GB2148651A

GB2148651A - Doppler speed measurement

Info

Publication number: GB2148651A
Application number: GB08423308A
Authority: GB
Inventors: Malcolm Geoffrey Cross
Original assignee: General Electric Company PLC
Current assignee: General Electric Company PLC
Priority date: 1983-09-14
Filing date: 1984-09-14
Publication date: 1985-05-30
Also published as: GB8423308D0; GB2148651B

Abstract

In a doppler radar velocity measurement device the received signal is divided into two channels. In the first channel there is a dispersive delay i.e. one which delay delays higher frequencies more slope- than lower frequencies whose characteristics are such, for a nominal aircraft velocity, the frequency versus time characteristics of the received signal are inverted (i.e. the frequency versus time graph of Fig. 1 becomes the graph gamma ). The other channel has a matching delay 3 which is non-dispersive. By comparing the signal envelope and hence (due to Gaussian filter 1) the signal frequency in the two channels over a period of time, a measure is obtained of the difference between the actual velocity and the assumed nominal velocity, since this is related to the value of the rate of change of Doppler Shift with time. A digital implementation is also described. <IMAGE>

Description

SPECIFICATION Velocity measurement apparatus This invention relates to a velocity measurement apparatus in which a beam of energy is transmitted and received after reflection from a surface relative to which the apparatus is moving, and in which a doppler frequency shift experienced by the energy on reflection is used to give an indication of velocity. The invention arose in connection with an airborne radar system for ground mapping purposes operating in the microwave region of the electromagnetic spectrum. The invention is however, applicable to other fields, for example to acoustic systems such as sonar.

When, as is sually the case, a beam of energy transmitted from say an airborne radar system diverges before being reflected from the ground or other surface it illuminates a finite area of that surface. It follows that different Doppler shifts are experienced by different parts of the beam. Determination of the velocity of the radar system is not therefore a simple matter of measuring a single well defined Doppler shift. The velocity measurement is further complicated by the fact that different parts of the illuminated area may have different reflectivities. For this reason it is not possible to assume that the strongest frequency component is derived from the centre of the beam.

This invention provides velocity measurement apparatus comprising a dispersive delay and comparator means for comparing portions of the received signal which have and have not passed through the said dispersive delay to give an indication of velocity.

The invention also provides a method of measuring the velocity of a body relative to a background, in which: a beam of energy is transmitted from the body and received after reflection from the background; the received signal is passed through two channels at least one of which contains a dispersive delay such as to reverse the sign of the slope of the frequency versus time characteristics of a notional signal in one but not the other channel, the said notional signal being derived from a single point of the background; and the outputs from the two channels are compared to provide an indication of velocity.

Fig. 1 shows at X the relationship between Doppler frequency shift fd and t for that component of a received signal which is derived from a point of the ground surface at the centre of the beam (i.e. on boresight) at a time t = 0.

The invention is based on a theory that, if the received signal as shown at X are passed through a dispersive delay device, i.e. a device which delays different frequencies by different amounts, the slope of the illustrated line X will be changed from its initial value S and certain characteristics of the signal will accordingly be changed by an amount which depends not just on the properties of the dispersive delay device but also on the original slope S. That this theory is correct can be appreciated if one considers the particular situation where the slope of the frequency v time characteristics of the dispersive delay is equal to - 25. In this situation the effect of the dispersive delay is to invert the component of the signal shown at X to the form as shown at Y on Fig. 1.The other components of the signal, derived from other parts of the illuminated area of ground surface, will also be inverted and, since the inversion is exact, it can readily be appreciated that some characteristics of the received signal (e.g. the area beneath portions of the lines X and Y occupying similar time periods) will be the same before and after passing through the dispersive delay. Any differences between such characteristics can be used as a measure of the difference between half the slope of the dispersive delay and the signal slope. Since the slope of the dispersive delay is known the signal slope and therefore the velocity can be calculated.

Various different comparison techniques can be used. The preferred technique is to compare the integral of amplitude over a period of time. Alternatively it would be possible to compare the integrals of other amplitude dependent functions (e.g. received energy) over a period of time.

Another possibility would be to compare, e.g. using a correlator, the shapes of curves representing the variation with time of a function such as amplitude or energy of the two portions of the received signal. Yet another possibility would be to compare (again using a correlator) the spectra of the two portions of the received signal after performing a frequency analysis.

The result of the comparison can either be used as the required measurement in itself or, more preferably, can be used as a feedback signal which is used to control the characteristics of the dispersive delay or delays in a way such as to minimise the output of the comparator. In the latter case the principal velocity measurement is obtained by observing the current setting of the characteristics of the or each dispersive delay; though the output of the comparator means can be looked upon as giving an indication of velocity since over a period of time that output determines the setting of the dispersive delay.

Whilst the invention is considered to have particular application to situations where the transmitted energy is reflected from a surface e.g. the earth's surface it is also applicable to situations in which the reflections occur from other background material for example stationary clutter or particles in a turbid medium.

Two ways in which the invention may be performed will now be described with reference to Figs. 2 to 5 of the accompanying drawings in which; Figure 2 shows a velocity measuring apparatus constructed in accordance with the invention; Figure 3 is a diagram for assistance in understanding the operation of the apparatus of Fig. 2.

Figure 4 shows an alternative to the components 1, 2 and 3 of Fig. 2; and Figure 5 is a diagram for assistance in understanding Fig. 4.

Electromagnetic radiation at a particular frequence f, is transmitted from an aircraft (not shown) and received after reflection from an area of ground surface. The received signal is thus subjected to a range of Doppler shifts. It is then mixed with a local signal of frequency (f1-f0) and the real part of the output of the mixer, whose frequency components represent Doppler shifts from different parts of the illuminated area of the ground surface, is passed through a Gaussian bandpass filter 1 centred on the frequency f0 (Fig. 2). The component of the output from the filter 1 derived from a single point on the ground surface in line with the boresight of the radar antenna is shown in Fig. 3 at A'. The line A represents the expected characteristics based on a nominal aircraft velocity.

One portion of the output from the filter 1 is passed through a dispersive delay 2 having characteristics shown by the line D of Fig. 3 whose slope is the negative value of twice the slope of the line A. The effect of this dispersive delay on the signal represented by the line A is to delay and invert it as shown at B. The effect on the line A', representing a component of the actual signal received from a particular point on the ground surface, is shown at B'.

Another portion of the output from the filter 1 is passed through a matching delay 3 whose delay is equal to that of the dispersive delay 2 at the centre of the passband of filter 1. The effect of this delay 3 is to produce an output having a component for a single point on the illuminated surface, which is represented by the line A'D on Fig. 3 as compared with the line AD appropriate to the nominal velocity of the aircraft.

From a consideration of Fig. 3 it is apparent that the displacement of line A', dependent upon the actual velocity, from the nominal line A results in the signal from the dispersive delay 2 being slightly compressed in time and the signal from the delay 2 being slightly expanded in time. Whilst Fig. 3 relates only to the component of the received signal received from one particular point, similar considerations apply to all other points of the illuminated area of the ground surface. Thus the relationships between amplitude and time for the outputs of the delay circuits 2 and 3 (after passing through detectors 4 and 5) are shown schematically on Fig. 2 by the curves alongside the outputs of circuits 4 and 5 which assume a single point target. The areas under these curves are derived by low pass filters 6 and 7 which act as integrators.

The outputs from integrators 6 and 7 are subtracted and added at 8 and 9 respectively and the result of subtraction is then divided at 10 by the result of addition. The output of the divider 10 is a measure of the difference in slope between lines A and A' which is in turn a measure of the difference between the actual velocity and the nominal velocity. A mathematical proof of this is:- Let the nominal sweep rate be K0 and the actual sweep rate be K where K=Ko(1 +) (1) For a target centred on time t = 0, the instantaneous frequency is given by f=f0+Kt (2) The phase is therefore: Kt2 (t) = 2%(fit +2 ) (3) 2 and the input waveform is represented by: Kt2 Ao exp (j2n (fot + )} (4) 2 where Ao is assumed constant.

Now denoting "=" to represent Fourier transformation, if g(t)=F(f) (5) then g(t-to) = exp {-j2xfto} . F(f) (6) xt2 and exp #- #=#ss.exp {-xssf2} (7) p where ss is complex with its real part#0.

Using (5), (6), (7) with (4), the spectrum of the input sweep is given by: A0/#K exp {-j x/K (f-f0)} (8) (any constant phase terms are omitted).

The Gaussian filter frequency response is assumed to be: exp { - b2(f-fo)2} (9) and the spectrum of the signal at its output is given by: A0/#K exp { - (b + jx/K) (f - f0)} (10) The dispersive line is assumed to have a flat amplitude response, but delay (X) given by: T = - 2/K0 (f - f0) + Tc (11) where Tc is a constant, which is non-zero for an analogue realisation of the netowrk.

1 d@ Since T = - # (12) 2x df the dispersive line spectral response is given by: exp [ j2x { f2/K - (2 F0/K + Tc)f}] (13) 0 The spectrum at the dispersive line output is the product of (10) and (13), and is: A0 exp {(-b + j#α)(f-f0)}. exp{-j 2##Cf} (14) #K where α = 2/K - 1/K (15) Ko K Using (5), (6) and (8), the waveform at the bandpass filter output is:

where

Using (14), the waveform of the dispersive network output is:

where

Waveform (16) is delayed by Tc and its envelope is obtained to give:

and the envelope in the dispersive channel is:

Low-pass filters in each channel then follow, and these are assumed to be of narrow bandwidths compared to the signal bandwidths (20) and (21), such that the integration of (20) and (21) is a good representation of the low-pass filter relative amplitudes over most of their output waveforms.

Thus (20) gives an output

Likewise (21) gives low-pass filter output

and the divider output is given by:

From (17) and (19), assuming e 1 in (1),

There are three cases, depending upon the relative values of K0 and b.

X Case 1 b2 -. In this case V = 0 for all sweep rates.

K0 X Case 2b2=-.

K0 Here ## - #/4 and the divider output thus gives a measure of e, the error sweep rate.

X Case 3 b2 -.

Ko # Here ##- 2 and again there is a measure of error sweep rate, but with twice the sensitivity.

The actual values proposed are as in case (2) with K0 = 292 Hz/sec and b = 0. 104. This gives a bandpass filter with - 3 dB bandwidth of 11.3 Hz. The centre frequency can be taken as 100 Hz. The low-pass filter bandwidths are assumed in the region of 0.5 Hz, which is onetenth of the bandwidth of their inputs.

Whilst an analogue system has been described an equivalent digital version will sometimes be preferred in which case K0 will be made zero and the full information in the received signal will be preserved by use of in-phase and phase quadrature channels as is well known. In such an arrangement the filter 1 could be incorporated as part of circuits 2 and 3 and the value of Tc will become zero.

The method as described has limited dynamic range (i.e. the range of values of # which outputs are proportional to X, the sweep rate error, is not large). The dynamic range can be greatly improved by feedback, in which the output (V) is used to control the bandwidths of the bandpass and low-pass filters, and to control the nominal delay slope (- 2) K0 of the dispersive delay circuit such control being a simple task when digital circuitry is used. If such feedback is employed a large range of aircraft forward velocities can be measured (feedback aims always keeping V = 0).

The particular example described above uses a dispersive network of slope K0 to measure the frequency sweep rate (positive slope) of an input signal. The dispersive hardware appears in one channel of a two-channel comparison method.

The sensitivity of measurement can be improved at the expense of dynamic range (i.e. the range of sweep rate values which can be measured) by splitting the dispersive network into two unequal portions as shown on Fig. 4 whose components 1, 2 and 3 of Fig. 2 are replaced by components IA, 2A and 3A.

This method applies with advantage to the case in which the Gaussian filter is relatively wide, and where the total dispersion hardware amount is large (case 3 where b2 ir in the mathematical analysis).

K0 A dispersive slope of -1 K0 would exactly match the nominal slope of the signal (+ 1 ), (see Fig. 5) K0 and the two delays are chosen to be on either side of this slope value, at slopes -(1 -m)and -(1 + m), K0 K0 where m < 1. (Note that m = 1 yields the original case of the Fig. 2 version). A bandwidth widening factor F is defined as

and is the increased Gaussian filter bandwidth (for F > 1) beyond case 2 of the patent. F < 1 and F > 1 correspond to cases 1 and 3 of the patent.

In Figs. 4 and 5, nominal and actual signal input sweeps are exactly as in Fig. 3 except that their bandwidths have been widened, as mentioned above. The dispersive delay slopes x and y are shown on Fig. 5, and the dispersive network outputs B and C. If these outputs were exactly horizontal, the signal and dispersive slopes would be matched-but instead, small differences above and below matching exist.

The nominal signal sweep would give identical amplitudes for comparison, but a signal sweep with a small error gives one output closer to the matched case than the other. This gives rise to a measure of the sweep rate, as in the Fig. 2 embodiment.

It can be shown theoretically that there is an optimum measurement sensitivity when m takes the value m= 1 F2 and that for this value the divider output V"" - F2e 4 which shows that sensitivity is increased by F2 over the case 2 (F = 1). A further advantage is that the peak amplitudes of the signals at B and C are increased by a factor F, which gives an improvement in signal/noise performance. To benefit from this, signal/noise threshold detectors must be placed before the low-pass "ingegrating" filter, since there is no amplitude increase at their outputs.

A disadvantage is that the dynamic range of slope measurement is reduced by a factor 1/F2, but this may not be important if feedback is used to maintain signal sweeps close to the matched condition previously mentioned.

A more positive disadvantage is that an increase in hardware complexity occurs as F increases.

Claims

1. Velocity measurement apparatus comprising a dispersive delay and comparator means for comparing portions of the received signal which have and have not passed through the said dispersive delay to give an indication of velocity.

2. Velocity measurement apparatus according to claim 1 in which the comparator means is designed to compare the integral of an amplitude dependent function over a period of time for the portions of the received signal which have and have not passed through the dispersive delay.

3. Velocity measurement apparatus according to claim 1 or 2 including a second dispersive delay whose slope, i.e., rate of change of delay with respect to frequency, is different from the slope of the first mentioned dispersive delay and in which the comparator means is arranged to compare two portions of the received signal which have passed through the first and second dispersive delays respectively.

4. Velocity measurement apparatus according to any preceding claim including a feedback loop arranged so that an output of the comparator means adjusts the slope of the delay versus frequency characteristics of the or each dispersive delay thereby tending to minimise the comparator output.

5. Velocity measurement apparatus according to any preceding claim for measuring the velocity of a body relative to a background, the apparatus including means for transmitting a beam of energy from the body to the background and means for deriving the said received signal from reflections of the transmitted energy off the said background.

6. A method of measuring the velocity of a body relative to a background, in which: a beam of energy is transmitted from the body and received after reflection from the background; the received signal is passed through two channels at least one of which contains a dispersive delay such as to reverse the sign of the slope of the frequency versus time characteristics of a notional signal in one but not the other channel, the said notional signal being derived from a single point of the background; and the outputs from the two channels are compared to provide an indication of velocity.

7. A method according to claim 6 in which an output from the comparator means is fed back to the or each dispersive delay to control the characteristics thereof in such a way as to minimise the said output.

8. A method of measuring the velocity of a body substantially described with reference to the accompanying drawings.