GB2444542A

GB2444542A - A missile angle tracking radar

Info

Publication number: GB2444542A
Application number: GB8408642A
Authority: GB
Inventors: Peter Graham Pawsey; Nigel Stanfield
Original assignee: AMS DYNAMICS Ltd; Marconi Co Ltd; Alenia Marconi Systems Ltd; MBDA UK Ltd
Current assignee: AMS DYNAMICS LIMITED; MBDA UK Ltd
Priority date: 1983-04-13
Filing date: 1984-04-04
Publication date: 2008-06-11
Anticipated expiration: 2004-04-04
Also published as: DE3446236B3; GB8408642D0; GB8309889D0; FR2907231A1; IT8567019A0; GB2444542B

Abstract

A steerable antenna 1 is stabilised by remote gyros 11 strapped down to the missile body. Target angle off boresight is derived to provide antenna tracking control and missile guidance signals. The gyro signals are employed to decouple the body motion from the target sightline signals. Imperfection in the gyro scale factor leaves residual body motion coupling and consequent tracking and guidance error. The invention provides means for correlating body motion components in the sightline signals with body motion gyro signals and decoupling this component according to the degree of correlation. A 3-d Kalman filter provides one correlation system. Alternatively, two 2-d Kalman filter systems are cross-coupled and either employ an extension of the filters to accommodate the correlation or employ direct correlation of the 2-d outputs with body rate signals about 3 axes.

Description

Angle-Tracking Radar System This invention relates to missile guidance

systems and particularly to the design of an angle tracking system for providing guidance signals. The invention is particularly suited to an active radar seeker, i.e., in which the radar signals are produced and processed on the missile, since considerable signal processing facility is then already available, but can also be applied to other forms of seeker.

A common form of missile guidance law is that known as proportional navigation in which the demanded lateral acceleration of the missile is proportional to the rate of displacement of the missile target sightline and of the closing velocity, that is: A =1KV W d n c s where, Ad = demanded lateral acceleration in me t r e s / s e c on d2 navigation constant (typically Vc missile-target closing velocity in metres/second and, = missile-target sightline spin (i.e. displacement) rate in radians/second.

This may be modified if the target acceleration perpendicular to the sightline (At) is known:

A

Ad K v ( + This modified form of the proportional navigation guidance law gives enhanced accuracy by predicting the change in the position of impact which is caused by the target accelera- tion -The principal components of a typical seeker and missile guidance system are illustrated diagrammatically in the, accompanying Figure 1. The missile has a steerable antenna 1 and is mounted on gimbals to permit tracking of a target in azimuth and elevation.

Azimuth and elevation servo motors 3 & 5 drive the antenna in the two planes respectively under the control of output signals from an angle tracking filter 7 with which the present invention i_s particularly concerned.

A transmitter/receiver unit 9 feeds a radar signal to the antenna to illuminate the target. The target reflection is received by the antenna and processed by the receiver to give target range, velocity and angle information.

An inertial reference unit (IRU) 11 consists of three gyros and three accelerometers aligned with the missile roll, pitch and yaw axes respectively to measure the angular velocities and accelerations of the missile.

The l.RU and receiver outputs are fed into the angle track-ing filter 7 for production of output signals for an autopilot unit 13. The autopilot controls fins 15 on the missile by way of servo motors to cause the required missile manoeuvre. -.3-

In addition to steering the antenna for the purpose of tracking the target, the antenna must be stabilised against missile movements. The direct way of achieving such stabilisatjon is to mount gyros on the antenna itself the gyros then responding to all movements of the antenna whether from body (missile) movement or tracking movement. Gyroscopes of a quality suitable for missile guidance systems are very expensive and quite massive. Three such gyros mounted on an antenna severely limit the scan rate and increase the expense.

It is therefore one object of the present invention to provide a missile guidance system employing remote stabilisatjon of the antenna (where a physically steerable antenna is employed) without loss of accuracy and response that might otherwise result from employing the strapped-down' gyros of the inertial reference unit, in view of their scale factor inaccuracies.

Since the invention also has application to beam steering antennae where there is no mechanical steering of the antenna the advantage in this ease lies primarily in the accommodation of inaccuracy in the strapped down gyro scale factor.

The invention is therefore concerned specifically with seekers that use strap-down' stabilisation. The primary seeker output is the sightline spin rate in space axes. In a seeker that uses strap down stabilisation, is derived from the angle rate sensors (e.g. gyros) of the IRU mounted on the body of the missfle, together with an angle tracking loop (e.g. an antenna mounted on a steerable gimbal mechanism) which tracks the target and can therefore indicate target bearing with respect to the missile body.

_LI_

The performance of an anti-air missile system employing strapdown seekers has been found to be extremely sensitive to the bodyrate gyro scale factor accuracy. In the case of remotely stabilised antennae using gimbal angle pick-off for position feedback, the pick-off scale factor has also to be of equivalent accuracy to the gyro scale factor, which varies with time, manufacturing tolerances and environmental conditions. Radome aberration gives a further error that is effectively added on to the gimbal pick-off error. The underlying problem with any seeker of this class is in the coupling of body motion onto the line of sight by system imperfections, thereby corrupting the estimation of sightline rate for use in the guidance command.

Short range engagement of a target requires a highly manoeuvrable missile and body rates of 500 /sec are not uncommon, especially at high altitude where the missile incidence lag (i.e., the lag between imposition of a steering control and the resulting track correction) is likely to be quite high. Any error in measuring the body rate will corrupt the homing head output to the autopilot and possibly dominate over the desired g' command, i.e.,Ad above, since the sightline rates generated in an engagement are of much lower order, being in the range of 0.10/sec to 10 /sec maximum.

A preferred embodiment of this invention provides a design which simultaneously compensates for errors in: (i) gyro scale factor (ii) gimbal pick-off (iii) radome aberration Furthermore the preferred system is designed to give optimal filtering to remove the noise-like effects of:- (I) Seeker thermal noise (ii) Interference and jamming noise (iii) Target glint and to provide best estimates of and At for the guidance law in both missile planes (e.g., azimuth and elevation).

According to the present invention, an angle tracking radar system for a target seeking missile employing a steerable beam antenna, and comprising a receiver for providing a boresight error signal indicative of' target sightline by comparison of sum and difference signals derived from target reflection, means for controlling the antenna beam in response to said boresight error signal, and means for providing missile guidance signals in response to said boresight error signal, also comprises stabilisation means for stabilising the antenna beam in space, said stabilisatjon means employing angle rate sensing means adapted to be mounted on the missile body for providing a body rate signal, means for combining the body rate signal with the antenna and missile guidance signals in such manner as to tend to decouple the antenna and guidance control from missile body movement, and means for correlating the body rate signal with a signal indicative of the target sightline and further decoupling the sightline from body movement in dependence upon the degree of correlaLjon. The correlation may be performed by a Kalman filter having a state estimate based on random uncertainty of the gyro scale factor. The Kalman filter may additionally employ as state estimates: horesight error, sightline spin rate, target lateral acceleration and gyro scale factor.

In such a system for target tracking in three dimensions and employing an antenna beam steerable in azimuth and elevation, there are preferably included means for estimating azimuth and elevation beam steering demands, means for estimating si.ghtline yaw and pitch rates, means for estimating target transverse accelerations, and means for estiamting gyro correction factors in respect of missile yaw, roll and pitch, the Kalman filter employing state estimates corresponding to each of these factors.

According to one arrangement providing tracking in 3 dimensions, such a radar system may comprise Kalman filter sections respectively providing from azimuth and elevation outputs of the receiver estimates of azimuth and elevation boresight error, one such filter section employing state estimates comprising azimuth boresight error, sightline yaw rate, and target lateral transverse acceleration, and the other filter section employing state estimates comprising elevation boresight error, sightline pitch rate, and target vertical transverse acceleration, and the system then includes means for deriving the sightline roll rate, means for cross coupling the sightline yaw estimate from one filter seetion into the sightline pitch estimation of the other filter section and vice versa, means for cross coupling the target transverse acceleration estimation of the other filter section, means for introducing as a multiplying factor in each cross coupling a measure of the sightline roll rate, nd correlation means for correlating output signals of the receiver with yaw, pitch and roll body rate signals for producing scale factor correction factors in respect of yaw, pitch and roll gyros constituting the angle rate sensing means, the correction factors being applied to the derivation of azimuth and elevation body rate measurements arid to the derivation of sightl.ine roll rate, respectively.

The correlation means may be constituted by an extension of the Kalrnan filter.

Alternatively, there may be included means for deriving from the receiver azimuth and elevation outputs, residual azimuth and elevation body rate signals, means for resolving the residual signals into yaw, roll and pitch components and means for correlating the yaw, roll and pitch components with measured values of the misile yaw, roll and pitch and deriving corresponding gyro correction factors dependent upon the degree of correlation.

An angle tracking radar system in accordance with the invention will now be described, by way of example, with reference to the accompanying drawings, of which: Figure 1 is a schematic diagram of the basic elements of a missile active radar system employing a steerable antenna; Figure 2 is a schematic diagram of a radar receiver; Figure 3 is a diagram illustrating the various angles arising in relation to missile body, antenna dish and target sightline; Figure 24 is a schematic diagram of a Kalman filter angle tracking loop for a two-dimensional scheme; Figure 5 is a diagram of the various axis frames involved in a 3-dimensional system, namely, the missile, antenna and target sightline frames; Figure 6 is a diagram of the relation between the antenna and sightline frames; Figure 7 is a block schematic diagram of a Kalman filter angle tracking loop for a 3-dimensional scheme employing gyro scale factor correction within the Kalman filter, Figure 8 (a and b) is a schematic diagram of two 2-dimensional Kalman filter loops coupled together for the purposes of a 3 dimensional scheme; Figure 9 is a diagram illustrating the conversion of 3-dimensional missile gyro body rates to azimuth and elevation rates; Figure 10 is a diagram illustrating the derivation of transverse missile acceleration for use in the arrangement of Figure 8; Figure 11 is a diagram illustrating the conversion of azimuth and elevation receiver output signals to gyro scale factor correction values; Figure 12 is a diagram of an alternative arrangement for deriving gyro scale factor corrections by direct correlation of measured body rates with the receiver output signals; and Figure 13 is a block diagram illustrating the arrangement of Figures 8, 9, 10 and 11. _9...

Basic elements of a guidance system employing a steerable antenna have already been described with reference to Figure 1 Figure 2 shows the arrangement of a typical receiver and transmitter. The antenna 1 is operated in a known monopulse system and has four separate quadrant outputs from which are fed into the comparator 17 to form a sum signal S, an azimuth difference Daz signal and an elevation difference signal Dei* The three channels are mixed down to an intermediate frequency by means of a local oscillator 19 and mixers 19.

Electronic angle tracking elements 21 & 23 take the sum signal, multiply by az and and subtract this signal from the azimuth and elevation channels respectively in difference circuits 25 & 27. az and e1' described later, are obtained from the angle tracking filter 7 and are the estimated values of the difference to sum ratio, i.e. the boresight error angle.) The difference IF channels 29 & 31 contain the signal

D-S

which is zero when the estimate of boresight error, , is eo r r e c t.

The three channels are amplified in age amplifiers 33 which are controlled by an age circuit 35 from the sum channel 30. Phase sensitive detectors 37 (psd) between sum and difference channels generate the received outputs JzRx and F1Hx as products of the sum and difference channel signals.

J'he age action (35) normalises the sum channel to unity amplitude, i.e. the gain of the IF channels is where is the mean value of S. The azimuth psd output is given by

S D -S

-az az and similarly for the elevation output.

In an alternative configuration the Electronic Pngle tracking is omitted. In this case the psd output is given by

S D

and the receiver output is generated by subtracting to give az

S D az-c az

The transmitter 39 is coupled into the antenna via a circulator 141 in the sum channel.

Range and velocity tracking systems are included in the seeker but are not shown on the diagram since any of the standard techniques are satisfactory for the purposes of this invention. A further requirement is a system for measuring the signal to noise ratio. This can be achieved in several ways such as monitoring the age level or examining the received spectrum in the receiver. In summary the receiver gives the following outputs:--11-.

(i) Azimuth Rx (ii) Elevation Rx (iii) Missile-target range (H) (iv) Missile-target closing velocity (Va) (v) Signal to noise ratio.

The production of guidance signals will first be described for a single plane system. Alternative 3-dimensional systems will then be described subsequently.

Figure shows diagrammatically an angle tracking filter which provides an estimate of boresight error (angle of target off boresight) and which takes account of a number of factors which could contribute to errors in the estimate.

This accommodation is achieved by a Kalman filter angle tracking loop of which Figure is a representation. In order to employ such a filter it is necessary to construct a mathematical model of the signal derivation. In this embodiment this model consists of differential equations representing; the boresight error rate (s); the target sightline acceleration (); the target lateral acceleration (At); and scale factor of the strapped-down gyro.

These equations are implemented in the system of Figure subject to the app1eation of respective Kalman gains for the different equations. The derivation of the equations, and of the Kairnan gains, follows.

To avoid unnecessarily complicating the filter description it is assumed that the filter would he designed on the basis of' constant closing velocity. This initial assumption does not in principle alter the validity of the the resulting design concept as the filter equations can be modified to take this into account at a later stage.

Referring to the angle definitions given in Figure 3 the boresight error equation is written: s'1d (1)

-s d

The gimbal angle is written: -m (2) w _ g d m :: --i/ (3) s g m The sightline acceleration equation is written: (14) s t s tV c c where: t time-to-go' z RIV At target acceleration normal to the sightline A missile lateral aced eration normal to the m sightline closing velocity B separation range The target manoeuvre is modelled as bandlimited white noise: At -At nt (5) v--

C C C

where: wt target manoeuvre bandwidth and, Ent (t1) nt (t2) a(t1_t2) E being the expected value of the product ) n(t2) where: = 2jt (Spectral Density of target manoeuvre) =wtO*t It = r.ms. expected target manoeuvrability: so that -2w -Consider the measurement of body rate: measured, i.e. (V) = k i (6) m mm g m where kg is the gyro scale factor. -1)4_

Therefore IL m k mm g i.e., = k(Vm)m where k = 1/kg (7) Assuming that a perfect measure of gimbal rate is available we may then re-write Equation (3):- = -k (i' ) -"F s mm g It rriay also be assumed that the gyro scale factor is adequately represented by the following equation:-1< nk (8) where nk represents the random uncertainty in scale factor such that the following equation applies, in which t1 and t2 are the instants of correlation E k (tl),nk (t2) 6(t1-t2) Combining Equations (7), (4), (5) and (8), we get: C "F -k ("i' ) -w S mm g

A A

2 1 t 1 m "F -.w -.-----.--S I S t V -r V c c At At nt -Wt* c c C k = nk These four differential equations are the basis for the mathematical model referred to above. The implementation, of the four equations in a Kalman filter angle tracking loop can be seen in Figure LI.

The information provided to the electronic angle tracking (E.A.T.) receiver 11 consists of the sum and difference signals from which the boresight error angle is derived. This information is of course inadequate in so far as it requires accurate determination of the dish axis position. The error angle c, as shown in Figure 3, is equal to the angle between the antenna dish axis (the boresight) and the target sightline, i.e. I's -Pd, and is represented as such in Figure LI by the difference function )43.

The output of the angle tracking filter, the estimated value, of the boresight error, is applied to the EA.T. receiver (Figure 2), where it is multiplied by the sum signal and the result differenced with the difference channel signal. The output of the E.A.T.

receiver would then ideally be zero but is actually finite since the estimate of boresight error will not in general be completely accurate. In particular, the receiver output will contain a component of the body motion.

Tt is a feature of the present invention that the angle tracking receiver output is correlated with thc source of the error, in this case the missile body motion, arid a correction imposed corresponding to the degree of correlation.

In Figure LI the output signal of the E.A.T.

receiver is subjected to Kalman gain factors K1 to and to various process paths which implement the equations (9). The Kalman gains are calculated as will be explained -1 6-and are updated at very short intervals in accordance with perturbations in the receiver output due to sightline spin, target movement, missile body motion etc. The various factors which affect the final boresight error estimate are therefore controlled by respective Kaiman gains K1 to K4 to tend to produce a receiver output which, after taking account of the feedback estimate, is a nearly true indication of residual boresight error irrespective of variations resulting from body motion and associated gyro scale factor error. The object is therefore to make use of the correlation that exists between the receiver output and the body motion as apparent from gyros subject to scale factor error.

The implementation of the equations (9) can be seen as follows. Referring to Figure 4, and working back-wards from the point 47 at which the output () of the angle tracking loop is obtained, the output of integrator 61 is equal to + Wg the term g being the gimbal angle derived from the antenna gimbal within the dishloop subject to a gain factor K for the gimbal potentiometer.

At the input of the integrator 61 the signal becomes + g and before summing circuit 51 becomes, + + k(Vm)m where the symbol indicates an estimate, k is the estimated gyro scale factor, derived from Kalman gain K4 and integrator 71, m is the angular displacement rate of' the missile body, i.e., the body rate, and indicates a measured value.

Summing circuit 149 provides an output of'F, the estimated sightline angular rate, modified by Kalman gain so that: + k(W s g mm and c -k(W) -s mm g in accordance with the first of the four equations.

The sightline rate output from integrator 67 becomes Y output from summing circuit 65. The output of previous surnmng circuit 61 is therefore: *w* -_i s T 5 TV c

A

where is the output of integrator 63 as required by the original (modified) guidance law equation stated above.

Summing circuit 61 has a negative input of A /R which is the missile lateral acceleration divided m by the target range, the acceleration being provided by accelerometers in the IRU. The range is-equal to t.V with the result that the input to summing circuit 61 is:

A A

2 1 t+ m -T 5 T V c c which, if made zero by the Kalman gain factor K2, gives the second of the four equations.

As stated above, the output of integrator 63 is At/V0. The output of summing circuit 69 is therefore At/V and the output of Kalman gain factor 1<3 is: Target manoeuvre has been assumed to be represented by band limited white noise Thus the output of 1<3 can be represented as nt/V0 so that nt At At = Ut V*-

C C C

which is in accordance with the third equation.

In the case of the gyro scale factor correction, the estimated scale factor 1 is employed as a multiplier for the measured value of the missile body rate in multiplier 73. The integrator 71 therefore requires the output of Kalman gain factor K to be k. Since the scale factor is represented by the random uncertainty k' With regard to this last correction factor, the measured body rate mm is imposed on the sight line estimation (by way of summing circuit 51) so that if the measured value were true, the sightline estimate would be decoupled from the missile body motion. However, the uncertainty of the gyro scale factor upsets this conclusion and a body motion component creeps into the sightline estimate and hence into the receiver output at point )45 This body motion component is correlated with the body motion by the Kalman filter and the resulting signal indicative of the degree of correlation is produced to modify the measured body rate value. k will tend to settle at a value at which there is zero body motion component in the receiver output. The outputs of integrators 63 and 67 i.e. At/V and are applied to guidance law circuitry 75 and thence to the autopilot control.

A state-space representation of the above four equations is given by the following standard vector equation, in which u and n are input and noise vectors respectively: Ax + ii + Ii (10) In this equation: o 1 0 -(P mm 0 2/r l/t 0 A= 0 0 WT 0 0 0 0 0 0 c

A

-0 Is The basic measurement from the receiver is boresight error: E C V m i.e., measured error equals the true error plus noise = Hx + v where H=[1 000] arid x is as defined above.

V defined by: E V(t1) V(t2) = rô(t1-t2) (12) where r rg + rth rg and rth being gint and thermal noise spectral densities.

These in turn are defined as: 2a g 2 -1 P rad /rad/sec R'w g LI1 s where is expected r.m.s. glint in metres R is measured separation range in metres Wg is expected glint bandwidth in radians/second is the zero-frequency-spectral-density of thermal noise given by: -1 2 radian2/radian/second S 11it B * S (1 c2)

S S

where, B is the receiver bandwidth in Hertz,

S

S is antenna static split sensitivity in volts! volt / radian, is (signal power)/(noise power) measured in the receiver Kalman Filter Equations Defining our state estimates as: 1T - ;At/V; K] where T indicates a transpose to the column matrix given above.

In present conditions the standard equation (10) gives the following state estimator equations: X A x + u K -where y H x + v see (11) m m -y = c =Hx and K the Kalman gain is given by: K=PHTr1 (13) where P is the covariance matrix, HT is the transpose of the H matrix above and r is given by equation (12).

The covariance matrix P is found by solving the following rnaLrix Riccati algorithm, a matrix differential equation:- = AP + PAT -PHT r HP + Q Q = diag (0 0 q/V The covariance matrix, F, is symmetric and can be written: P2 P3 P5 P6 P7 P3 P6 1)8 P9 P)4 P7 P9 Equation (1k) in its expanded form reveals the following differential equations.: = 2(P2 -"mm P)) -XP 1 -(21)2 + P3)/t + -"mm7 XP1P2 P3 = 16 -mm 9 P13 -l3 P)4 = 1)7 -"mm - = 2(2P5 + P6t -(15) = (2P6 + P8)It -w P6 -XP2P3 1)7 (21)7 + P9)It -XP2P p8 -2w P8 -XP + p9 w -34 P10 = and the Kalman gains are, from equation (13):-

K

-where = r, r being K2 -2X given by equation (12) K3 = = Equations (15) are solved on line in the angle tracking filter processor as the engagement progresses because the measured body rate (f') directly affects the solution and is unique to the engagement.

Initialisation of the Covariance Equations In accordance with normal procedures for solving these covariance equations, the P matrix needs to be initialised given our knowledge of the system. Only the diagonal elements (variances) are considered for initialisation since we have no useful knowledge of the covariances (off-diagonal terms).

E (c(o) -(o) ) (e (o) - (o) ) P5(o) = E ((o) -(o) ) ((o) -(o)) r6 A (o) (o) A (o) A (o) P8(o) = E ( -Vc) C Vc P10(o)= E { (k(o) -(o)) (o) -(o) ) P1(o) is initialised according to knowledge of the angular lay-on accuracy, i.e. the accuracy with which the target sightline can be aligned with the target.

P5(o) can be initialised according to the uncertainty in knowledge of sightline rate at the beginning of the engagement.

Past experience leads to initialsing the variance on target acceleration estimate to zero to avoid any deviation from the initial target acceleration estimate until the other filter states have settled down. This technique tends to reduce the estimation errors early in the engagement. Therefore 8 is set to equal 0.0.

P10(o) is initialised according to the quality of gyro used and is essentially the variance about the nominal scale factor of unity.

Initialisation of the Kalman Filter States It is important that the filter states are initialised to values that are close to the true values of state as this minimises the mean square estimation error and consequently improves the overall missile performance.

Wrong initialisation of the estimates does not change the settling time of the filter but it does increase the mean square deviation of the estimates from the true state.

In the event that, at the initiation of an engagement, insufficient information is available to initialise some of the filter states with any confidence, those states are set initially to zero. This strategy also helps to minimise the mean square deviation of' the estimates from their true state.

The initial condition of the parameter estimate (k) (i.e. the gyro scale factor reciprocal) is set to unity as this is its expected value.

The implementation of the arrangement of Figure LI is achieved using integrated circuits, separate chips being emp'oyed for the various sections,e.g., the dish loop 53, the Kalman filter itself, the guidance control circuit, etc. A 3-dimensional development of the above 2-dimensional Kalman filter tracking loop of Figure 24 will now be described with reference to Figures 5, 6 and 7.

Figure 5 shows the missile 24 carrying the gimbal mounted antenna 1. The missile axes comprise the x axis longitudinally aligned with the missile and the m and Z axes transverse to the missile in the azimuth and elevation planes respectively.

The antenna axes x y and z move with the a' a a antenna and are aligned with the missile axes when the antenna is directed dead ahead'. The antenna boresight, i.e., the Xa axis, is then aligned with the axis Xm* The third reference frame is based on the target sightline, i.e., the line between the missile and the target 2. The x axis is aligned with this sightline while the y3 nd z axes remain orthogonal with it in azimuth and elevation planes respectively.

Figure 6 shows the relationship between the antenna and sightline axes. In an arbitrary situation in which the target 2 is not on boresight, i.e. the antenna axis Xa is not aligned with the sightline axis x3 there will in general be the following errors in alignment of the axes. The axes z and z will be at an angle e a s z but in a plane to which the axis y isnormal, and the axes y and y will he at an angle but in a plane to a y which the axis Za is normal. Such an arrangement will produce an arbitrary relationship between Sa and x5.

For alignment of the boresight and target sight-line, the antenna is first rotated through an angle about za (so that y and a coincide) and then rotated through an angle c about so that Xa and x (and also z and z) coincide. a s

Figure 7 illustrates in block schematic form the extra complexity introduced by the necessity to accommodate 3-dimensional tracking over and above the basic 2-dimensional arrangement of Figure 4.

In Figure 4, the estimated sightline spin rate is derived from body acceleration Am and target lateral acceleration At/V. In Figure 7 the sightline spin estimator 101 requires inputs (A)m from three body accelerometers 103 which inputs, being in missile axes, require resolution by function 105 (OgWg) to provide measured body acceleration in antenna axes, i.e. (A)m* Target lateral acceleration is provided by estimator 107 in sightline axes in azimuth and elevation planes, as sy sy.

At and At, for application to the sightline spin estimator 101. This estimator also receives as an input three body rate signals replacing the single signal mm of Figure 4. These three signals from the three body rate gyros 109 are the roll, pitch and yaw body rates (P, q, r)m in missile axes which are modified by the respective body rate gyro correction factors k in the "n" multiplier 111.

It will be appreciated that the double line signal paths incorporate at least triple signal connections.

The receiver output, ie, the boresight error signal, is provided as azimuth and elevation errors and cm in missile axes to the summing circuit 113 of the receiver. The output signal estimate of boresight error must also be provided as azimuth and elevation components cy, cz (to constitute the inputs c and Eel in Figure 2 and are converted from residual gimbal demands (output from summing circuit 115) by resolver 117 to which the measured gimbal elevation angle 0g is applied.

The gimbal azimuth and elevation angles Wg 0g are picked off by potentiometers 119 for use in the various resolutions required, e.g. in the sightline spin estimator 101, the resolver 105 and the boresight error estimator 121. The latter converts the receiver output signals as modified by Kaiman gain K1 to azimuth and elevation gimbal rate demands which are converted to gimbal angle demand estimates gd andegd input to summing circuit 115.

After subtraction of the measured gimbal angles the estimated gimbal demand errors are applied to the antenna controller 123.

It will be noted that the solid lines indicate kinematic, i.e. mechanical or physical, inputs.

The equations for the fully coupled (roll cross coupling) Kalman Filter of Figure 7 are presented. The filter is implemented as a continuous-discrete process where the filter state estimate and the error covariance matrix P are propagated continuously between discrete ?0 measurement updates.

Filter Propagation Equations: A + u Error Covariance Propagation Equations: = AP + PAT + Q At the measurement update time the state estimates and the error covariance matrix are corrected as follows: = (-) K[k -H()] P( ) [I -KH] P(-) where: (-) means before update (+) means after update I means identity matrix and the state estimates are: = Ar kr 0gd A, , q] the state matrix is: o Cos 0.rm 0 0 0 Q 0 g m 0 -2a 1/8 0 0 S 0 0 0

S

0 0 -w 0 0 0 Ps 0 0 r s 0 0 0 0 0 0 0 0 0 A = 0 0 0 0 0 1 0 PSinWg _qCosWg 0 p5 0 0 0 -2 -1/8 0 0 0 0 p 000 t 0 0 the input vector is: s T = [_P:sin _y, 0, 0, 0, 0, 0, 0] The Q matrix is a system noise spectral density matrix representing the uncertainty in the assumed mathematical model.

The gain K is a 9x2 matrix of Kalman gains given by: K4 P(-) HT[ HP(_)HT + RN 1_i where: [cosg 0 0 0 0 0 0 0 0 H:1 L 0 00001000 H A E vT) N (-4< ) is a noise covariance matrix representing the assumed measurement noise statistics.

and the discrete measurements are of boresight error.

C y = k c

is azimuth y c is elevation Three additional equations are required to complete the design, these being for p5 the sightline roll rate, the estimate of fl/H and 13 the estimate of R L;: + Cos + /Cosg A5X 2 s2 s2 m m' c. = -o + (r5) + (q5) --fl---+ Gcx(ci _ci.) = o.13 G13 (13m -where czm and 8m are measured values of /R and R respectively and G and are gains.

The discrete measurement noise R is constructed n partly from knowledge of the receiver signal-to--thermal noise ratio and partly by an assumed glint noise variance i.e., 2 2 2 2 Rn th + Gg1/8) radians where: th = 1 2 S2(1-+ c is signal-to-noise ratio in the measurement bandwidth S is the antenna static split sensitivity in volts/volt/ rad.

is assumed glint variance in metre2 is similar in both channels of measurement of boresight error.

When Range and Doppler measurements are unavailable, for example due to jamming, the gains G and are put to zero and the filter continues using its estirriates of R/H and H (i.e., c and 8). It will be necessary to put upper and lower hounds on and a lower bound on 8 depending upon the type of missile system being used.

Resolution of measured missfle accelerations into sightline axes: The accelerations of the mssfle body in space are measured by an orthogonal triad of accelerometers fixed to the body. These acce'erations must be resolved into sightline axes for use in the Kalman filter.

Assuming that the antenna is controlled such that its x-axis is pointing along the sightline we may resolve these body measured accelerations through the measured gimbal angles, i.e.: ASX ---mx m -Cose Cos'p (A) + Cos Sin (AmY)m_ Sin' (m)m m g g m g g m g m mx)m = Sin'i' (A + Cos (AmY)m m g m g m AS Sine Cos A) + Sine Sinq' (A) + Cose mx m " my m -(Am)m m g g m g g m g m mx m where (A) is measured longax (x-axis of body) m my)m (A is measured latax (y-axis of body) m m m (AM) is measured latax (-axis of body) Filter Initialisation 0 (0) 0 after lay-on g g(0) = after lay-on g = o') r (0) q5(0) 0 sy(Q) = 0 unless a-priori information available = 0J (0) = 1.0 p (0) 1.0 q(0) = 1.0 r Covariance Initialisation Only diagonal elements of P matrix are initialised and the actual values would be dependent upon the type of missile system being used. These values would be arrived at for a particular application.

KEY

Measured elevation gimbal angle (rads) Measured azimuth gimbal angle (rads) pm Measured missile roll rate in missile axes (rads/s) q Measured missile pitch rate in missile axes (radsis) r Measured missile yaw rate in missile axes (rads/s) Assumed target manoeuvre bandwidth axes (radsis) A5X Measured missile longax in sightline axes (mis2) A5 Measured missile latax (azimuth) in sightline axes m 2 (rn/s) A5 Measured missile latax (elevation) in sightilne axes (rn/s) Azimuth gimbal demand estimate (rads) 0gd Elevation Gimbal demand estimate (rads) r Azimuth sightline spin estimate in sightline axes (rads) Elevation sightline spin estimate in sightline axes (rads) ASY Azimuth target acceleration estimate in sightline axes (rn/s) ASZ Elevation target acceleration estimate in sightline t 2 -axes (m/s) k Roll rate gyro correction factor kq Pitch rate gyro correction factor k r Yaw rate gyro correction factor _3)4_ Two schemes alternative to the arrangement of Figure 7 will now be described. Referring to Figure 8, comprising sections 8(a) and 8(b), it can be seen that each of these sections is similar to the single plane filter of Figure, but excluding the 4th state estimate concerning the gyro scale factor. The additional components in each section are included to take account of the mechanics of implementing the Kalman filter tracking loop in 3 dimensions. As in Figure 7, the antenna is mounted on gimbals, one within the other, the inner gimbal providing an elevation angle 0g with respect to the outer gimbal which in turn provides an azimuth angle with the missile body.

In Figure 8(a) the receiver azimuth output (Rx) is subjected to the three Kalman gains K1 K2 and K3 as before. An input to summing circuit 131 is derived from Figure 10, being the missile (lateral) transverse acceleration in sightline axes, AYR. The sightline rate state estimate is in this 3-d case the yaw rate estimate r in sightline coordinates. Since demands are required in gimbal axes, this is converted by a function 133 to the azimuth gimbal frame.

After subtraction of the K1 gain component at 249 an output a' is taken for the circuit of' Figure 12.

A similar output b' is taken from Figure 8(b) to Figure 12.

A measured value of the missile azimuth body rate is derived from Figure 9 and subtracted at 51 to provide an azimuth gimbal angle demand estimate The azimuth gimbal angle is picked off at 135 and subtracted at 137 to leave a residual azimuth gimbal angle avg which is applied to the controller 139 of the dish loop.

The error signal avg is provided as the output signal for feedback to the receiver after conversion from a gimbal frame to an azimuth frame by the function 11.

The target acceleration estimate is again derived from integrator 63, but is now the lateral transverse component in sightline axes.

Figure 8(b) is similar in respect of the elevation receiver output (RX)el fewer frame conversions being necessary in view of the more direct relationship between the receiver elevation output and the gimbal elevation angle 0g* The Kalman gains in this section of the filter are referenced K5 K6 and K7 but correspond to the gains K1 K2 and K3 of section 8(a).

A degree of cross coupling between the two sections is necessary, involving the sightline roll rate p5, to take account of the rolling motion of the sight-line caused by missile roll/pitch motion, Sand antenna yaw motion in conditions of non-zero inner gimbal angle. The derivation of p is illustrated in Figure 9.

The sightline yaw and pitch rate estimates and are each cross coupled to the input of the sightline spin (rate) estimator of the other section by way of a multiplier 142, 13 having a multiplying input

S p5.

Again, the output of the target acceleration estimator (63) in each section is cross-coupled to the input of the target acceleration estimator (69) in the other section, also subject to multiplication by p in multipliers 145 and 1147.

Rate gyro scale factor correction in this embodiment is not a simple extension of the single plane version since there are three rate gyros measuring body roll pitch and yaw rates and two receiver outputs RXaz and RX1. The gyro correction factor estimates kq and kr are obtained as illustrated in Figure 11, employing a resolution circuit 11(a) and Kalman gains K14 K8 and K9.

Referring to Figure 11, the receiver inputs are resolved by gimbal angle estimate functions as shown, to produce three yaw, roll and pitch components 6r' and 6q* These are subjected to the Kalman gains K, K9 and K8 followed by integrators 1149, 151 and 153 as in Figure 14.

The Kalman gains are produced by the covariance propagation which is augumented to include these extra terms.

Referring now to Figure 9, the missile gyros 155, 157 and 159 are strapped down' to the missile body and produce angular rate' signals rm. m and qm for yaw, roll and pitch in missile axes. These signals are modified by the respective gyro correction factor estimates k, and kq derived from Figure 11 above, in multipliers 161, 163 and 165. Resolution of these signals in accordance with the gimbal angle functions shown, produces measured values of azimuth and elevation body rate signals (F) maz m and ( ) mel m Also produced is the sightline roll rate p derived from the body roll and pitch gyros, various gimbal angle functions as shown and the sightiine yaw estimate r derived from the output of integrator 67 in Figure 8(a).

These three outputs, azimuth and elevation body rates and sightline roll rates are applied to Figure 8 as described previously. -.37-

In an alternative arrangement for achieving 3-dimensional tracking, Figure 11 is replaced by Figure 12 to provide gyro scale factor correction without the above necessity to expand the Kalman filter. Processing time and complexity are thereby reduced. Referring to Figure 12, the receiver outputs (Rx) and (RX)1 are applied to respective summing circuits 167 and 169 which subtract the integrated version of the signal from the inputs. The integrators 171 and 173 are supplied with the summing circuit outputs subject to gains Gi. To the output of the gain circuits is added in summing circuits 175 and 177, the signals a' and b' derived from Figure 8(a) and (b) and representing the sightline yaw and pitch rate estimates.

The resulting signals are the residual azimuth and elevation body rates. These are applied to resolving circuitry identical to that of Figure 11(a) to produce yaw, roll and pitch signal components of the receiver output. Correlation is then provided by multiplying these signals directly with measured values of the body rate in yaw roll and pitch, derived from the gyros, this multiplication being performed in multipliers 179, 181 and 183.

After modification by gain functions G2, the signals are integrated (185) to produce the desired gyro scale factor correction estimates k k and k. These y' r p correction factors are applied to the multipliers of Figure 9.

The operation of the embodiment of Figure 12 may be explained as follows by reference back to the single plane scheme of Figure 14* Let the transfer function between the receiver output point 45 and the point 50 be F(s) where s is the Laplace Operator.

Let the signal at the receiver output be x s xF(s) -k('f' ) + -ks mm m Let k (i' ) -mm m m which is the residual body rate error after nominal scale factor correction x W _W -

D

Therefore s(W -x) Therefore (1P -x) = xF(s) -ôiIm When 0 = xF(s) + sx is assumed to be dominated by scale factor errors on m the gyros. The error is therefore correlated to the body rate. Figure 12 shows the derivation ofOWm in each plane where the signal at point 50 is xF(s) and the receiver outputs are differentiated to produce sx. These residuals are resolved into the body frame using the gimbal angles and then correlated with the corresponding gyro using multipliers 179, 181 and 183 as shown in Figure 12. The multiplier outputs are integrated and the integrator outputs stabilise when the correlation is zero. The integrator outputs are of course the respective gyro gain correction terms k k 1< on the yaw roll and pitch r' p q gyros. The gains Gi and G2 are optimised according to the quality of receiver output and the speed at which the gain correction is required.

When the system of Figure 12 is used to derive k, k, k, the values of K, K and K are unused in r p q 14 8 9 Figure 11 and the method of obtaining the remaining Kalman gains i.s simplified. The filter can be re-structured slightly to enable identical gains for each of the two sightline planes to be computed, i.e., K1 K5, K2 K6, K3 = K7, all of which are independent of body rate. It is also possible to further simplify by storing K1, K2 and K3 as pre-determined functions which can be provided in a look-up table. The need to solve the covariance equations in real time is then not required.

Figure 10 illustrates the derivation of lateral and vertical transverse accelerations of the missile body (i.e. A5'/H and A5ZIR) from three accelerometers of the m m missile I.R.U., these accelerometers being referenced A, A and A the subscripts indicating the axial direction y x z' of the component acceleration. The resolution is achieved by various gimbal angle functions as shown, together with dividing circuits having range inputs derived from the usual range tracking loop (not shown).

Figure 13 illustrates the two alternatives for achieving a 3-dimensional system by partial duplication of a 2-dimensional system. As explained above, the alternatives employ different methods of obtaining correlation of the body rriovement and the receiver output signals. _)4Q_

Claims

1. An angle tracking radar system for a target seeking missile employing a steerable beam antenna, and comprising a receiver for providing a boresight error signal indicative of target sightline by comparison of sum and difference signals derived from target reflection, means for controlling the antenna beam in response to said boresight error signal, means for providing missile guidance signals in response to said boresight error signal, stabilisation means for stabilising the antenna beam in space, said stabilisation means employing angle rate sensing means adapted to be mounted on the missile body for providing a body rate signal, means for combining the body rate signal with the antenna and missile guidance signals in such manner as to tend to decouple the antenna and guidance control from missile body movement, and means for correlating said body rate signal with a signal indicative of said target sightline and further decoupling said sightilne from said body movement in dependence upon the degree of correlation.

2. A radar system according to Claim 1, wherein said angle rate sensing means comprises a rate gyro having a randomly uncertain scale factor such that the gyro output signal is not a consistently accurate representation of the body rate.

3. A radar system according to Claim 2, wherein said correlation is performed by a Kalman filter having a state estimate based on random uncertainty of said gyro scale factor.

4. A radar system according to Claim 3, wherein said Kalman filter employs as state estimates: boresight error, sightline spin rate, target lateral acceleration and gyro scale factor.

5. A radar system according to Claim 3 or Claim 4, for target tracking in three dimensions and _LI 1-employing an antenna beam steerable in azimuth and elevation, and including means for estimating azimuth and elevation beam steering demands, means for estimating sightline yaw and pitch rates, means for estimating target transverse accelerations, and means for estimating gyro correction factors in respect of missile yaw, roll and pitch, said Kalman filter employing state estimates corresponding to each of these factors.

6. A radar system according to Claim 5, wherein said antenna is mounted on gimbals and is physically steerable in azimuth and elevation, said azimuth and elevation beam steering demands being respective gimbal demands.

7. A radar system according to Claim 1 or Claim 2, and comprising Kalman filter sections respectively providing from azimuth and elevation outputs of said receiver estimates of azimuth and elevation boresight error, one said filter section employing state estimates comprising azimuth boresight error, sightline yaw rate, and target lateral transverse acceleration, and the other said filter section employing state estimates comprising elevation boresight error, sightline pitch rate and target vertical transverse acceleration, the system including means for deriving the sightline roll rate, means for cross coupling the sightlirie yaw estimate from one filter section into the sightline pitch estimation of the other filter section nd vice versa, means for cross coupling the target transverse acceleration estimate of each filter section into the target transverse acceleration estimation of the other filter section, means for introducing as a multiplying factor in each said cross coupling a measure of the sightline roll rate, and correlation means for correlating output signals of said receiver with yaw, pitch and roll body rate signals for for producing scale factor correction factors in respect of yaw, pitch and roll gyros constituting said angle rate sensing means, said correction factors being applied to the derivation of azimuth and elevation body rate measurements and to the derivation of sightline roll rate, respectively.

8. A radar system according to Claim 7, wherein said correlation means are constituted by an extension of said Kalman filter.

9. A radar system according to Claim 7, including means for deriving from said receiver azimuth and elevation outputs, residual azimuth and elevation body rate signals, means for resolving said residual signals into yaw, roll and pitch components and means for correlating the yaw, roll and pitch components with measured values of the missile yaw, roll and pitch and deriving corresponding gyro correction factors dependent upon the degree of correlation.

10. A radar system substantially as herèinbefore described with reference to Figure 14

11. A radar system substantially as hereinbefore described with reference to Figure 7.

12. A radar system substantially as hereinbefore described with reference to Figures 8, 9, 10 and 11.

13. A radar system substantially as hereinbefore described with reference to Figures 8, 9, 10, 11(a) and 12.

Amendments to the claims have been filed as follows 1. An angle tracking radar system for a target seeking missile employing a steerable beam antenna, and comprising a receiver for providing a boresight error signal indicative of target sightline by comparison of sum and difference signals derived from target reflection, means for providing an antenna beam steering signal in response to said boresight error signal, means for providing a missile guidance signal in response to said boresight error signal, and stabilisation means for stabilising the antenna beam in space, said stabilisation means comprising angle rate sensing means adapted to be mounted on the missile body for providing a body rate signal, means whereby the antenna beam steering signal and the missile guidance signal are made responsive to said body rate signal in such manner as to tend to decouple the antenna and guidance control from missile body movement, and means for correlating said body rate signal with a signal indicative of said target sightline and further decoupling said sightline from said body movement in dependence upon the degree of correlation.

14 A radar system according to Claim 3, wherein said Kalman filter employs as state estimates: boresight error, sightline spin rate, target lateral acceleration and gyro scale factor.

5. A radar system according to Claim 3 or Claim 4, for target tracking in three dimensions and employing an antenna beam steerable in azimuth and elevation, and including means for estimating azimuth and elevation beam steering demands, means for estimating sightline yaw and pitch rates, means for estimating target transverse accelerations, and means for estimating gyro correction factors in respect of missile yaw, roll and pitch, said Kalman filter employing state estimates corresponding to each of these factors.

7. A radar system according to Claim 1 or Claim 2, and comprising Kalman filter sections respectively providing from azimuth and elevation outputs of said receiver estimates of azimuth and elevation boresight error, one said filter section employing state estimates comprising azimuth boresight error, sightline yaw rate, and target lateral transverse acceleration, and the other said filter section employing state estimates comprising elevation boresight error, sightline pitch rate and target vertical transverse acceleration, the system including means for deriving the sightline roll rate, means for cross coupling the sightline yaw estimate from one filter section into the sightline pitch estimation of the other filter section nd vice versa, means for cross coupling the target transverse acceleration estimate of each filter section into the target transverse acceleration estimation of the other filter section, means for introducing as a multiplying factor in each said cross coupling a measure of the sightline roll rate, and correlation means for correlating output signals of said receiver with yaw, pitch and roll body rate signals for 1) for producing scale factor correction factors in respect of yaw, pitch and roll gyros constituting said angle rate sensing means, said correction factors being applied to the derivation of azimuth and elevation body rate measurements and to the derivation of sightline roll rate, respectively.

10. A radar system substantially as heréinbefore described with reference to Figure)4 11. A radar system substantially as hereinbefore described with reference to Figure 7.