GB2185651A - Synthetic aperture radar - Google Patents

Abstract

In order to compensate for lateral motion of the antenna of an SAR which forms a synthetic aperture of N + 1 returns, for each range interval r the first N returns are used to estimate the phase of a map point tau rN/2 phi rN/2 and the estimated phase phi rN/2 used to correct the N + 1th return. The (N + 1)th corrected returns of a plurality of range intervals are then used to estimate the lateral motion phase error mu p which is used to compensate the (N + 1)th returns of all range intervals r for the error due to lateral motion. The compensated (N + 1)th returns are used in the next aperture where the previous steps are repeated for the (N + 2)th returns, and soon. The initial N returns may be compensated in the manner described in application 7936319. <IMAGE>

Description

SPECIFICATION Phase Estimation Technique of Synthetic Aperture Radar Phase Error Compensation The present invention relates to synthetic aperture radar (SAR).

In particular it relates to a phase estimation technique for compensating for phase errors due for example to motion of the antenna.

A synthetic aperture radar system comprises a coherent pulsed radar apparatus mounted on an aircraft to look transversely of the aircraft as it flies along a straight flight path. The system further includes a signal processor which focuses, using a correlation process, returns from a (nominal) point target received at a series of spaced apart positions called a "synthetic aperture" along the flight path. The effect of this is to produce a higher resolution than is achievable with a real aperture. A real scene effectively comprises a multiplicity of point targets and the SAR system scans the scene as the aircraft flies past to produce a map of the scene.

Ideally, the aircraft flies exactly along a straight path. However, in practice, the aircraft deviates from the path and can be controlled only to maintain it within a fixed range centred on the path.

The production of a high azimuth resolution SAR map requires that any lateral deviation from the straight path be measured to a high degree of accuracy. The lateral position of the phase centre of the radar antenna must be known to within a fraction of a wavelength over the time required to form the synthetic aperture.

It has been proposed to measure the lateral deviation using an inertial navigation system. However, the accuracy required approaches the limit feasible with present technology, and furthermore a suitable inertial navigation system is very expensive.

According to one aspect of the invention, there is provided a method of compensating for phase errors due to lateral deviation of the antenna of a synthetic aperture radar system from its nominal path of movement or equivalent phase errors, comprising the steps of: A) for each of a plurality of range intervals, Al) using the first N-n returns, where N is an even integer and n is an integer greater than or equal to zero, associated with that range interval, of N+ 1 returns forming one synthetic aperture, which N-n returns are compensated for said errors, to estimate the phase of the map point associated with that range and aperture, and A2) correcting the phase of the (N+i)th return of that aperture and range, (which return is not compensated for the said errors) by the phase estimated in step 1);; B) B1) summing the corrected (N+1)th returns over all, or at least selected ones, of the plurality of range intervals, and estimating the said phase error due to lateral deviation from the sum, B2) using the estimated phase error to compensate the (N+1)th returns of all the plurality of range intervals for the said error, and B3) using the compensated (N+l)th returns in the next synthetic aperture; and C) repeating steps A and B for the next aperture.

According to another aspect of the invention, there is provided a synthetic aperture radar processor comprising an iriput arrangement for receiving signals representing radar returns produced by a coherent pulsed side-looking radar apparatus, and signal processing means arranged to operate according to said one aspect.

According to a further aspect, there is provided a synthetic aperture radar system comprising: a coherent pulsed side locking radar apparatus; and a synthetic aperture radar processor according to said another aspect.

For a better understanding of the invention and to show how the same may be carried into effect, reference will now be made, by way of example, to the accompanying drawings, in which: Figure 1 is a schematic block diagram of an SAR system, Figure 2 illustrates the geometrical arrangement of an SAR system, and Figure 3 is a schmetic flow diagram illustrating the operation of an SAR signal processor in accordance with the invention.

Referring to Figure 1 an SAR system comprises a known coherent pulse radar apparatus 1 mounted on an aircraft. The antenna of the system is mounted to irradiate, and receive returns from, a region to one side and below the flight path of the aircraft.

The returns received are fed to a SAR signal processor to produce a map of the region. The processor of the present invention operates in the manner described hereinafter to compensate for errors due to lateral deviation of the aircraft from its flight path.

Referring to Figure 2 the SAR is mounted on the aircraft which flies along a nominally straight flight path 21. The radar emits pulses, and receives returns at each of a series of N+1 spaced sampling positions numbered 0 to N and one of which is indicated byp; the synthetic aperture comprises this series of positions. The returns are reflections from resolution cells of a scene 22, below and to one side of the aircraft, comprising range cells rnumbered 1 to M perpendicular to the path 1, and N+1 azimuth cells d parallel to the path 1, (N being an even number), corresponding in position to the sampling positions p.

For the purposes of explaining the invention the following assumptions are made:- 1) The radar antenna has a "square" beam illuminating N+1 scatterers which are equally spaced in azimuth.

2) The synthetic aperture length is identical to the illuminated length and comprises N+1 equispaced radar returns.

3) The final azimuth resolution cell size is the space occupied by one scatterer.

4) The depression angle from the aircraft to the scene does not vary appreciably with range and all ranges considered are within the depth of focus of one SAR correlator.

These assumptions do not result in any loss of generality and deviations from them in practice can be accommodated.

Considering only the range r, the pth radar pulse receives returns from all the azimuth cells, d, at that range, at ground positions p-n i.e. at positions N N P - -,..., O,...p + -, 2 2 where there are (N+1) returns (N even) over the synthetic aperture length.

Thepth return, at range can be written as

where #r@(p-n) is the phase of a scatterer at position (p-n) and at range when viewed from position n=o (i.e. perpendicular to the centre of the aperture) and p is zero, #n/N is the amount by which the phase of that scatterer differs from r, (p-n) when viewed from position n in the aperture centred on n=O, and llp is the phase error due to deviation of the aircraft laterally from the path 1.

To form the final map image of a single cell (r, each return 5rp of a set of (N+1) returns is compensated for quadratic phase (nn2/N) and the returns are summed. For instance, taking the set (Srp, p=O,... N), each term after quadratic phase compensation is given by

where

is the phase compensation factor.

Thus,

=Z(r, p)+#(r, N/2) expj[#r, N/2+ p] (2a) If the cross-track motion has been fully compensated, so that up=0 over all p, the summation of all the N+1 terms 5'r,p in the aperture will give the final map image of the resolution cell #(r, N/2).

The first term in equation 3 is the coherent sum representing the amplitude ar, N/2 and phase #r, N/2 of the required map point The second term is the noisy background ("clutter") due to the sidelobe responses of the N scatterers to each side of that cell in the synthetic aperture.

It can be seen that if [(N+1)#r, N2)] is sufficiently greater than N # Z(r,p) p=o then a good estimate of #r, N/2 will be obtained.

For the system according to the invention it is assumed that across-track motion for N of the (N+1) radar returns has been accurately compensated, so that p=0 for p=0,...(N-1), and it is required to estimate 11N, the phase error due to deviation of the aircraft from the flight path associated with the Nth return in the aperture.

The first step is to estimate #r, N/2, where #r, N/2 is the phase associated with the resolution cell at ranger and ground position p-n=(N/2) using the first N out of (N+1) returns in the synthetic aperture, in a similar manner to equation 3. The values of #r, N/2 obtained at each range rare then used to phase shift their respective phase compensated radar returns 5,r, N associated with range rand the last return N in the aperture. The second step is to determine the across-track motion ,UN for the returns S'r,N (equation 2). This can be estimated by summing, over all ranges (r=1,... M), the phase shifted terms S'r,N.

The range sum required is

If the first term is sufficiently large compared with the second, a good estimate of ,I1N should be obtained.

It can be seen that the #r1(N/2-n); n=1,2... could also be estimated, using only (N-n) out of (N+1) returns in the synthetic aperture and if these estimates are still accurate, the across-track motion N could be estimated by coherently adding the terms in Q (N2-n) over all range There may be some correlation between the background noise components of these estimates but this should be mainly eliminated by the effects of the different phases in each set of coherent additions.

Number of Samples Required It is apparent from the foregoing that two estimates of phase must be made during the processing. The first is the estimate of the phase p)r, N/2 from the resolution cell ar, N/2 derived from the SAR map, and the second is the estimate of the phase error 'iN due to lateral motion of the aircraft from the flight path.

Estimation of SAR Map-Cell Phase r, N!2 Defining the desired response as "signal" and the background noise, due to sidelobe responses from other scatterers, as "clutter", a signal-to-clutter ratio can be derived from the SAR map.

The peak signal voltage will have an amplitude Na, for coherent addition of N returns of amplitude a.

The mean sidelobe power level for one scatterer will be ya2, where y is the mean sidelobe power for a unity scatterer ISLR~&gamma;/N. The final clutter level is due to contributions from N sidelobes with random phase and so the final signal-to-clutter power ratio will be S (Na)2 ~= = (5) C Ny(a2) y(H2) The sidelobe power level y can be varied by adjusting the correlator amplitude weighting. For a uniform amplitude weighting y-1, but typically it may be of the order of -1 Od B.

It can be seen that unlessUZ a2, the signal-to-clutter ratio will be large (e.g. for N = 100, y= - 10 dB, 02I=1, S/C=30 dB).

Estimation of Phase Error N due to Lateral Motion Lateral motion is estimated from radar returns which include a scatterer of known phase in each range interval.

It is assumed that averaging is undertaken over M range intervals, with each return consisting of one scatterer of known phase , estimated from the SAR map, and N scatterers of random phase.

After averaging, the mean signal power level will be aM2(H)2, whilst the clutter level will be a MN ( Z).

Thus M(#) S/C=-- N(#) and to obtain a desired signal-to-clutter ratio, the number of range samples M required can be derived accordingly.

The solution for M given above assumes that there is negligible error in estimating the phase zp of individual scatterers. As the phase error increases the mean signal power level will be < M25)2. The accuracy of estimates is determined by the value of S/C given by equation 5. In a sparse map with areas of low reflectivity, the scatterer magnitude a2 will often be much less than the mean level 2. A full appreciation of this can only be gained with a detailed knowledge of the spatial amplitude distribution of the scatterers. A guide to performance may be obtained by assuming that the presence of a scatterer in a resolution cell will ensure a good estimate of its phase 4), whilst the absence of any scatterer would produce a completely spurious estimate due to adjacent sidelobes.If the fraction of scatterers in the map giving an accurate phase is k, but no account of this is taken in processing the range samples, then the number of range intervals M required to give a desired value of S/C is N(#) S M=-- # - K(#) C If it were possible to estimate which of the scatterers were producing a poor estimate of phase, then only the kM range intervals with good phase estimates need be used. In this case the total number of range intervals required (including those rejected) is N# S M=-- # - .

k# C Results comparable to this might be achieved by weighting each of the range returns according to the estimated S/C ratio found when estimating the scatterer phase 4). This estimate of S/C ratio may be difficult to obtain reliably if the scatterers are not uniformly distributed or when there are azimuth or range sidelobes from very large adjacent scatterers present.

Figure 3 is a schematic flow diagram illustrating the operation of one channel, associated with one range of an SAR signal processor. The processor comprises a plurality of such channels associated with respective ranges, or groups of ranges.

The shown channel comprises an input 200 for receiving signals representing the amplitude and phase of successive radar returns Sr, p associated with one range rand azimuth cells p-n (see equation 1 above).

It is assumed th tthe first synthetic aperture of N +1 returnsO to N, are produced in such a way that the lateral deviation from the flight path 1 is accurately known for all the first N of those returns and that they are compensated before being applied to the system shown in Figure 1. The manner in which this may be done is described in our co-pending application, of even date, 7936319 entitled "Doppler Technique of SAR Motion Compensation".

The N+1 (of which the first N are corrected) quadrature phase components land 0 of the returns of the first aperture are applied via a buffer stage 201 to a further store stage having N storage sections 0 to N-l for storing the first N (corrected) pairs of quadrature phase components; the (N+1)th (uncorrected) pair (numbered N) are stored in the buffer store stage 201.

The pairs of components in the stores stage 202 are applied to an SAR correlator stage 203 where they are correlated with a reference function.

to form the sum N 2 S r,P.

p=O indicated by equation 3 above, indicating the phase and amplitude of a single resolution cell 0r,W2 The phase component 4)r,Nt2 is then estimated as indicated by stage 204.

The (N+1)th return 5,,N is phase compensated to form S'rN, as indicated by stage 205, and isthen applied to a phase shifter stage where the phase 4)r,Nl2 iS applied to it to form the value S elm r,N/2 which is applied to a summing stage 207.

The stage 207 is common to all channels and receives all the uncorrected values SlrN.e-k r,N12 associated with all the ranges rand sums them to form SN as indicated by equation 4 above.

From this sum 5,,N' the value of phase error ,UN due to across-track motion is evaluated as indicated by stage 208 and applied to shift the phase of the value Sr,N stored in the buffer store stage 201 as indicated by stage 209 to compensate for the phase error .lln in it due to across track motion. The corrected value Sr,N expj[,UN] iS then fed back to the store 201 to replace the uncorrected value.

The entire N+1 corrected pairs of quadrature phase components are fed to a further correlator stage 210 where they are correlated with the reference function to produce the final map output.

As further returns are received (and further synthetic apertures formed), the shift register stage 202 is kept full of values corrected for across track motion, which values are successively received from the buffer store stage 201. These values are used in the manner described above to correct the successive new values stored in the buffer store.

In summary, the illustrative method of correcting for lateral-deviation of the aircraft from its flight path is as follows:- 1. Store returns from side looking radar over the required along-track length and from M range intervals.

2. At each range interval (i) take N-l successive radar returns for which across-track motion has been corrected. (i=n,. .

n+N-l).

(ii) form the synthetic aperture map point using the N-l returns, and (iii) estimate the phase of the map point given by 2(ii).

3. Take the next (n+N)th radar return, following the N-1 returns in 2(i), and after quadratic phase compensation adjust the phase by that given by 2(iii).

4. Sum the compensated and adjusted returns of 3 over all M range intervals and estimate the across-track motion error.

5. At all ranges correct (n+N)th radar return for across-track motion and compute synthetic aperture map point using N returns.

6. At each range interval (i) take N-i successive returns (i=n +1 n+N) and continue as 2(i), etc.

Presumming In a conventional SAR system the motion compensation, derived from accelerometers or other inertial sensors, is applied to the radar returns on a pulse by pulse basis, by phase shifting the coherent reference oscillator, prior to recording or processing the returns. It is normally arranged that the map processing will take place about zero or some other fixed baseband frequency. In this case, data reduction can often be achieved by presumming the returns to give the minimum bandwidth for the resolution desired.

In the system described here the motion compensation is applied during the map processing. It may still be desirable to use some presumming for data reduction but this would now be applied before motion errors are compensated. The effect of uncompensated phase errors will be to shift and broaden the spectrum of the returns. The bandwidth reduction which can be effected by presumming without any distortion of the final signal will be reduced. As a general guide it is reasonable to suppose that presumming can be undertaken provided the phase error does not vary appreciably over the samples being summed.

Beam Pointing Accuracy An important factor in the scheme discussed here is the beam pointing accuracy required for the real antenna. For the present system it is assumed that the map processing is finally uidertaken about zero Doppler. In general if only one look in azimuth is used, only a small sector of the main beam is used for forming the synthetic aperture. Small errors in beam pointing can then be tolerated since the returns required about zero Doppler are still contained in the main beam. For example to obtain 3m azimuth resolution a one-way beamwidth of about 0.3 is required. If the real aperture has a beamwidth of 1", a pointing error of about to.350 could be tolerated.

Once the pointing error exceeds the above limits the system could, in theory, compensate for the resulting phase error when the processing was running correctly. It might be preferable, however, to incorporate some beam steering based on the long term average Doppler return in the real beam to remove large drift angle errors.

Variations in yaw angle which occur over a time comparable to the aperture synthesis interval can be tolerated provided they are within the limits set above for small errors. If this high frequency yaw amplitude exceeds these limits some parts of the ground will never be properly illuminated by the radar and the error will not be recoverable by any signal processing. It may be possible to reduce any such yaw of the antenna by suitable mechanical damping.

Whilst the invention has been described in relation to compensation for lateral motion of the antenna from its desired course, the invention may be used to compensate for equivalent phase errors produced in the beam path length by atmospheric conditions when the antenna does not deviate from its course.

Claims (9)

1. A method of compensating for phase errors due to lateral deviation of the antenna of a synthetic aperture radar system from its nominal path of movement or equivalent phase errors, comprising the steps of: A) for each of a plurality of range intervals, Al) using the first N-n returns, where N is an even integer and n is an integer greater than or equal to zero, associated with that range interval, of N+1 returns forming one synthetic aperture, which N-n returns are compensated for said errors, to estimate the phase of the map point associated with that range and aperture, and A2) correcting the phase of the (N+1)th return of that aperture and range, (which return is not compensated for the said errors) by the phase estimated in step 1), B) Bi) summing the corrected (N+i )th returns over all, or at least selected ones, of the plurality of range intervals, and estimating the said phase error due to lateral deviation from the sum, B2) using the estimated phase error to compensate the (N +1 )th returns of all the plurality of range intervals for the said error, and B3) using the compensated (N+1 )th returns in the next synthetic aperture; and C) repeating steps A and B for the next aperture.

2. A method according to claim 1, wherein n is zero.

3. A synthetic aperture radar processor, comprising an input for receiving signals representing radar returns produced by a coherent pulsed side-looking radar apparatus, and signal processing means arranged to operate according to the method of claim 1 or 2.

4. A synthetic aperture radar system comprising a coherent pulsed side-looking radar apparatus, and a processor according to claim 3 arranged to receive at the said input the said signals from the radar apparatus.

5. A system according to claim 4 wherein the radar apparatus is in accordance with any one of the claims of copending application 7936319.

6. A system according to claim 4 or 5, or a processor according to claim 3, wherein the processing means comprises: for each range interval, means for storing the signals representing at least the first N-n returns of a synthetic aperture of N+1 returns, which N-n returns are compensated for said phase errors, means for storing a signal representing the (N+1) return, means arranged to derive from the said N-n returns a signal representing the phase of the map point associated with the said synthetic aperture, means for correcting the phase of the (N+ 1 )th return by the phase of the map point; means for summing the phase corrected (N + 1 )th returns overall, or at least, selected ones of the range intervals and for estimating from the sum the said phase error associated with the said aperture; ; and means for compensating the phase of the said (N+ 1 )th returns of the said range intervals with the said estimated phase error, and means for forming the mapping point for the said aperture from the said (N+1) phase compensated returns.

7. A method for compensating for phase errors in a synthetic aperture radar system, substantially as hereinbefore described.

8. A synthetic aperture radar processor substantially as hereinbefore described with reference to Figures 2 and 3 of the drawings.

9. A synthetic aperture radar system substantially as hereinbefore described with reference to Figures 1 to 3 of the drawings.