GB1571379A

GB1571379A - Measurement of closest approach

Info

Publication number: GB1571379A
Application number: GB3381075A
Authority: GB
Original assignee: Microwave and Electronic Systems Ltd
Current assignee: Microwave and Electronic Systems Ltd
Priority date: 1976-11-10
Filing date: 1976-11-10
Publication date: 1980-07-16

Description

(54) MEASUREMENT OF CLOSEST APPROACH (71) We, MICROWAVE AND ELEC TRONIC SYSTEMS LIMITED, a British Company of Lochend Industrial Estate, Newbridge, Midlothian, Scotland, do hereby declare the invention for which we pray that a patent may be granted to us, and the method by which it is to be performed, to be particularly described in and by the following statement: This invention relates to a radar system for measuring the closest distance of approach of two relatively moving objects. The invention has application in weapon trials where it is desirable to be able to measure the distance by which a missile or weapon misses a target at which the missile or weapon is aimed.

In firing a missile at a target, which will normally be moving as in the case of a surface-to-air missile, it has been found desirable to give the person launching the missile an indication of the distance by which the missile misses the target, assuming that a miss occurs.

It is difficult and expensive to track both missile and target sufficiently accurately from the ground to measure the distance of closest approach. It is preferable to obtain measurement data from the target but since the latter may be expendable it is desirable that the measuring apparatus in the target should be inexpensive.

The present invention is based on the concept of providing a device within the target to record a parameter that varies with varying range; signalling that parameter back to the ground; and processing the parameter data on the ground to obtain the miss distance.

The parameter chosen is not itself a direct measure of range. The target carries a Doppler radar and the parameter recorded is the Doppler shift frequency which is a function of the rate of change between missile and target and thus of the approach velocity of the two objects. As will be shown more fully below, a plot of the variation of the Doppler shift frequency as the missile moves past the target is uniquely related to the miss distance, i.e. the range at the point of closest approach. At this point the Dbppler shift instantaneously falls to zero.

Although the invention has been developed in connection with the problem of measuring the miss distance of a missile aimed at a target, it will be appreciated that the principles and teachings of the invention can find wider application in measuring the closest approach of two relatively moving objects. It is not necessary that both objects be moving nor is it necessary that the movement be in three dimensions as in the surface-to-air situation specifically discussed; for example the invention could be applied to the closest approach of two objects both on the ground - a two dimensional situation.

In cases where both objects are moving it is convenient to take one object as the frame of reference and merely consider the movement of the other in relation to it. This approach will be adopted throughout this specification, the "target" object being taken as the frame of reference - According to one aspect of the present invention there is provided a system for measuring the closest approach of two relatively moving objects comprising:: a Doppler radar apparatus carried by a first object and having means for angle modulating the radar carrier in accordance with the Doppler shift frequency signal derived by the radar apparatus from echoes received from a second object moving relatively to the first object; a receiver installation remote from said first object for receiving the angle-modulated radar carrier to recover the Doppler shift frequency information therefrom and provide a signal carrying such information; and a signal processing apparatus responsive to the last-mentioned signal to derive from the Doppler shift frequency information the value of the distance of closest approach of said first and second objects.

In another aspect of the invention there its provided apparatus for obtaining a value for the distance of closest approach of two objects from a Doppler shift frequency signal representing the relative velocity between the two objects, comprising: a frequency discriminator responsive to said Doppler shift frequency signal to generate a signal at the time of minimum Doppler shift; means responsive to said Doppler shift frequency signal to provide digital signals representing the durations of successive Doppler cycles;; data storage means for storing said digital signals, said data storage means being responsive to the generation of said minimum shift signal to accept thereafter digital signals to occupy only half of the storage capacity of the data storage means so as to store data relating to Doppler cycles extending over a period centred on the time of generation of said minimum shift signal; means responsive to said minimum shift signal to provide a signal indicating the time at which it occurred; and a computer coupled to said data storage device responsive to said time of minimum shift signal to compute from the stored Doppler data the distance of closest approach, said computer being operable to perform a curve-fitting technique to find a curve in accordance with equation (2a) given hereinafter that matches the stored data.

In a still further aspect of the invention there is provided a Doppler radar apparatus in which, in operation, the extracted Doppler shift frequency signal is caused to angle-modulate the radar carrier output of the apparatus.

In order that the invention may be better understood an embodiment of it for measuring the miss distance of a missile aimed at a target will now be described with reference to the accompanying drawings, in which: Figure 1 shows the geometry in three dimensions of a missile passing a target; Figure 2 is a graphical illustration showing typical curves of the variation of Doppler shift with time at miss distances M and different missile velocities V; Figure 3 shows graphically normalized versions of these curves; Figure 4 is a block diagram of a Doppler radar system carried by the target; Figure 5 is a block diagram of a second embodiment of a Doppler radar system carried by the target; Figure 6 is a block diagram of a ground receiver installation for use with the Doppler radar system of Figure 5; and Figure 7 is a more detailed block diagram of one form of signal processor shown in Figure 6.

Referring to Figure 1, a target and its direction of movement are indicated by the arrow T. A missile W is fired at the moving target.

The weapon has a heading H but its track relative to the target is indicated by the heavy line Tr. As indicated above the target is used as the frame of reference.

Thus the target is assumed to be stationary and a vector correction applied to the missile velocity relative to ground to obtain the track of the missile relative to the target. The picture is a three-dimensional one as indicated by the reference co-ordinates x, y and z. However, for the purposes of deriving the mathematical equations given below, we need only consider the two-dimensional situation in the plane containing the missile path Tr and the target T.

At any point along the track the instan- taneous range of the target is R. The missile has a velocity V along the track Tr. The approach velocity (Vr) of the missile and target is directed along R toward the target. At the point of P of closest approach the range has a minimum value M and the line PT is perpendicular to the track Tr. Thus at this point the velocity component Vr of the weapon toward the target reduces to zero. It can be seen from inspection that as the weapon moves along track Tr the velocity component Vr in the direction of the target will increase towards the value V with increasing distance (Vt) from the closest approach point P.If curves are drawn of the variation of Vr, or a parameter dependent on it, with time as the missile moves along track Tr it will be found that the curve has a shape dependent on the miss distance M as will be shown later.

Assume the target T is carrying a Doppler radar which is receiving echoes from the missile W. As is well known the echo will be shifted in frequency relative to the emitted signal by a Doppler shift frequency fd given by Vr fd=2-. fo = 2Vr/lt - (1) c where f0 and A are the radar transmission frequency and wavelength respective and c is the free space velocity of light. fd is thus a measure of Vr and will instantaneously reduce to zero at the point of closest approach P. By recording fd as the weapon moves along the track Tr, the time at which the weapon reaches the point P can be determined. The actual miss distance M at this point can then be determined by the shape of the curve of fd plotted against time t.

Each velocity V will have a unique set of curves of fd v. t for different miss distances M. Since the weapon velocity relative to the target along the track Vr is not known directly, if the miss distance is to be obtained the velocity dependence of the sets of curves must be removed i; subjected to a normalising process. How this is done will now be described with reference also to Figures 2 and 3.

Firstly it can be shown that the instantaneous Doppler frequency fd given in equation (1) can be expressed in terms of the geometry of Figure 1 by fd = 2V/A. [1+ (M/V.T)2] - (2) where time t is measured from the closest approach point P. The first part of this ex pression, 2V/A, is the maximum Doppler shift that can be achieved at the velocity V and is a value which fd approaches at relatively long range from the target where R t V.t M so that VroV. As practical guide, sufficient accuracy is achieved by taking fd to be its maximum fm when R > 3M.

Looking now at Figure 2 the two full line curves 21 and 22 show the variation of fd with time t in accordance with equation (2) for miss distance M = lm. and M = 5m. respectively and a missile velocity V of 400m/sec. The actual values of fd given are those obtained at an operating frequency of 1.5 GHz (7 = 200mm.).

It is noted that as the miss distance decreases the sharpness of the curve increases, i.e. a more sudden transition to fd = O at t = O. The two broken line curves 23 and 24 are plotted for the miss distances of 1 and 5m. respectively but for half the velocity, i.e. V = 200 m/sec..

The curves are shallower (lower values of fm) and the transition in time less sharp due to the lower velocity.

By manipulation of equation (2) the curves of Figure 2 can be subjected to a normalisation procedure and reproduced as shown in Figure 3 in which the ordinate now represents the ratio fd/fm and the abscissa represents a normalised time variable t.fm - The curves 21 and 23 of Figure 2 now become a single curve 31 in Figure 3 and likewise curves 22 and 24 become a single curve 32 demonstrating that for a given miss distance M a unique curve independent of velocity is obtained by the normalising procedure graphically illustrated in Figure 3.

Another way of appreciating the physical justification for the normalising procedure can be seen from Figure 1. Instead of considering the Doppler shift frequency, it can be seen that a Doppler cycle occurs each time that the range R between the missile and target changes by a half-wavelength, #/2. R is simply related to the distance d along the track from the point of closest approach P by R = M + d ....-.. (4) Thus for a succession of values of R at which a change of n 12/2 occurs, i.e. integral number of Doppler cycles n from point P, there will be a corresponding set of values of d uniquely related to the R values for a given value of M.

Therefore, Doppler cycles occur at distance increments along the track Tr which are independent of the missile velocity V.

More specifically the ranges Rn at which Doppler cycles are completed are given by Rn = M + n.A (5) 2 where n is the number of Doppler cycles from the miss point and from equation (4) the corresponding distances dn along the track Tr are given by dn = [(M + n -A/2)2 ~ M2 l 3i . . . - - - (6) Thus the period tn of the nth Doppler cycle is given by tn = (dn - dn- (7) The periods of successive Doppler cycles are, of course, obtainable from the Doppler shift frequency signal. There will be described later with reference to Figure 7 a signal processor which measures successive tn values and by use of a computer provides not only the value of M appropriate to the variation of tn with time but also derives the velocity V.

It should also be noted that differentiation with respect to time of both sides of equation (4) produces dR=Vr=d(M2 +d2Y. d(d) dt dt putting d(d)/dt = V, d = V.t and Vr = #fd/2 immediately reproduces equation (2).

Reverting to the normalisation procedure used to obtain Figure 3 the only parameter needed on the ground is the instantaneous value of fd, frn being one particular value of fd- No other measurements nor any calculations need be made in the target. All it need contain is a Doppler radar to derive fd and a means for telemetering fd back to a ground installation. In fact, all the procedures described herein require only the telemetering of fd back to the ground installation. Embodiments of the Doppler radar apparatus for so doing are shown in block diagram form in Figures 4 and 5.

Figure 4 shows a CW Doppler radar appar-2 atus. A transmitter 41 feeds an antenna 42 which irradiates the surrounding space; a receiving antenna 43 picks up Doppler-shifted echoes from nearby objects, e.g. the missile W (Figure 1) and delivers them to a mixer 44 which is also supplied with a small proportion of the transmitter energy via a coupler 45. A low frequency band-pass amplifier 46 extracts the Doppler frequency component fd. This much is conventional. Normally the Doppler frequency component would pass directly to signal processing equipment to extract the missile information required. In the present case it is telemetered back to the ground in a particularly convenient way by returning the Doppler shiftsignal fd back to the transmitter to angle modulate the transmitter. In this apparatus frequency modulation will be assumed.

To this end, the transmitter can comprise an oscillator 47 which is capable of delivering up to a few tens of milliwatts at a frequency, fO, in the microwave region, say 1.5 Go, and which is readily frequency modulated. The Doppler shift frequency signal is applied to a modulator device 48 which modulates oscillator 47. This superimposing of the Doppler signal upon the transmitter frequency for simultaneous telemetry as the Doppler signal is derived does not significantly affect the Doppler frequency fd extracted by amplifier 46.

As an example, of a device as shown in Figure 4, if f0 is 1.5 GHz and the maximum relative missile velocity is taken to be 1,200 m/sec. say, then the maximum Doppler shift fm is 12 kHz. Advantage is gained in signalto-noise ratio at the ground installation by having a high modulation index m for the frequency modulation of the oscillator 47 by the output of amplifier 46; but this has to be balanced against bandwidth limitations which have to be observed. A value for m of say 3 is suitable.

The device of Figure 4 is simple and inexpensive but may suffer two disadvantages.

Firstly since the Doppler-shifted echoes at fo + fd are but little removed from the outgoing transmitter frequency, fO, noise on the transmitter signal will appear as low frequency noise from the mixer 44 and fall within the passband of amplifier 46; Secondly, strong echo returns may be received from parts of the target which are obviously very close to the antennas and which are vibrating thereby producing Doppler-shifted signals so that spurious responses may result.

These disadvantages can be mitigated by the apparatus shown in Figure 5. This apparatus is of the FMCW type. In this embodiment, a transmitter 51 comprises a microwave oscillator which is continuously frequency modulated by a voltage controlled oscillator (VCO) 52 having a nominal frequency ft. The transmitter 51 energises a common transmit/receive antenna 53 via a circulator 54 which also couples the antenna to a first mixer 55 to pass the received Doppler-shifted echoes thereto. A coupler 56 supplies a proportion of the transmitter output to the mixer. (This single antenna plus circulator arrangement can also be used in the apparatus of Figure 4).

Unlike the Figure 4 apparatus, however, the mixer 55 is followed by a bandpass amplifier centred at the frequency ft of the VCO 52. As is known in FMCW radar the mixer output not only contains a direct low frequency component at the Doppler shift frequency fd but that also Doppler-shifted sidebands are obtained at frequencies p.ft, where p is an integer, ie. sidebands p-it + fd. The amplitudes of the sidebands associated with a given frequency p.ft is proportional to Jp(X) where X is a function which depends upon the range and modulation frequency ft, and Jp is 9 Bessel itinction of first kind and order p. The Doppler signals associated with any value of p may be extracted at the output of mixer 55. In the present apparatus the p = 1 signal is extracted.This technique is well known and a more detailed explanation of it is to be found in Skolnik: Introduction to Radar Systems, pp. 100-103.

The amplifier 57 is, therefore, centred at ft and extracts a pair of Doppler-shifted sidebands having amplitude proportional to J1 (X).

The use of the J1 component has various advantages. Firstly by choosing ft reasonably high, low frequency noise on the transmitter signal does not fall within the passband of the amplifier 57. This is even truer of higher order components. Secondly, like higher order components, the value of J1 in theory falls to zero at zero range. Thus responses from parts of the target close to the antenna are minimized. Thus the two disadvantages of the apparatus of Figure 4 are both mitigated. As compared to selecting higher order components the J, component rises more steeply in amplitude at short ranges making it preferable for the particular application of the invention measuring the miss distance of a missile.

In order to recover the Doppler shift frequency fd, the output of the amplifier 57 at ft ± fd is applied to a second mixer 58 to which is also fed some signal from VCO 52 at frequency ft. The resultant output component of the mixer 58 at fd is extracted by a low fre- quency, bandpass filter 59 which feeds an amplifier 60. The output of the amplifier 60 is returned to the VCO 52 as a modulation signal therefor via a gate 61. The gate is controlled by a threshold circuit 62 connected to the output of amplifier 60. The threshold circuit only opens gate 61 if sufficient signal is received from aplifier 60. Thus if the signalto-noise ratio becomes too ponr no fd information is transmitted to ground.

The value of fd obtained is the same as with the apparatus of Figure 1 and the filter 59 should have a high frequency cut-off at say 12 kHz for a maximum velocity of 1200 m/sec..

The lower frequency cut-off is chosen to remove clutter and is typically about 1 kHz. The operating frequency ft of the V.C.O. is conveniently 500 kHz, control being exercised by a variable capacitance diode. The Doppler shift signal in the range 1-12 kHz is arranged to produce a maximum deviation of the VCO frequency ft of say 40-50 kHz, i.e. a modulation index m in the region of 3 to 4. The modulation index between VCO 52 and the transmitter 51 is conveniently unity.

In the two embodiments of the Doppler radar and telemetry apparatus so far described, it will be apparent that the orientation of the missile to the target cannot be known. For this reason the antenna should have as omnidirectional a radiation pattern as possible. Such an antenna is thus of necessity of not more than unity gain. The echo signal strength is a function of the fourth power of range R and of the radar cross-section of the missile. In practice, a range of up to 50 m. on a missile with a radar cross-section of 0.1m2. is found to be achievable with a transmitter power of say 50mW.

Turning now to the ground installation this comprises a receiver for receiving the telemetry and for recovering the Doppler-shift frequency signal fd and a signal processor for deriving the miss distance from the variation in Doppler shift frequency with time.

Figure 6 shows such an installation in block diagram form, the receiver having design appropriate to demodulation of the telemetry encoded FMCW signals from the apparatus of Figure 5 and supplying the demodulated Doppler shift signals fd to a signal processor 90 described hereafter with reference to Figure 7.

In the receiver installation the signals are received by an antenna 71 which can be of a directional type, providing gain to give a better signal-to-noise ratio over the target to ground path. The antenna feeds an RF amplifier 72 having a bandwidth wide enough not only to cope with the spectrum of the encoded FMCW signal but also to allow for frequency drift in the transmitter. The signal from amplifier 72 goes to a mixer 73 which is fed with the output of a local oscillator 74 to produce an IF signal at any convenient frequency, say 30 MHz, which passes through an IF amplifier 75 and limiter 76 which have to meet the same bandwidth requirements as the RF stage.The limited signal is now applied to a first FM/AM converter or discriminator 77 operable at the intermediate frequency to recover the Dopplermodulated ft signal at 500 kHz in the specific example being described.

The Doppler-modulated ft signal passes through a bandpass filter 78 at the frequency ft, an amplifier 79 and onto a second FM/AM converter or discriminator 81 via limiter 80.

The converter 81 is operable at the ft frequency and from it the Doppler-shift frequency fd is recovered. The fd signal is filtered by a Doppler filter 82 having a passband of say 1-11 kHz for the particular application in mind. The Doppler shift frequency signal fd is now available for- subsequent processing in a processor 90 to obtain the miss distance information.

In each of the FM/AM converters 77 and 81, advantage can be taken of the properties of FM to improve the signal-to-noise ratio by a factor equal to 3m2(m + 1), where m is the appropriate modulation index abovementioned and equals the ratio of the maximum deviation to modulating frequency. If as in the FMCW radar of Figure 5 two superimposed frequency modulations are detected the improvement variesas9m?m22(m1 +1cm2 + 1), where m1 relates to the modulation of the transmitter frequency f0 by the VCO frequency ft and m2 relates to the modulation of ft by the Doppler shift frequency fd. In the specific figures given by way of example mt = 1 and my = 3.The gain in signal-to-noise ratio is about 28dB.

It will be appreciated that the recovery of the Doppler-shift signal from the simpler Doppler-modulated CW radar of Figure 4 is readily achievable with a simplification of the receiver of Figure 6 of omit stages 78 to 81. The first FM/AM converter 77 is followed directly by the Doppler filter 82 and an amplifier.

The processing of the Doppler frequency signal to derive the miss distance can be done in various ways. It would be possible to process the signals to display them in the form of the normalised curves shown in Figure 3, these curves being matched by the operator with curves representing standard miss distances to provide the best estimate of miss distance.

For quicker and more accurate indication of the miss-distance calculations can be made on the incoming data with the aid of a computer. Such calculations can be performed in different ways but it is presently preferred to use a method in which calculations are made to ascertain the miss distance which gives a best fit of the incoming data to a known curve. This curve-fitting method will now be described with reference to Figure 7.

Going back to equation (2), it can be rearranged in the form

Considering the relationship between 1 /t2 and 1/fd2, it is linear with a gradient 4V4 /M2 2 and an intercept at V2 /M2. The data from the ground receiver gives fd as a function of time (t), M can be calculated on the basis of the linear curve of the form given in equation (2a) that best fits the incoming data. However, in equation (2a), t is the time from the point of closest approach (P in Figure 1). Consequently in practice an initial estimate of to at the point P has to be made to give a time origin for calculations and the optimum straight line is determined from the available yalues of t and fd.

Additionally an error function is determined to give an estimate of how good a straight line fit is obtained. A revised value of to is then used to obtain another error estimate and the procedure repeated to find the to that was the minimum value of the error function. Having now settled to, this value is used in calculating the miss distance M and, if required, the velocity V.

The above calculations are performed with the aid of a computer. The production of the necessary programs is well within the scope of those in the computer art and will not be set out in detail here. Figure 7 shows in block diagram form how the data is handled and stored in order to enable the computer to perform the necessary calculations with it. The signal processor 90 receives the Doppler signal fd from the ground receiver and this signal is supplied to a frequency discriminator 91 and to a period encoder 92 which responds to the zero crossing of the cycles of the Doppler shift signal fd and with the aid of a clock source 93 encodes the duration of successive Doppler cycles into digital form. The digitised successive Doppler cycle periods are passed via an interface unit 94 into a data storage device 95.

The frequency discriminator 91 provides a voltage output corresponding to the curves of Figure 2 witch a voltage minimum at the time when fd drops to zero at the point of closest approach P. A detector unit 96 receives this voltage. detects the minimum and with the aid of the clock pulses provides a first estimate of to to a computer 97. The latter has access through the interface unit 94 to the Doppler cycle duration data in storage device 95 and with this information performs the best fit calculations described above by which the best straight line curve fitting the incoming data is deduced and the miss distance M obtained. The final calculated value of miss-distance M is then displayed on any suitable display unit 98.

In order to provide the computer 97 with the most relevant data on the Doppler cycles and to to minimise the storage capacity required in device 95, the detector unit 96 also serves an additional purpose of controlling the total period covered by the digitised cycles stored in the storage device 95 so as to select those most pertinent to the calculation of M. This period is centred on to. Under the control of the computer. the cycle duration data is continuously shifted through the storage device 95 until the minimum of the output voltage of the frequency discriminator 91 is detected by unit 96. The computer then only allows further data to be stored beyond the minimum (to) point to equal to half the storage capacity of device 95.Further data entry is then prevented so that device 95 stores data encompassing equal times on either side of the point which is the most relevant data for the calculations to be performed.

The curve-fitting technique has two particular advantages; firstly that it is not essential to have a continuous set of data - as long as the gap is noted so that time information is correct.

Gaps in data are ignored and a best fit is made to the good information. The second advantage is that the curve-fitting averages over all the data available and therefore is not particularly sensitive to local distortions due to crosssection effects, etc.

WHAT WE CLAIM IS: 1. A system for measuring the closest approach of two relatively moving objects comprising: a Doppler radar apparatus carried by a first object and having means for angle-modulating the radar carrier in accordance with the Doppler shift frequency signal derived by the radar apparatus from echoes received from a second object moving relatively to the first object; a receiver installation remote from said first object for receiving the angle-modulated radar carrier to recover the Doppler shift frequency information therefrom and provide a signal carrying such information; and a signal processing apparatus responsive to the last-mentioned signal to derive from the Doppler shift frequency information the value of the distance of closest approach of said first and second objects.

2. A system according to claim 1 in which said Doppler radar apparatus is of the FMCW type having a radio frequency oscillator determining the nominal carrier frequency of the apparatus and a voltage controlled oscillator arranged to frequency modulate said ratio frequency oscillator, and wherein said modulating means is arranged to apply said Doppler shift frequency signal to modulate said voltage controlled oscillator.

3. A system according to claim 2 in which said receiver installation is operable to recover the Doppler shift frequency signal from a side band component of the received carrier offset from the nominal carrier frequency by a frequency p.ft, where p is an integer (not including zero and preferably "one") and ft is the nominal frequency of the voltage controlled oscillator.

4. A system according to any preceding claim in which said signal processing apparatus includes means for providing data signals representing the duration of successive Doppler cycles, means for storing said data signals, and a computer operable to compute from the stored data signals the value of the distance of closest approach.

5. A system according to claim 4 in which said computer is operable to derive a curve in accordance with equation (2a) given hereinbefore which matches the stored Doppler cycle data and to derive the value of the distance (M) of closest approach from the derived curve.

6. A system according to claim 5 in which said signal processing apparatus includes means for deriving from the Doppler shift data a signal representing the estimated time of the minimum Doppler shift and for supplying the estimated time signal to said computer for use thereby in deriving said matching curve.

7. A system according to claim 6 in which said data storing means is operable to shift data representing the duration of successive Doppler cycles therethrough, and said estimated time signal deriving means is operable to supply a signal to said data storage means at the time of minimum Doppler shift, said data storage means being responsive to this last-mentioned signal to accept thereafter data on further Doppler cycles occupying

**WARNING** end of DESC field may overlap start of CLMS **.

Claims

**WARNING** start of CLMS field may overlap end of DESC **. signal processor 90 receives the Doppler signal fd from the ground receiver and this signal is supplied to a frequency discriminator 91 and to a period encoder 92 which responds to the zero crossing of the cycles of the Doppler shift signal fd and with the aid of a clock source 93 encodes the duration of successive Doppler cycles into digital form. The digitised successive Doppler cycle periods are passed via an interface unit 94 into a data storage device 95. The frequency discriminator 91 provides a voltage output corresponding to the curves of Figure 2 witch a voltage minimum at the time when fd drops to zero at the point of closest approach P. A detector unit 96 receives this voltage. detects the minimum and with the aid of the clock pulses provides a first estimate of to to a computer 97. The latter has access through the interface unit 94 to the Doppler cycle duration data in storage device 95 and with this information performs the best fit calculations described above by which the best straight line curve fitting the incoming data is deduced and the miss distance M obtained. The final calculated value of miss-distance M is then displayed on any suitable display unit 98. In order to provide the computer 97 with the most relevant data on the Doppler cycles and to to minimise the storage capacity required in device 95, the detector unit 96 also serves an additional purpose of controlling the total period covered by the digitised cycles stored in the storage device 95 so as to select those most pertinent to the calculation of M. This period is centred on to. Under the control of the computer. the cycle duration data is continuously shifted through the storage device 95 until the minimum of the output voltage of the frequency discriminator 91 is detected by unit 96. The computer then only allows further data to be stored beyond the minimum (to) point to equal to half the storage capacity of device 95.Further data entry is then prevented so that device 95 stores data encompassing equal times on either side of the point which is the most relevant data for the calculations to be performed. The curve-fitting technique has two particular advantages; firstly that it is not essential to have a continuous set of data - as long as the gap is noted so that time information is correct. Gaps in data are ignored and a best fit is made to the good information. The second advantage is that the curve-fitting averages over all the data available and therefore is not particularly sensitive to local distortions due to crosssection effects, etc. WHAT WE CLAIM IS:

1. A system for measuring the closest approach of two relatively moving objects comprising: a Doppler radar apparatus carried by a first object and having means for angle-modulating the radar carrier in accordance with the Doppler shift frequency signal derived by the radar apparatus from echoes received from a second object moving relatively to the first object; a receiver installation remote from said first object for receiving the angle-modulated radar carrier to recover the Doppler shift frequency information therefrom and provide a signal carrying such information; and a signal processing apparatus responsive to the last-mentioned signal to derive from the Doppler shift frequency information the value of the distance of closest approach of said first and second objects.

half the available data storage space such that the eventual stored data relates to a period substantially centred on the time of minimum Doppler shift.

8. Apparatus for obtaining a value for the distance of closest approach of two objects from a Doppler shift frequency signal representing the relative velocity between the two objects, comprising: a frequency discriminator responsive to said Doppler shift frequency signal to generate a signal at the time of minimum Doppler shift; means responsive to said Doppler shift frequency signal to provide digital signals representing the durations of successive Doppler cycles; data storage means for storing said digital signals, said data storage means being responsive to the generation of said minimum shift signal to accept thereafter digital signals to occupy only half of the storage capacity of the data storage means so as to store data relating to Doppler cycles extending over a period centred on the time of generation of said minimum shift signal;; means responsive to said minimum shift signal to provide a signal indicating the time at which it occurred; and a computer coupled to said data storage device responsive to said time of minimum shift signal to compute from the stored Doppler data the distance of closest approach, said computer being operable to perform a curve-fitting technique to find a curve in accordance with equation (2a) given hereinbefore that matches the stored data.

9. A doppler radar apparatus in which, in operation, the extracted Doppler shift frequency signal is caused to angle-modulate the radar carrier output of the apparatus.

10. A Doppler radar apparatus according to claim 9 which is of the FMCW type having a radio frequency oscillator determining the nominal carrier frequency, and a voltage controlled oscillator arranged to frequency modulate said radio frequency oscillator, and further including means whereby said Doppler shift frequency signal is applied to said voltage controlled oscillator to modulate same.

11. A system for measuring the distance of closest approach of two relatively moving objects substantially as hereinbefore described with reference to Figs. 1, 2, 3, 4, 5 and 7 or Figs. 1,2,3, 5,6 and 7 of the accompanying drawings.

12. Apparatus for obtaining a value for the distance of closest approach of two objects from a Doppler shift frequency signal representing the relative velocity between the two objects substantially as hereinbefore described with reference to Fig. 7 of the accompanying drawings.

13. A Doppler radar apparatus substantially as hereinbefore described with reference to Fig.

4 or 5 of the accompanying drawings.