METHOD AND SYSTEM FOR DETERMINING THE RANGE AND VELOCITY OF A MOVING OBJECT
FIELD OF THE DISCLOSED TECHNIQUE The disclosed technique relates to range finders in general, and to methods and systems for determining the range and velocity of a moving object, in particular.
BACKGROUND OF THE DISCLOSED TECHNIQUE The range of an object can be determined by emitting a pulse, such as laser, radar, or sound, toward the object and measuring the time that elapsed until the echo from the object is detected. The range S is determined by computing,
where C is the speed of light (in case of laser pulse or radar pulse) or the speed of sound (in case of a sound pulse), and T
R is the time for the round trip of the pulse from a transmitter to a receiver. However, a shortcoming of this method is that the energy of the pulse is generally low, thereby causing difficulties in measuring the range of distant objects. This is due to the fact that the energy of the reflected pulses decreases very rapidly with increasing distance, and reliable readings can not be obtained. Methods and systems to circumvent this problem are known in the art. US Patent No. 6,100,516 issued to Nerin et al., and entitled "Velocity Measurement Device and Laser Range Finder Using a Coherent Detection", is directed to a device for amplifying the laser pulse reflected from a target, and using this amplified laser pulse to determine the range and velocity of the target. The device includes an optical means for pumping a laser amplifier material, a cavity having two quality factors Q
MAX and QM
IN, an optical separating means, an optical emission means and a detection assembly. The cavity includes the laser amplifier material, and
three mirrors M M
2 and M
3. Mirror M
1 is located on one side of the laser amplifier material and mirrors M
2 and M
3 are located on the other side of the laser amplifier material. Mirror M
3 is placed in the center of the laser amplifier material and mirror M
2 is placed around mirror M
3 on the same face. The cavity is located between the optical means and the optical separating means. The optical emission means is located between the target and the optical separating means. The association of mirrors My and M
3 forms an optical resonator whose quality factor is QMAX- The association of mirrors My and M
2 forms an optical resonator whose quality factor is QMIN- A laser oscillation is maintained in the central zone of the cavity, where the quality factor is Q
MAX, a d a laser beam is emitted by mirror M
3. The laser beam is separated by the optical separating means, one part of which passes to the detection assembly as a reference beam, and another part of which is supplied to the target by the optical emission means. The laser beam is reflected or diffused by the target toward the optical emission means (which now operates as an optical reception means). The optical reception means re-reflects the laser beam to an amplifying region of the cavity constituted by the laser amplifier material and mirrors My and M
2. After amplification in this structure, the laser beam returns in the direction of the beam separating means (which now operates as a beam recombination means). The beam recombination means supplies part of the amplified signal to the detection assembly, where it interferes with the reference beam, and the detection assembly extracts the velocity information respective of the target, according to this interference.
SUMMARY OF THE DISCLOSED TECHNIQUE It is an object of the disclosed technique to provide a novel method and system for determining the range and velocity of a moving object. In accordance with the disclosed technique, there is thus provided a device for determining a range of a moving object. The device includes a sampler for producing a plurality of sampled signals, a multi-process array running a plurality of processes, and a selector coupled with the multi-process array. The sampler produces the sampled signals, by sampling a received signal respective of a sequence of pulses transmitted toward the moving object. The multi-process array is coupled with the sampler, wherein each of the processes is associated with a respective sampler. Each of the processes is associated with a respective time shift which is determined according to a respective radial velocity assumption of the moving object with respect to the device. Each of the processes is further associated with the pulse rate of the sequence of pulses. Each of the processes produces a signal summation by sequentially shifting the sampled signals by the respective time shift, and adding together the sampled signals. The selector determines the range of the moving object according to at least one signal summation which includes a summed pulse event. In accordance with the another aspect of the disclosed technique, there is thus provided a method for determining a range of a moving object. The method includes the procedure of shifting a plurality of sampled signals relative to one another by a respective time shift, for each of a plurality of radial velocity assumptions for the relative radial velocity between a transceiver and the moving object. The method further includes the procedure of adding together the shifted signals for each of the radial velocity assumptions, thereby producing a signal summation for each of the radial velocity assumptions.
The method further includes the procedures of detecting a summed pulse event within at least one of the signal summations, and determining the range of the moving object according to the detected summed pulse event. Each of the sampled signals represents a respective received signal detected across a period of time. Each of the received signals is received by the transceiver and associated with a respective pulse echo reflected by the moving object, wherein the respective pulse echo is assumed to be included in the received signal. Each of the respective time shifts is determined for a respective one of the radial velocity assumptions. Each of the respective time shifts represents an assumed shift in detection times of two consecutive received signals, due to the respective radial velocity assumption.
BRIEF DESCRIPTION OF THE DRAWINGS The disclosed technique will be understood and appreciated more fully from the following detailed description taken in conjunction with the drawings in which: Figure 1A is a schematic illustration of a system for determining the radial velocity of a moving object, constructed and operative in accordance with an embodiment of the disclosed technique; Figure 1B is a schematic illustration of the operation of the processors of the system of Figure 1A, together with the sampler of the system; Figure 1C is a schematic illustration of the operation of one of the processors of the system of Figure 1 A; Figure 1 D is a schematic illustration of the operation of the selector of the system of Figure 1 A; Figure 1 E is a schematic illustration of a modified sampled signal, constructed from a sampled signal of Figure 1 B, according to another embodiment of the disclosed technique; Figure 2 is a schematic illustration of a system for determining the radial velocity of a moving object, constructed and operative in accordance with a further embodiment of the disclosed technique; and Figure 3 is a schematic illustration of a method for operating the system of Figure 1A, operative in accordance with another embodiment of the disclosed technique.
DETAILED DESCRIPTION OF THE EMBODIMENTS The disclosed technique overcomes the disadvantages of the prior art by providing a system and a method which directs a sequence of pulses toward a moving object and shift-sums detected signals which are supposed to include echoes reflected from that moving object. It is noted that when the moving object is outside the range of conventional systems, the echo in a single detected signal, is of the order of the ambient noise and hence cannot be extracted there from. By shift-summing a plurality of detected signals, the method of the disclosed technique provides a summed representation of such an echo, which can be identified and detected. Thus, the disclosed technique can be used to extend the detection range of conventional pulse operated radar systems. It is noted that the disclosed technique is applicable to any pulse operated range detector known in the art, such as laser, acoustic, RF, and the like. The system samples each of the detected signals across time, and determines a number of different radial velocity assumptions for the moving object, according to different relative radial velocities between the moving object and the system. For each radial velocity assumption, the system determines a respective time shift, by which a subsequent pulse is assumed to be shifted with respect to a previous one. For each radial velocity assumption, the system shifts the sampled signals of each pulse, relative to the sampled signals of the previous echo, by the respective time shift, and produces a signal summation, by adding together the respective shifted sampled signals. When the system detects a summed pulse event within at least one of the signal summations, the system determines the radial velocity of the moving object according to radial velocity assumptions associated with those signal summations in which the summed pulse event was detected. Furthermore, the system determines the range of the moving object, according the detected summed pulse event.
The term "maximal range" herein below, refers to a maximum distance between the system and the moving object, at which the system is capable to determine the radial velocity and the range of the moving object. The term "useful range" herein below, refers to a distance between the system and the moving object, at which the system is capable to determine a radial velocity substantially close to the true radial velocity of the moving object. The term "summation efficiency" herein below, refers to the ratio of the SNR of a summation of the required number of the incoming signals, to the SNR of an individual incoming signal. The term "pulse" herein below, refers to laser pulse, radar pulse, acoustic pulse (e.g., ultrasound), infrared pulse, and the like. The term "transmitter" herein below, refers to a laser source, radar transmitter, sound source, infrared source, and the like. The term "receiver" herein below, refers to a laser detector, radar receiver, sound detector, infrared detector, and the like. Reference is now made to Figures 1A, 1 B, 1C, 1 D and 1 E. Figure 1A is a schematic illustration of a system for determining the radial velocity of a moving object, generally referenced 100, constructed and operative in accordance with an embodiment of the disclosed technique. Figure 1 B is a schematic illustration of the operation of the processors of the system of Figure 1A, together with the sampler of the system. Figure 1C is a schematic illustration of the operation of one of the processors of the system of Figure 1A. Figure 1 D is a schematic illustration of the operation of the selector of the system of Figure 1A. Figure 1 E is a schematic illustration of a modified sampled signal, generally referenced 142, constructed from a sampled signal of Figure 1 B, according to another embodiment of the disclosed technique. System 100 includes a transmitter 102, a receiver 104, a sampler 106, a sampled signal memory 108 and a radial velocity determining unit 110. Radial velocity determining unit 110 includes a plurality of processors 112-), 1122 and 112N, and a selector 114. Receiver
104 is generally unidirectional (i.e., adapted to cover a predetermined section in space). Selector 114 includes a processor 116 and a threshold memory 118. Processors 11215 1122 and 112N include shift-sum memories 120^ 1202 and 120N. Each of processors 112^ 1122 and 112N is in form of an independent hardware. Alternatively, each of processors 112^ 1122 and 112N is a different computational process running in a single processor operating in a multitasking mode. Sampler 106 is a device (e.g., an analog to digital converter) which digitizes an analog signal. Processors 1121 s 1122 and 112N can be integrated with processor 116. Each of sampled signal memory 108, threshold memory 118 and shift-sum memories 120-ι, 1202 and 120N can be a magnetic memory unit (e.g., floppy diskette, hard disk, magnetic tape), optical memory unit (e.g., compact disk), volatile electronic memory unit (e.g., random access memory), non-volatile electronic memory unit (e.g., read only memory, flash memory), and the like. Each of sampled signal memory 108, threshold memory 118 and shift-sum memories 120ι, 1202 and 120N can be a part of sampler 106, a part of radial velocity determining unit 110, or a part of a remote memory module (not shown). A beam splitter 122 is located between transmitter 102 and an object 124. Beam splitter 122 is located in such a position relative to receiver 104, that beam splitter 122 transmits a portion of a pulse 126A from transmitter 102 toward object 124, and beam splitter 122 reflects a portion of a reflected pulse 126B reflected by object 124, toward receiver 104, as reflected pulse echoes 126C. Transmitter 102, receiver 104 and beam splitter 122 can be incorporated in a transceiver (not shown). Object 124 is a land to land missile (e.g., short range missile, intercontinental ballistic missile - ICBM), land to air missile (e.g., antiaircraft missile), air to land missile, air to air missile, aircraft, and the like. Hence, object 124 can be launched from a stationary or a moving platform located on land, from a stationary platform located on or below
the surface of water (e.g., from a warship or a submarine), from an aircraft (e.g., an airplane, a rotorcraft), or from a spaceship. Sampler 106 is coupled with receiver 104 and with sampled signal memory 108. Sampled signal memory 108 is coupled with sampler 106 and with processors 1121 s 1122 and 112N. Each of processors 1121 a
112
2 and 112
N is coupled with selector 114. Processor 116 is coupled with threshold memory 118. With reference to Figure 1A, object 124 is moving toward system 100 at a radial velocity V relative to system 100. However, a system similar to system 100 can determine the radial velocity of an object which is moving away from the system. Transmitter 102 transmits a sequence of pulses 126A, toward object 124 through beam splitter 122, at a pulse rate of R
P. Thus, the interval 7 between consecutive pulses 126A is,
If the object was stationary and substantially close to the system, then the system would have been able to determine a range S thereof according to Equation 1. Furthermore, the system can determine the average radial velocity V
A of object 124 according to the information respective of two consecutive pulses, by computing,
where Sy and S
2 are determined according to Equation 1. If object 124 is moving toward system 100, then object 124 gets closer to system 100 by a differential range ΔS between the emission of two consecutive pulses 126A, such that, AS =V
A -T
P (4)
Due to this movement, echo 126C reaches receiver 104 by a period AT (i.e., shortening time) sooner than a reflected pulse (not shown) would reach the receiver, if the object was stationary, where,
In the case of the disclosed technique, the range S of object 124 from system 100 is so great that the intensity of reflected echoes 126C relative to the background noise is low (i.e., the SNR of reflected echoes 126C is substantially small). Hence, system 100 is unable to distinguish the echo from ambient noise and to determine the range S and the average radial velocity V
A of object 124 according to Equations 1 and 3, respectively. System 100 determines a plurality of different radial velocity assumptions Vy, V
2 and V
N, for object 124 and a plurality of shortening times ΔT
1t ΔT
2 and ΔT
N, respectively. Each of the shortening times ΔT-,, ΔT
2 and ΔT
N (i.e., time shifts), represents the assumed shift in detection time of a subsequent pulse relative to that of a previous one, were object 124 moving at radial velocity assumptions V V
2 and V
N, respectively, relative to system 100. System 100 stores digitized information respective of the last previous Λ/
P-1 echoes 126C in different sets Q, (i = 1 , 2, 3...N), respective of radial velocity assumptions V,-. System 100 shifts the digitized reflected pulses in each of sets C„ by an amount respective of shortening times ΔT„ and adds together the N
P -1 digitized reflected pulses, and a new digitized reflected pulse, in each of sets Q. Due to accumulation of N
P substantially weak received signals in a set, in case a target (i.e., object 124) is actually present, at least one set will indicate a peak. System 100 selects one or more sets which indicates a peak and determines the average radial velocity V
A of object 124 according to the amplitude and the relative locations of the peaks. In case the spacing between radial velocity assumptions V-i, V
2 and V
N is substantially small relative to the average radial velocity V
A of object 124, one set with a peak is adequate for system 100 to determine the average radial velocity V
A of object 124. Object 124 reflects pulses 126A as reflected pulses 126B toward beam splitter 122. Beam splitter 122 reflects reflected pulses 126B as
echoes 126C toward receiver 104. It is noted that the object can reflect the pulses directly toward the receiver, in which case the system can operate without the beam splitter. In the example set forth in Figures 1 B and 1C, the predetermined number of echoes 126C N
P, is arbitrarily set to four. During the interval between detection of the first one and the last one of the four echoes 126C, processors 112
1 ; 112
2 and 112
N determine radial velocity assumptions V V
2 and V
N, respectively, for the average radial velocity V
A of object 124. The values of radial velocity assumptions V V
2and V
N may be distributed between a minimum radial velocity V
MIN, and a maximum radial velocity V
MAX, either uniformly or non-uniformly. Furthermore, processors 112
1 s 112
2 and 112
N determine rounded shifts Hy, H
2) H
N, respectively, respective of shortening times zl7
~y, ΔT
2 and ΔT
N, respectively. Receiver 104 detects four echoes 126C in sequence, at a rate of
R
P and sends four reflected pulse signals referenced 128 respective of the four echoes 126C, to sampler 106. Reflected pulse signal 128 is herein below referred to as "received signal". Sampler 106 samples each of the four echo signals 128 at a sampling rate of R
s and produces four sampled signals 130^ 130
2, 130
3 and 130
4. Each of sampled signals 130-ι, 130
2, 130
3 and 130
4 includes a plurality of samples N
s, where, N
S = 2R
MAXR
S/C (6) and where R
MAX is the maximal range. For example, sampled signal 13Oι includes a plurality of samples 132-), 132
2 and 132
N. In this manner, sampler 106 digitizes each of the four echo signals 128. Sampler 106 stores sampled signals 130^ 130
2, 130
3 and 130
4 in sampled signal memory 108. With reference to Figures 1 B and 10, processor 112ι computes an accurate shift H
A according to,
In most cases H
A is a real non-integer number. Since sampled signals 130^ 130
2, 130
3 and 130
4 are to be aligned relative to one another, with a resolution of an integral multiple of a sample and not a fraction of a sample, H
A has to rounded to the closest integer. This is performed by computing a rounded shift H
R according to, H
R = Round (H
A +R
e) (8) where R
e is a remainder according to, R
e = H
A -H
R (9) R
e is initially set to zero. Processor 112
1 copies sampled signal 130
! from sampled signal memory 108 to shift-sum memory 120 . Processor 112 shifts shift-sum memory 120
! by rounded shift H and adds sampled signal 130
2 to shift-sum memory 120
!. The first shifted samples are discarded, while the last shifted samples are set to zero. Processor 112
! shifts shift-sum memory 120
! by rounded shift Hi and adds sampled signal 130
3 to shift-sum memory 120
!. Processor 112 shifts shift-sum memory 120 by rounded shift Hy and adds sampled signal 130
4 to shift-sum memory 120
!. By shifting sampled signals 130 , 130 , 130
3 and 130
4 by rounded shift Hy prior to adding together sampled signals 130
!, 130
2, 130
3 and 130
4, these sampled signals are substantially aligned as in a situation which mimics a stationary object (i.e., a shortening time ΔT-
t which corresponds to the radial velocity assumption V is determined, and the rounded shift H
1 is in turn determined according to shortening time zlTy). In this manner, processor 112 produces a signal summation 134
!. In the same manner, processors 112
2 and 112
N produce signal summations 134
2 and 134
N, by incorporating rounded shifts H
2 and H
N (not shown), respectively, while adding together sampled signals 130ι, 130
2, 130
3 and 130
4. Rounded shifts H
2 and H
N correspond to shortening times ΔT
2 and ΔT
N, respectively. It is noted that processors 112
!, 112
2 and 112
N operate in parallel, thereby saving scarce computation time.
Signal summation 134
! includes a plurality of summed samples 136
!, 136
2 and 136
N (Figures 1 B and 1 C). Since the echoes 126C are substantially weak and may contain a substantially large amount of noise, system 100 attempts to pinpoint the echo (not shown) which would be reflected by object 124, by examining a sum of N
P echoes 126C (i.e., artificially raising the SNR of echoes 126C). System 100 increases this SNR by a factor of approximately -JN - the example set forth in Figure
1 B the predetermined number of echoes 1260 is four and the improvement factor is 4 = 2. System 100 regards a signal summation whose relative values of summed samples, such as summed samples 136
!, 136
2 and 136
Ν are substantially the same, as a noise signal and ignores this signal summation. On the other hand, system 100 regards another signal summation which includes a summed sample with a peak value substantially above that of the other summed samples, as a signal summation which represents a summed pulse echo. System 100 determines the average radial velocity V
A of object 124 according to one of the radial velocity assumptions V V
2 and VN which corresponds to this signal summation (i.e., a signal summation which indicates a peak). Each of signal summations 134 , 134
2 and 134
N in Figures 1 B and 10 is shown in form of a sequence of summed samples, whereas each of the same signal summations in Figure 1 D is shown in form of a bar graph which indicates the relative value of each summed sample. Processors 112
!, 112 and 112
N send signal summations 134
!, 134
2 and 134
N, respectively, to selector 114. A threshold value T
SH is stored in threshold memory 118 (Figure 1 D). As illustrated in Figure 1 D, the dispersion of the values of summed samples 136
!, 136
2 and 136
N of signal summation 134
! is substantially uniform. Processor 116 compares the value of each of summed samples 136
!, 136
2 and 136
N with the threshold value T
SH and determines that the
value of each of summed samples 136
!, 136
2 and 136
N is lower than the threshold value T
sw. Thus, processor 116 determines that signal summation 134
! is mostly noise, that signal summation 134ι does not correspond to radial velocity assumption V and therefore selector 114 ignores signal summation 134
!. Signal summation 134
N as illustrated in Figure 1 D, includes mostly noise and therefore selector 114 ignores signal summation 134
N in like manner. Signal summation 134
2 on the other hand, includes a summed sample 138 (Figure 1 B) whose value (i.e., summed sample value) represented by a peak 140 - Figure 1 D (i.e., a summed pulse event), is substantially greater than that of the other summed samples of signal summation 134 , and also greater than the threshold value T
SH. Processor 116 compares the value of each of the summed samples (not shown) of signal summation 134
2 with the threshold value T
SH, and determines that the value of summed sample 138 is greater than the threshold value T
SH, and that the value of all other summed samples is less than the threshold value T
SH- Therefore, selector 114 selects signal summation 134
2 as a signal which represents an echo, selector 114 associates signal summation 134
2 with radial velocity assumption V
2, and determines that the average radial velocity V
A of object 124 during the interval that the four echoes 126C were processed, is V
2. Selector 114 selects signal summation 134
2 also when the value of peak 140 is substantially equal to threshold value T
SH- When sampler 106 samples a fifth (i.e., new) reflected pulse (not shown), sampler 106 stores this new sampled signal in sampled signal memory 108. Each of processors 112
1 ; 112
2 and 112
N determines a new radial velocity assumption for the average radial velocity V
A of object 124. Each of processors 112
!, 112
2 and 112
N subtracts sampled signal 130
! (i.e., the least recent sampled signal) from shift-sum memories 120
!, 120
2 and 120
N) respectively, and adds the most recent sampled signal (i.e., the
new or the fifth sampled signal) to shift-sum memories 120
!, 120
2 and 120
N, respectively. Processors 112 , 112
2 and 112
N shift shift-sum memories 120
!, 120
2 and 120
N, respectively, by rounded shifts Hy, H
2, H
N, respectively, before adding the new sampled signal to shift-sum memories 120
!, 120
2 and 120
N, respectively. In this manner each of processors 112
!, 112
2 and 112
N produces a new and a different signal summation (not shown), and sends this new signal summation to selector 114. Selector 114 compares the value of each of the summed samples of each of the new signal summations with the threshold value T
SH, selects the signal summation which exhibits a peak. Furthermore, selector 114 determines the average radial velocity V
A of object 124 according to the radial velocity assumption which corresponds to this selected signal summation. System 100 repeats the same cycle, when receiver 104 detects a further new reflected pulse. To keep the summation efficiency at a substantially high level, it is necessary that, H
MAX « N
S (10) where H
MAχ is the maximum accurate shift. H
MAχ after N
P echoes in units of samples is expressed by, H
MAX = 2N
PV
MAXR
S/CR
P (1 1 ) In case more than one of signal summations 134
!, 134
2 and 134N exhibits a peak, selector 114 selects all those signal summations which exhibit a peak, to determine the average radial velocity V
A of object 124. It is noted that since more peak values are available, processor 116 is able to determine the average radial velocity V
A of object 124 more accurately. Furthermore, radial velocity assumptions V V
2 and V
N are updated according to the peak of each of signal summations 134
!, 134
2 and 134
N, in order to narrow down the range of V
Mm and V
MAX, and increase the accuracy of the average radial velocity V
A which selector 114 determines. If system 100 detects that the value of one or more of the
summed samples of either signal summations 134
!, 134
2 or 134
N is saturated (i.e., it has reached the maximum value or is substantially close to the maximum value), system 100 lowers the value of N
P. The sensitivity of system 100 increases as the threshold value T
SH is increased. If the threshold value T
SH is set too low, processor 116 saves the location of a summed sample of a signal summation whose value is greater than the threshold value T
SH and processor 116 saves this location in threshold memory 118. Processor 116 checks whether the next signal summation respective of the same radial velocity assumption, includes a peak at approximately the location of the summed sample of the previous signal summation. If the outcome is negative, then processor 116 ignores the signal summation. If the outcome is positive, then processor 116 detects a peak at this location and selects this signal summation for determining the average radial velocity V
A of object 124, for further determining the range of object 124. If the threshold value T
SH is set too high, then the probability of detecting signal summations with peaks, at small number of integration cycles, is lower, and thus more time is required in order to determine the average radial velocity V
A of object 124. System 100 sets the threshold value 7
~ SH according to the expected enhanced SNR of echoes 126C (i.e., the SNR of the signal summation which is larger than the original SNR by a factor of
and according to the expected value of the enhanced signal (e.g., the value of peak 140 in Figure 1 D), in addition to other considerations which may be introduced by the designer or the operating user. System 100 is unaware of the exact time that echo 126C is supposed to reach receiver 104. Sampler 106 samples a detected signal across a period of time T T
2, which represents a range S S
2 of distances from system 100 in which object 124 is expected to be located, wherein
The resolution of system 100 is of the order of the sampling rate. Hence, it is imperative that the difference between the rounded shifts of every two consecutive processors be equal to or less than two samples. This difference is herein below referred to as "relative shift". Otherwise, system 100 would be unable to detect all echoes 126C which include information respective of the average radial velocity and the average range of object 124, and neither one of radial velocity assumptions V V
2 and V
N will be close enough to the average radial velocity V
A of object 124. The lower the number of processors 112
!, 112 and 112
N, the greater the difference between radial velocity assumptions V V
2 and V
N. Since the number of processors 112
!, 112
2 and 112
N is limited, if the difference between V
MAX and V
Mm is substantially large, the value of one or more of the relative shifts can exceed two samples. In this case, the radial velocity assumptions V V
2and V
N are off by a substantially large amount from the true average radial velocity V
A of object 124 (i.e., the respective rounded shifts are unsuitable for the true average radial velocity ^), the amplitude of the peak in the respective signal summation is substantially low (i.e., the summation efficiency is substantially low), and the signal respective of the reflected pulse is spread around the putative peak. Furthermore, the SNR of the signal summation is too low for system 100 to arrive at a radial velocity sufficiently close to the true average radial velocity V
A. In case the value of one or more of the relative shifts is equal to or greater than two samples, the system produces one or more filtered signal summations, and the selector determines the average radial velocity V
A of object 124, according to these filtered signal summations. Following is a description of a method for producing a filtered signal summation. With reference to Figures 1 B and 1 E, sampled signal 130
! includes a plurality of samples 132
!, 132
2> 132
3) 132
4, 132
5, 132
6, 132
7, 132
8, 132
9, 132ιo, 132n and 132
12. Modified sampled signal 142 includes a plurality of samples 144 , 44
2, 144
3 and 144
4. Processor 112ι produces
modified sampled signal 142, by adding together N
υ (herein below referred to as "aggregation number") samples located symmetrically about every sample of sampled signal 130
!, where Nu = 3,5,7...2n+1 , where n = 1 ,2,3... In the example set forth in Figure 1 E, Nu = 3. Hence, processor 112
! produces sample 144
1 ; by adding sample 132 to the left of sample
1322 and sample 1323 to the right of sample 1322 to sample 1322. Processor 112! produces sample 1442 by adding together samples 1322,
132
3 and 132
4. Processor 112
! produces sample 144
3 by adding together samples 132
3, 132
4 and 132
5. Processor 112
! produces sample 144
4 by adding together samples 132
4, 132
5 and 132
6. Processor 112
! determines the value of the aggregation number N
υ according to the value of rounded shift H
R, such that N
υ is preferably the smallest odd integer which is still greater than H
R. For example, if H
R = 4, then N
υ = 5. However, N
υ can be determined according to other criteria not described here. Processor 112
! shifts shift-sum memory 120
! by the value of rounded shift H
R, produces another modified sampled signal (not shown) according to sampled signal 130
2, and adds the new modified sampled signal to shift-sum memory 120
!. Processor 112
! repeats this cycle N
P times for other sampled signals, thereby adding N
P modified sampled signals (in this case four modified sampled signals), while shifting shift-sum memory 120
! by the value of rounded shift H
R, before each addition. Thereafter, processor 112ι subtracts the least recent modified sampled signal from shift-sum memory 120
!, before adding a new modified sampled signal to shift-sum memory 120
!. As long as the value of the relative shift is equal to or greater than two samples, processor 112
! repeats this cycle, thereby producing a filtered signal summation (not shown). In a like manner, processors 112
2 and 112
N produce different filtered signal summations each, and send these filtered signal summations to selector 114. Alternatively, only those processors for which the value of the relative shift is equal to or greater
than two samples, produce filtered signal summations, while other processors produce signal summations. By employing filtered signal summations, the summation efficiency of system 100 increases. More particularly, the SNR of a filtered signal summation is greater than that of the respective signal summation, by a factor of /N . Alternatively, system 100 can produce a filtered signal summation (not shown) according to each of signal summations 134
1 ; 134
2 and 134
Ν. System 100 produces this filtered signal summation, by adding together Nu surrounding samples located symmetrically about every central summed sample of each of signal summations 134
1 ; 134
2 and 134
N. When the value of one of the radial velocity assumptions Vy, V
2 or V
N is off by a substantially large amount from the true average radial velocity V
A of object 124, the signals in the respective sampled pulse mix with noise and the SNR of the signal summation in fact drops. To mitigate this problem, it is necessary for system 100 to produce the filtered signal summation, by employing a relatively small value for the aggregation number N
υ. Another remedy is for selector 114 to compare the threshold value 7
~ SH with the summed samples of both the signal summations (i.e., non-aggregated summed samples) and the summed samples of the filtered signal summations (i.e., aggregated summed samples). In case the value of one or more of the relative shifts is equal to or greater than two samples, system 100 modifies the values of radial velocity assumptions V V
2ox V
N, and hence, the values of rounded shifts Hy, H
2, H
N, respectively. This operation is possible, as long as it is performed before receiver 104 detects a new reflected pulse echo. As long as a sufficient number of incoming signals (i.e., N
P echoes 1260) are not added together, at a given radial velocity assumption which is closest to the true radial velocity of object 124, the
distance between system 100 and moving object 124 does not drop to a range which is useful (i.e., the useful range). It is imperative for sampler 106 to start sampling the required number of echoes 126C (i.e., N
P echoes) at the maximal range, in order for system 100 to start operating at the useful range, earlier. The difference ΔS
P between the maximal range and the useful range is expressed in units of length, by, M
P = N
PV
MAX/R
P (12) In case a system similar to system 100 is able to estimate the radial acceleration of the object at a time in the future, each processor can shift the sampled signals by different (e.g., dynamic) rounded shifts and not for example by a constant rounded shift Hy. The samples in each of sampled signal memory 108 and shift-sum memories 120
!, 120
2 and 120
N can be addressed by pointers. The pulse rate R
P of transmitter 102 should be low enough that an echo 126C reflected from object 124 at a maximal range, is detected by receiver 104 before transmitter 102 emits a new pulse 126A. If the pulse rate R
P is substantially high, then a system similar to system 100 can include a mechanism, such as a pulse shape controller, and the like, to reduce the uncertainty in determining the average radial velocity V
A and the average range S
A of object 124. It is noted that system 100 performs the procedures necessary to determine the average radial velocity V
A of object 124, including production of the filtered signal summations, modifying the values of rounded shifts, and the like, during the interval which receiver 104 detects two consecutive echoes 126C. Object 124 can move at a radial velocity relative to system 100 which is out of the range of radial velocity assumptions V l
2 and V
N. In this case, a shortening time ΔT is less than a sampling period T
s of sampler 106, where,
and thus, sampler 106 receives a new reflected pulse before sampler 106 has finished sampling the previous reflected pulse. Thus, it is imperative to set the sampling rate R
s according to the maximum radial velocity V
MAX (herein below referred to as "maximum detectable velocity value") of object 124 which system 100 is constructed to determine. In case object 124 is located at an average range S
A greater than the maximal range, pulses 126B do not reach object 124 and no reflected pulse reaches receiver 104. System 100 can determine the average range S
A of object 124 during the interval that the four reflected pulses are detected, according to peak 140. This can be performed by measuring a time T
R since transmitter 102 emits pulse 126A until peak 140 is detected, and by plugging in T
R in Equation 1. It is further noted that a system similar to system 100 can be employed for determining the average radial velocity of an object which is receding relative to the system. In this case, each processor similar to processor 112
! (Figure 10), shifts the sampled signals in the respective shift-sum memory, in the opposite direction. It is noted that system 100 can be a moving system and not a stationary one (e.g., coupled with a ground vehicle, marine vehicle, aircraft, rotorcraft, satellite, and the like). In this case the radial velocity assumptions V V
2 and V
N refer to a set of radial velocities of object 124 relative to the velocity of system 100. Reference is now made to Figure 2, which is a schematic illustration of a system for determining the radial velocity of a moving object, generally referenced 160, constructed and operative in accordance with a further embodiment of the disclosed technique. System 160 includes a receiver 162, a plurality of samplers 164
!, 164
2 and 164
N, a plurality of processors 166
1 ; 166
2 and 166
N and a selector 168. Processors 166
!, 166
2 and 166
N can be a multi-process array. Receiver 162 is coupled with samplers 164
!, 164
2 and 164
N. Samplers 164
!, 164
2 and
164
N are coupled with processors 166
!, 166
2 and 166
N, respectively. Processors 166
!, 166
2 and 166
N are coupled with selector 168. For each processor 166
!, 166
2 and 166N, the respective accurate shift is determined as an integer number of samples, of the respective sampler, associated therewith. It is noted that the sampling rates of samplers 164
!, 164
2 and 164
N may be updated dynamically, according to the radial acceleration or radial deceleration of the object. Accurate shift H
A1 in seconds is expressed by,
Likewise, accurate shifts H
A2 and H
AN can be expressed in seconds, by T
A2 and T
AN, respectively. Samplers 164
!, 164
2 and 164
N sample reflected pulses (not shown) at sampling rates of R
Sι, Rs
∑ and R
SN, respectively, and send the respective signals 17Oι, 170
2 and 170N to processors 166
!, 166
2 and 166
N, respectively. Sampling rates R
Sι, Rs
2 and R
SN correspond to sampling periods 7
Sy, T
S2 and 7
SΛ/, respectively. System 160 sets sampling rates of Rsι, Rs2 and R
SN, such that, T =τ
M (15) T =τ
A2 (16) and T T
SN ==Tτ
AN (17) Signal 170
! is associated with a sequence of sampled signals (not shown) each sampled at sampling periods of T
Sy. Therefore, it is no longer necessary for processor 166
! to shift the sequence of the sampled signals by a rounded shift, but it can directly apply the accurate shift H
A1. Similarly, processors 166
2 and 166
N apply accurate shifts H
A2 and H
AN \o the respective sequence of the sampled signals. Thus, system 160 can determine the average radial velocity V
A of a moving object (not shown), much more accurately than system 100 (Figure 1A). Reference is now made to Figure 3, which is a schematic illustration of a method for operating the system of Figure 1A, operative in
accordance with another embodiment of the disclosed technique. In procedure 190, a sequence of pulses is transmitted toward a moving object. With reference to Figure 1A, transmitter 102 transmits pulses 126A toward object 124. In procedure 192, for each transmitted pulse, a received signal which is reflected by the moving object and which is supposed to include an echo of the pulse, is detected. With reference to Figure 1A, receiver 104 detects a received signal which may include echoes 126C, if echoes 126C are the reflections of pulses 126A, by object 124. In procedure 194, each of the detected signals are sampled across a period of time. With reference to Figure 1B, sampler 106 samples echo signal 128 at a sampling rate of R
s, and produces sampled signals 130ι, 130
2, 130
3 and 130
4- In procedure 196, a plurality of radial velocity assumptions is determined for the moving object, wherein each radial velocity assumption represents a different relative radial velocity between a transceiver and the moving object. With reference to Figure 1A, processors 112
1 ; 112
2 and 112
N determine radial velocity assumptions V \ and V
N, respectively, for object 124, relative to the velocity of the transceiver. In procedure 198, for each radial velocity assumption, a respective time shift by which a subsequent pulse is assumed to be detected with respect to a previous pulse, is determined. With reference to Figures 1A and 1 C, processor 112
! determines that were object 124 approaching detector 104 at a radial velocity l y, receiver 104 would detect two consecutive echoes 126C, at an interval shorter by ΔT (i.e., a time shift) than if the object was stationary. Processor 112
! determines according to time shift ΔT, the value of rounded shift Hy by which to shift shift-sum memory 120
! sequentially, as described herein above in connection with Equations 7, 8 and 9.
In case more than one sampler, such as samplers 164
! (Figure 2), 164
2 and 164
N are employed in the system, each processor sets the sampling rate of the respective sampler according to the determined accurate shift. In the same manner, processors 112
2 and 112
N determine the values of rounded shifts H
2 and H
N, respectively. In case processor 112
! determines that the value of the relative shift (i.e., the difference between rounded shifts Hy and H
2 or between rib and H
N), is equal to or greater than two samples, processor 112
! produces modified sampled signal 142 (Figure 1 E), as described herein above. In procedure 200, for each radial velocity assumption, the sampled signals are shifted relative to each other, by the respective time shift. With reference to Figure 10, processor 112
! sequentially shifts shift-sum memory 120 by rounded shift Hy, as processor 112
! receives sampled signals 130
!, 130
2, 130
3 and 130
4 from sampler 106. In procedure 202, for each radial velocity assumption, the shifted sampled signals are added together, thereby producing a signal summation. With reference to Figures 1 B and 10, processor 112
! determines signal summation 134ι according to N
P sampled signals 130 , 130
2, 130
3 and 130
4, by sequentially shifting shift-sum memory 120
! by the value of rounded shift Hy, and adding the next one of N
P sampled signals 130
!, 130
2, 130
3 and 130
4 to shift-sum memory 120
!. Processors 112
2 and 112
N determine signal summations 134
2 and 134
N, respectively, in a similar manner. In procedure 204, a summed pulse event is detected within at least one of the signal summations. With reference to Figure 1 D, processor 116 detects peak 140 in signal summation 134
2. In case after procedure 194 processor 112
! determines a plurality of modified sampled signals similar to modified sampled signal 142 (Figure 1 E), in procedure 202 processor 112
! adds together these modified sampled signals after sequentially shifting shift-sum memory 120
!, thereby producing a filtered signal summation, and in procedure 204 processor 116 detects the peak
in the filtered signal summation. Alternatively, the filtered signal summation is produced by modifying the signal summation, similar to the way each of sampled signals 130
!, 130
2, 130
3 and 130
4 is modified. In procedure 206, the radial velocity of the moving object is determined according to radial velocity assumptions associated with signal summations, in which the summed pulse event was detected. With reference to Figure 1 D, processor 116 determines that the average radial velocity of object 124 is V
2, according to signal summation 134
2 in which peak 140 was detected. In procedure 208, the range of the moving object from the transceiver is determined, according to the detected summed pulse event. With reference to Figure 1 D, processor 116 determines the range of object 124 by measuring a time T
R since transmitter 102 fires pulse 126A until peak 140 is detected, and by plugging in T
R in Equation 1. It will be appreciated by persons skilled in the art that the disclosed technique is not limited to what has been particularly shown and described hereinabove. Rather the scope of the disclosed technique is defined only by the claims, which follow.