GB2292032A

GB2292032A - Radar ranging system

Info

Publication number: GB2292032A
Application number: GB8220470A
Authority: GB
Inventors: Eric Arthur North Whitehead
Original assignee: Marconi Avionics Ltd
Current assignee: Allard Way Holdings Ltd
Priority date: 1981-07-31
Filing date: 1982-07-21
Publication date: 1996-02-07
Anticipated expiration: 2002-07-21
Also published as: FR2725526A1; GB8123408D0; GB8220470D0; SE8204526L; SE8204526D0; GB2292032B

Abstract

In an airbourne ground-ranging monopulse radar system the sum (S), azimuth difference (A) and elevation difference (E) signals derived from a plurality of statistically-independent radar returns are analysed to obtain an estimate of the orientation of an iso-probability-density surface defining (with respect to corresponding coordinate axes) S, A and E amplitude combinations of a particular probability density. The orientation of this iso-probability surface indicates the target elevation off boresight, and is independent of any across-track ground slope. In a practical embodiment (fig. 8) the two difference signals are first split into separate in-phase and quadrature components A', A", E', E" relative to the sum signal S. Variances and co-variances of these four components and S are then derived (10 - 15), and an appropriate function thereof computed (16 - 22). <IMAGE>

Description

Radar Ranging System This invention relates to a radar system for air-to-surface ranging employing a monopulse beam-split arrangement. A basic such arrangement is illustrated in elevation in Figure 1 and in plan view in Figure 2.

Figure l(a) shows the split-beam characteristics of an antenna having two elevation elements. The beamsplit direction, i.e. the line of symmetry between the beams, is the only direction from which ground returns to the two elements can produce signals of equal magnitude and phase. The individual responses of the two elements are shown in Figures l(b) and l(c). It can be seen that as the transmitted pulse strikes the surface progressively, the magnitude of the returns increases and decreases as the'point of reflection moves through the axis of the element, i.e. the most sensitive direction of the element.

Since the axes of the two elements are displaced in elevation the peaks of the responses will occur from position (or at times) P and 4. When the transmitted pulse is incident at point R, which lies on the boresight of the antenna, the two elements receive equal signals of the same phase. Coherent subtraction of the two signals therefore produces a signal of envelope waveform shown in Figure l(d). A determination of the timing of the crossover point N in relation to the time of transmission of the radar pulse will therefore give a measure of the distance of the point R from the aircraft, the point R being clearly defined by the boresight of the antenna.

The above explanation sssumes an infinitesimally narrow pulse and an infinitesimally narrow beam in azimuth.

In practice, the finite pulse length and beamwidth imply that integration of the ground returns takes place and this integration is over ground which, ignoring large discrete targets, is uncorrelated. Consequently a noise like characteristic is superimposed on the characteristic shown in figure 1 which introduces an uncertainty in the crossover range. This effect is referred to as residual clutter and is one of the primary sources of range uncertainty in a ground ranging radar.

Figure 2(a) shows a plan view of the ground surface throughout its illumination by the incident pulse and it can be seen that the monopulse null arises from a line on the ground across the track of the aircraft.

When the antenna is rotated about its roll axis relative to the ground, or when the ground is sloping across the track of the aircraft, the effect is to twist the line L of null response, as shown in Figure 2(b).

The line is still strsight but is no longer orthogonal to the beam pointing direction. This results in the slope of the characteristic of Figure l(d) being reduced. The system is, therefore, more sensitive to residual clutter, and the range error increases. In addition, the monopulse null on the ground is distributed in range, which provides a further degradation of ranging accuracy. The depression angle of the antenna boresight is typically quite small and even for small roll angles the effect just described can increase the ranging error very significantly, e.g.

from about 30 m to 200 m.

One method of reducing these errors is described in UK Patent Application No. 8209539, in which a two axis sum-and-difference monopulse system is employed, having four beams disposed on the corners of a square. The signals from the four beams are linearly combined to provide a signal having the elevation characteristics described above, and a second difference signal having the same characteristics in azimuth. The sum of the signals from all of the four beams provides the signal normally referred to as the sum signal. A further linear combination, not usually used and sometimes referred to as the nonsense signal, is then used to give an indication of the roll alignment, and the elevation and azimuth signals are combined in proportions which are related to this indication to reduce by a substantial amount the ill effects of the misalignment in roll.

It is the object of the present invention to provide a ground ranging radar system which takes account of across-track ground slope.

According to the present invention, in an airborne monopulse radar system for air-to-surface ranging, in tich target return signals are added and subtracted to provide: a sum signal; an azimuth difference signal; and an elevation difference signal; said sum and difference signals being dependent upon target position off boresight, there is included computing means adapted to determine from target return signal samples having a degree of statistical independence the orientation of an isoprobability surface defining, with respect to corresponding coordinate axes, sum, azimuth and elevation difference signal amplitude combinations of a particular probability, and thereby provide an elevation/ range indication or response independent of the acrosstrack ground slope.

The system preferably includes means adapted to provide statistically independent quadrature components of each of the sum, azimuth difference and elevation difference signals from the single return pulse, the two sets of quadrature components providing said statistically independent target return signal samples.

The computing means may employ the ratio of the co-variance of the azimuth and elevation difference amplitudes to the variance of the sum signal, the azimuth difference signal or the elevation difference signal.

One embodiment of a radar system for air-tosurface ranging in accordance with the invention will now be described, by way of example, with reference to the accompanying drawings, of which: Figure 1 shows an elevation beam-split pattern and resulting individual and difference signals; Figure 2 shows a plan view of such a beam-split pattern intercepting the ground in different ground-slope circumstances; Figure 3 is a two-dimensional diagram illustrating, on coordinate axes, a probability contour of sum and elevation difference amplitude, Figure 3(a) representing a signal return on the boresight and Figure 3(b) off boresight; Figures 4,5,6 and 7 illustrate similar constant probability contours but in three dimensions and at various dispositions of the radar axes and target positions off boresight;; and Figure 8 is a block diagram of a radar system incorporating statistical computational processes in accordance with the invention.

Figures 1 and 2 have already been described as illustrating conventional beam-split arrangements and the difficulties associated with them.

Figure 3(a) illustrates the distribution of various sum and (elevation) difference amplitude combinations of a particular probability value, each such combination comprising the sum and difference amplitudes of a particular signal element received. Thus each point on the graph corresponds to one received signal element.

The ellipse shown is merely one of a family of similar contours all centred on the origin. They may be seen as probability contours ranging from a maximum value on the origin to a (zero) minimum value at large values of S & E. The contours thus form a ridge-like hill surface having a peak on the origin, indicating that the most probable values of S & E are zero.

Figure 3(a) is appropriate to a situation in which the azimuth axis of the radar is accurately aligned with the local ground 'horizontal' and the signals are coming from rsnges which straddle the boresight. In this case S & E are uncorrelated, that is, a known sum signal amplitude for a particular signal element gives no information as to the other component of the combination, the elevation signal amplitude.

In Figure 3(a) the major and minor axes of the ellipse are aligned with the predetermined S and E axes.

However, if the range from which the signals are reflected is such that the signals arrive from above (or below) the azimuth axis, then E will be correlated with S, that is, knowledge of a value of S will give information as to the most probable value of E (and vice-versa). The isoprobability density ellipses will thus be inclined to the axes as shown in Figure 3(b), but it will be found that the eccentricity of the ellipses is not greatly altered.

It may be noted that conventional signal processing for ground ranging makes an estimate of the tangent of the angle of inclination of the ellipse for successive range elements, and when this angle is estimated to be zero, the indicated range is taken to be that of the range of the ground on the boresight. If, however, the azimuth axis of the radar is not accurately aligned with the ground plane, then the eccentricity of the ellipse is much reduced, and the accuracy with which the radar estimates the inclination is likewise reduced.

In the above two-dimensional representation of sum and elevation difference amplitudes the third dimension was used to indicate the probability, as in the ridge-like hill analogy above. However, if the third dimen sion is required for the azimuth difference signal component the probability value can only be represented by the sample density. The three signal components form a triplet whose amplitudes in any sample may be plotted as a point in a three dimensional graph, where the A axis has been added to the other two to form the orthogonal cartesian axes (A, E, S), along which are measured the corresponding signal amplitudes. Surfaces of equal probability-density now replace the previous two-dimensional curves, and the surfaces for such a mutually normal probability triplet are well known to be ellipsoids.If the signals are reflected from ranges on or near the boresight, and lying along the azimuth axis of the radar, then these signals will be uncorrelated one to another and it follows that the three axes of the iso-probability ellipsoids will be coincident with the A, E and S signal axes as depicted in Figure 4 where a single such surface is shown. By consideration of the disposition of the ground from which the signals are being reflected with respect to the radar axes, it will be appreciated that the principal epsoid axis coincident with the sum signal axis will be the greatest of the three, that axis coincident with the azimuth axis will be the next greatest, and that coincident with the elevation axis much the smallest. The ellipsoids will thus be like elongated discs.An analysis of one idealised radar beam gave the ratios of the principal axes to be approximately 20 : 10 : 1, sum : azimuth : elevation.

If the range resolution cell on the ground from which the signals come is parallel to, but above the azimuth axis of the radar, then the azimuth signal is again uncorrelated with either the sum or the elevation signal, but these last two are somewhat mutually correlated, and it follows that the intermediate axis of the ellipsoid is again coincident with the azimuth axis, about which the ellipsoid is tilted so that the major axis of the ellipsoid now leans towards the elevation axis as depicted in Figure 5.

If, on the other hand, the range resolution cell is centred on the boresight, but the radar is rolled about the boresight, then there will be correlation between the elevation and azimuth signals, but no correlation between the sum signal and either of the other two. It follows that the major axis will remain coincident with the sum signal axis, but the ellipsoid will be rotated about this axis as depicted in Figure 6. It is important to note that the smallest principal axis is still perpendicular to the sum axis in these circumstances.

If both the above deviations from symmetry are imposed at the same time, then the disposition of the ellipsoid will be a combination of the two last considered, as depicted in Figure 7.

Analysis has shown that although the isoprobability ellipse changes its disposition, the ratios of the principal axes do not alter greatly, and therefore since the smallest axis is considerably smaller than the other two, a statistical sample of the signals can be used to define its disposition relative to the signal axes with considerable accuracy. Any plane surface adjusted to minimise the square of the distances of the samples to the plane will, with a considerable degree of confidence, be approximately perpendicular to the smallest principal axis. Moreover, the angle between this axis and the sum axis will change in a smooth fashion from being greater than a right angle (when the range cell lies below the boresight) to being exactly a right angle (when the range cell is on the boresight) to being less than a right angle (when the range cell lies above the boresight).

The cosine of this angle, or some other convenient function of it, can therefore be used as an indicator to determine the range cell which lies on the boresight and therefore the range of the ground on the boresight.

It is well established by the theory of sampling of co-normal random variates that, given a number of statistically independent samples of the associated variables, all the information which can be deduced about the underlying statistics is contained in the simple sums and the sum of the squares of each individual variate, and the sum of the products of associated variates taken two at a time. When divided by the number of samples taken, these form the sample means, variances and co-variances respectively. In the present case we know that the underlying statistics have zero means, so the sample means add no information. Two points are required to define a plane known to pass through the origin, and hence at least two independent samples are required to establish the disposition of the normal to the plane.

In the description so far it has been assumed that each return pulse from a particular range cell provides only a single sample in each channel. However, it will now be shown that each pulse can in fact provide statistically independent samples.

The narrow band microwave signals received in the four beams reflected from the ground and falling within any given range gate may be represented by: A Cos (#t-γA), B Cos (#t-γB), C Cos (#t-γC) and D Cos (t-yD) where A, B, C, D are the four amplitudes, w is the angular velocity of the phase of the signals, and γA, γB, γC, YD are the phases of the signals. The azimuth difference, elevation difference and sum channel signals are then formed by linear combinations of these signals, and denoting them by DA, DE, S respectively, we may put ( ) DA = A Cos (#t-γA) + B Cos (#t-γB) ( ) ( ) C Cos (#t-γC) + D Cos (#t-γD) ( ) DE = A Cos (#t-γA) + D Cos (#t-γD) ( ) B Cos (#t-γB) + C Cos (#t-γC) ( ) S s A Cos (#t-γA) + B Cos (#t-γB) + C COS (#t-γC) + D Cos (wt-yD) By the application of elementary trigonometric manipulation, these may be rewritten:: ( ) DA = (AcosγA + BcosγB) - (CcosγC + DcosγD)) Cos#t ( ) + ( (AsinγA + BsinγB) - (Csinγc + DsinγD) ) Sin#t ( ) DE = (AcosγA + DcosγD) - (BcosγB + CcosγC) Cos#t ( ) + (AsinγB + Dsinγc) - (BsinγB + CcosγC) ) Sin#t ( ) S =( AcosγA + BcosγB = CcosγC + DcosγD) Cos#t ( ) ( ) + AsinγA + BsinγB + CsinγC + DsinγD Sin#t ( ) The coefficients of Cosut may be designated to be t-he amplitudes of the in-phase components of the signals, and those of Sinot the quadrature components.

If the ground is of uniform roughness, then the signals received by reflection will be random in character, and as the angle of incidence of the radar beam on the ground changes during flight, or as reflections from a different patch of ground fall into the given range gate, or if the frequency of the transmitter is changed, then the amplitudes of the in-phase and quadrature components will each behave as a random variable following the type of statistics known as 'Normal'.

Moreover, it may be demonstrated that the amplitudes of the in-phase and quadrature components of any one of the signals are uncorrelated, but for any given range gate will have the same expectation of mean power. The actual statistics may, due to the nature of the ground or the objects on it, not exhibit accurately the statistics of a normal random variable, but for a wide range of circumstances such statistics form a good approximate description which will be adopted for the purpose of the present explanation. Such a reflecting surface is sometimes referred to as a 'Lambertian reflector'.

If the aerial system and receiver have been carefully designed and manufactured, then signals due to a single point reflector will have substantially the same phase in each of the three signal channels, or if this is not so it will be possible to insert phase shifters in two of the three signal channels to make it so, and then the property will hold, more or less, for any reflector within the major portion of the beams and over the bandwidth of frequencies for which the system has been designed. It can be demonstrated by theory that 8 consequence of this phase equality is that the in-phase and'quadrature components of the signals arising from the ground returns form two separate and independent (uncorrelated) sets of signals, and the statistical relationship between the signals in each of the three channels can be described by reference to the in-phase components only.Any rules stated in relation to the inphase components will then apply to the statistical relationship between the quadrature components also.

It may be seen therefore1 that because of the statistical independence of the quadrature sets of signal components, each pulse of target returns will provide the minimum two samples necessary to determine the orientation of the ellipsoid and of its minor axis, i.e.

the smallest principal axis.

The greater the number of samples employed to determine the orientation of the ellipsoid, the more accurate the determination.

Further samples can be obtained within any range-gate from subsequent pulses, and the samples can be made statistically independent by frequency agility.

Alternatively they may become statistically independent by the motion of the aircraft changing the angle of incidence with the ground, or, if the aircraft is travelling substantially parallel to the ground so that the range to the point at which the bore sight meets the ground is not changing rapidly, it may be satisfactory to take successive samples from different patches of ground as the aircraft flies along it.

To proceed with the derivation of a range indication which accommodates ground slope, it is convenient here to adopt the widely used convention of representing the amplitudes of the in-phase and quadrature components of signals by the real and imaginary parts of complex numbers, and we will use the complex quantities A, E and S to represent these attributes of the azimuth, elevation and sum signals used to differentiate between successive samples, then the required sample statistics are the six quantities:

The asterisk is being used to denote the complex conjugate of the quantities, and the usual conventions are being followed to indicate the modulus or the real or imaginary parts. N denotes the number of pulses from which the samples are obtained.

Instead of the unweighted averages which have been represented above, there will be occasions when weighted averages are more appropriate, either because the quantities are being derived by analogue means, in which case weighted averages cannot be avoided, or because a continuous smoothing of the range measures is required. The weighting factors should then be substantially the same for all six quantities, and if the weighting factors are denoted by Wn we have:

The amplitude of the return pulses is affected by many unknown physical circumstances and they are not a reliable source of information taken singly, so it is always ratios of the above quantities or functions of the ratios which are used for the present purpose. It will be appreciated that it follows that the divisions implied in the above formulae do not have to be performed.

It is the essence of the system presently described that means are provided for extracting and using either explicitly or implicitly one or more of the three ratios which can be formed from the statistics listed above, involving rAE.

Conventional statistical theory and solid geometry show that the best estimate of the cosine of the angle between the smallest principal axis of the probability ellipsoid and the sum axis is obtained by choosing the least of the three solutions to the cubic equation in,

A AE #E2-# rSE = O rSA rSE Where A is the square of the length of the axes of the ellipsoid.

The following ratio may then be formed: (#A2-#)rSE-rAErSA ( ) [(#A2-#)(#S2-#)-rSA2]2+[(#S2-#)rAE-rSArSE]2+[(#A2-#)rSE-rAErSA]2 ( ) In the case of the least of the three solutions for , i.e. where airs the square of the length of the smallest axis of the ellipsoid, this is usually small compared with 2 and #S2, , so that little or no accuracy is lost by causing A to be zero in the above ratio.In this case the cubic equation need not be solved, and the following ratio gives the required result:

Further analysis reveals that in many circumstances the second two squared terms in the denominator are small compared with the first, and if this is so they may be ignored in which case the required ratio becomes approximately: 2 eR rSE - rdSA #A2#S2 - rSA2 Other approximations and simplifications can be made in appropriate circumstances but if the result is successfully to avoid a significant proportion of the error which has hitherto been experienced in ground ranging by radars due to the misalignment of the radar azimuth axis and the ground, then a ratio of rAE to one or more of the other statistical quantities will always explicitly or implicitly feature in such approximations.

Figure 8 shows a block diagram of one possible arrangement incorporating the invention. In the diagram, singly and doubly primed letters are used to denote the in-phase and quadrature components respectively of signals. Azimuth, Elevation and Sum signals are obtained by conventional means and are fed into the three phase sensitive detectors, 2, 3 and 4. The sum signal is used as the phase reference for these detectors, after passing through the limiter (1). Each of the phase detectors 2 and 4 are in fact two such detectors, suitably arranged to give both the in-phase and quadrature component outputs. Naturally, since in this arrangement the sum signal is being used as the phase reference, there is no quadrature output from the sum signal detector.The signals are then converted from analogue to digital form (units 5, 6, 7, 8 and 9) with a clock rate appropriate to the range resolution, so that successive outputs represent successive range gates.

Arithmetic units 10, 11, 12, 13,14 and 15 then form the squares, sum of squares and products representing the variances and co-variances of the pairs of sample sets, arising from a single pulse in each range gate, while the accumulators 16, 17, 18, 19, 20 and 21 assemble the weighted sums (one set for each range gate being examined) which are proportional to the sample statistics. The computer 22 then solves the cubic equation in X given above, and forms the required function of the statistical quantities.

If the value of A may be assumed to be zero, the cubic equation is not required to be solved, and then units 14 and 20 are not required. The output of the computer 22 is used in exactly the same way as the elevation indication in a conventional ground ranging radar, the elevation being given for each range gate value.

Claims

CLAIIG

1. An airborne monopulse radar system for air-tosurface ranging, in which target return signals are added and subtracted to provide a sum signal, an azimuth difference signal and an elevation difference signal for determining a target position off boresight, including computing means adapted to determine from statistically independent target return signal samples the orientation of an iso-probability surface defining with respect to corresponding coordinate axes, sum, and azimuth and elevation difference signals amplitude combinations of a particular probability, and thereby provide an elevation/range indication or response independent of the across-track ground slope.

2. A radar system according to Claim 1, including means adapted to provide statistically independent quadrature components of each of said sum, azimuth difference and elevation difference signals from a single return pulse, the two sets of quadrature components providing said statistically independent target return signal samples.

3. A radar system according to Claim 1 or Claim 2 wherein said computing means employs the ratio of the co-variance factor of the azimuth and elevation difference amplitudes to the variance factor of the sum signal, the azimuth difference signal or the elevation difference signal.

4. An airborne monopulse radar system for air-tosurface ranging, substantially as hereinbefore described with reference to the accompanying drawings.

Amendments to the clans have been filed as follows 1. An airborne monopulse radar system for air-tosurface ranging, in which target return signals are added and subtracted to provide a sum signal, an azimuth difference signal and an elevation difference signal, said sum and difference signals being dependent upon target position off boresight, including computing means adapted to determine from statistically independent target return signal samples the orientation of an iso-probability surface defining with respect to corresponding coordinate axes, sum, azimuth and elevation difference signal amplitude combinations of a particular probability, and thereby provide an elevation/range indication or response independent of the across-track ground slope.