair of base signals being transformable to a symmetric signal relative to a time reference by adding a constant phase angle to the phase at each frequency; and (5) each pair of such base signals occupying at least partially non-overlapping band of frequency from the other pairs;
b) said means for introducing phase distortions comprises means introducing phase distortions, characterized by other than a simple time delay and having a component independent of frequency which vary in a known and single valued manner according to desired angular information into the signal propagation path, differing angular information being introduced in differing frequency bands;
c) said means for processing comprises means for processing the received reflections to ascertain the angular information for at least one of such targets in the target field.
a) said means for producing comprises means for producing a signal pattern comprising at least two signals each said signal being a linear pair combination of base signals each having the properties of:
(1) sharing a common amplitude spectrum which is essentially flat or smoothly unimodal occupying a contiguous band of frequencies;
(2) having a finite time interval before and after which each signal of each said pair of base signals is zero;
(3) each base signal of such a pair being in phase quadrature to the other member of the pair;
(4) each of such pair of base signals being transformable to a symmetric signal relative to a time reference by adding a constant phase angle to the phase at each frequency; and (5) each pair of such base signals occupying at least partially non-overlapping band of frequency from the other pairs;
b) said means for introducing phase distortions comprises means introducing phase distortions, characterized by other than a simple time delay and having a component independent of frequency which vary in a known and single valued manner according to desired angular information into the signal propagation path, differing angular information being introduced in differing frequency bands;
c) said means for processing comprises means for processing the received reflections to ascertain the angular information for at least one of such targets in the target field.
20. The system of claim 16, wherein:
a) said means for producing comprises means for producing a signal pattern comprising at least two signals each said signal being a linear pair combination of base signals each having the properties of:
(1) sharing a common amplitude spectrum which is essentially flat or smoothly unimodal occupying a contiguous band of frequencies;
(2) having a finite time interval before and after which each signal of each said pair of base signals is zero;
(3) each base signal of such a pair being in phase quadrature to the other member of the pair;
(4) each of such pair of base signals being transformable to a symmetric signal relative to a time reference by adding a constant phase angle to the phase at each frequency; and (5) each pair of such base signals occupying at least partially overlapping band of frequency from the other pairs;
b) means for phase encoding positional information about plural angles in each signal;
c) said means for processing comprises means for processing the received reflections to ascertain the angular information for at least one of such targets in the target field.
a) said means for producing comprises means for producing a signal pattern comprising at least two signals each said signal being a linear pair combination of base signals each having the properties of:
(1) sharing a common amplitude spectrum which is essentially flat or smoothly unimodal occupying a contiguous band of frequencies;
(2) having a finite time interval before and after which each signal of each said pair of base signals is zero;
(3) each base signal of such a pair being in phase quadrature to the other member of the pair;
(4) each of such pair of base signals being transformable to a symmetric signal relative to a time reference by adding a constant phase angle to the phase at each frequency; and (5) each pair of such base signals occupying at least partially overlapping band of frequency from the other pairs;
b) means for phase encoding positional information about plural angles in each signal;
c) said means for processing comprises means for processing the received reflections to ascertain the angular information for at least one of such targets in the target field.
Priority Applications (3)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA303,851A CA1127749A (en) | 1978-05-23 | 1978-05-23 | Echo location system transmitting and receiving component signals of known initial time interval for determination of angular information |
| CA000392368A CA1137209A (en) | 1978-05-23 | 1981-12-15 | Echo location system transmitting and receiving component signals of known initial times for determination of range |
| CA000392367A CA1137208A (en) | 1978-05-23 | 1981-12-15 | Echo location system transmitting and receiving component signals of known initial time interval for determination of velocity as well as velocity and range range |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA303,851A CA1127749A (en) | 1978-05-23 | 1978-05-23 | Echo location system transmitting and receiving component signals of known initial time interval for determination of angular information |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA1127749A true CA1127749A (en) | 1982-07-13 |
Family
ID=4111520
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA303,851A Expired CA1127749A (en) | 1978-05-23 | 1978-05-23 | Echo location system transmitting and receiving component signals of known initial time interval for determination of angular information |
Country Status (1)
| Country | Link |
|---|---|
| CA (1) | CA1127749A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4800541A (en) * | 1987-02-12 | 1989-01-24 | Canadian Patents And Development Limited | Method for underwater acoustic direction sensing |
-
1978
- 1978-05-23 CA CA303,851A patent/CA1127749A/en not_active Expired
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4800541A (en) * | 1987-02-12 | 1989-01-24 | Canadian Patents And Development Limited | Method for underwater acoustic direction sensing |
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