Abstract:
Emitter target range and heading are estimated from bearing measurements enhancing bearings-only estimator convergence to a target track, and permitting optimization of an observer position relative to the target at the end of the total bearing measurement period. One or more estimates of the target range, speed and heading made from bearing measurements before an observer maneuver are used to determine the most appropriate observer maneuver giving complete bearings-only target-motion-analysis observability. A set of parameters characterizing a set of potential emitter signal sources is generated based on measured emitter characteristics. A most probable set of emitter platforms is identified and the emitter operating mode and corresponding platform set are associated with a kinematic regime set. A specific speed or discrete set of speeds best adapted to a set of all possible platform missions, emitter speed as a continuous function of emitter range, and emitter range are all determined.

Description:
RELATED APPLICATION 
     The present application is related to co-pending patent application entitled “A METHOD OF PASSIVELY ESTIMATING AN EMITTER&#39;S POSITION AND VELOCITY USING BEARINGS-ONLY WITHOUT REQUIRING OBSERVER ACCELERATION” Ser. No. 10/419 193 and assigned to the instant assignee and filed on even date herewith and is hereby incorporated by reference into the present specification in its entirety. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates generally to radars, and more particularly, to bearings-only passive emitter tracking. Even more particularly, the present invention is related to a method of and apparatus for determining the optimum observer heading change in bearings-only passive emitter tracking. 
     A moving observer, e.g. an aircraft, able to measure bearings to an emitter, generates the range, speed and heading of the emitter based on the measured bearings. This bearings-only passive emitter tracking is called target motion analysis (TMA). Passive TMA is useful because emitters can be detected and tracked at much longer ranges than possible using active radar. 
     However, passive emitter tracking or ranging is intrinsically less accurate than active radar tracking and requires many bearing measurements, and hence, additional time to converge to a solution. Also bearings-only TMA requires the observer to maneuver at some point during the bearing measurement period. The fact that the observer does not know the emitter&#39;s location or velocity until after the observer has maneuvered introduces a large element of risk when aircraft use TMA for target tracking. 
     To combine bearing measurements with the requisite maneuver, the observer typically flies a doglegged course. Constant velocity tracks with frequent heading changes allow the estimator, i.e. the observer, to uniquely determine range and velocity based on the bearing measurements if the emitter is flying a constant velocity track. When a unique solution exists, the target location, speed and heading is said to be “observable.” The general concept of estimator observability is presented in Anderson and Moore,  Optimal Filtering , Prentice-Hall, New Jersey 1979. Fogel and Gavish, in “N th -Order Dynamics Target Observability from Angle Measurements”,  IEEE Transactions on Aerospace and Electronic Systems , AES-24, 3 (May 1988), describe the observability problem specifically for bearings-only passive emitter tracking. In particular, they demonstrate that heading change is sufficient to provide convergence to a unique solution when tracking a constant velocity target. 
     Prior methods of bearings-only target tracking, such as the method described by U.S. Pat. No. 5,877,998 (the &#39;998 patent) to Aidala, et at. in “Recursive Method for Target Motion Analysis” emphasize such observer motion. The &#39;998 patent refers to observer tracks as data collection legs. In the &#39;998 patent, bearing measurements from the first and second leg, are filtered to produce a smoothed bearing estimate, a bearing-velocity estimate, and a bearing-acceleration estimate. These estimates are used to generate target range and velocity. Further, the &#39;998 patent finds it desirable to incorporate at least a third, and possibly more, measurement legs to reduce estimation error. 
     The method disclosed in the &#39;998 patent and other current techniques for doing bearings-only TMA, fail to exploit the results presented by B. J. McCabe in “Accuracy and Tactical Implications of Bearings-Only Ranging Algorithms”,  Operations Research , Vol. 33, No. 1, 1985. McCabe showed that there is a preferred method in performing data collection over the first two legs. McCabe defines the tracking observer, or tracker, as leading the emitter if the velocity vectors  100 ,  101  (FIG. 1 a ) are on the same side of the line-of-sight (LOS) vector  105  when the first data collection leg begins. The tracker lags if tracker velocity vector  102  (FIG. 1 b ) and the target velocity vector  103  are on opposite sides of the LOS vector  106 . 
     Hence, a two leg maneuver, as required by Aidala, may be either a lead followed by a lag, or vice-versa. A lead-lag observer maneuver occurs when both emitter and observer velocity vectors are initially on the same side of the line-of-sight, then after performing a maneuver the vectors are on opposite sides. A lag-lead observer maneuver occurs when the observer velocity vector is initially on the opposite side of the line-of-sight to the emitter&#39;s velocity vector, then the velocity vectors are on the same side after performing a maneuver. The two leg maneuver could also be a lead-lead or a lag-lag maneuver. McCabe describes that among all possible two leg maneuvers the lead-lag (FIG. 1 a ) is much preferred in conventional TMA. For instance, the estimated range error at the end of the lead-lag maneuver can, theoretically, be only 20% of the lag-lead (FIG. 1 b ) error. Thus, if the lead-lag maneuver is performed, a third leg  104  (FIG. 1 b ) to reduce estimation error would not be required in a significant number of cases. Furthermore, by a straightforward extension of McCabe&#39;s work it can be shown that both lead-lag and lag-lead maneuvers are generally superior to the other dogleg maneuver combinations. 
     As McCabe noted, conventional TMA implementations, such as that described by Aidala, are unable to take advantage of the above facts. At the start of TMA, the tracker does not know whether it is leading or lagging the emitter because the emitter&#39;s velocity vector is not known. Because of the observability constraint discussed by Fogel and Gavish, the velocity vector is not obtained until the second leg. 
     This has potentially dire tactical consequences when the observer is a high-speed aircraft , such as an air-intercept (AI) jet, engaging a high speed threat. Not only can McCabe&#39;s results not be exploited, but if the Al aircraft is initially leading the target, inadvertently performing a suboptimal lead-lead maneuver may put the aircraft in a vulnerable position. But executing the optimal lead-lag maneuver, i.e. turning away on the second leg, may cause the aircraft to fail to intercept the target. Thus, it is vitally important for tactical aircraft performing TMA to know where they will be relative to the emitter at the end of the data collection legs, both for self-protection and the potential for enhanced performance from data collection maneuvers. However, the tracker must obtain the emitter heading prior to executing the first turn in order to determine the target&#39;s relative position. In current TMA implementations, the observer cannot determine the target&#39;s relative position prior to executing the first turn based on the above-described observability constraint. 
     One way to avoid both the “require the track to best estimate the track” paradox and the TMA observer-maneuver vulnerability problem is using the technique described in the present inventor&#39;s patent disclosure entitled, “A Method for Passively Estimating an Emitter&#39;s Position and Velocity Using Bearings-Only Without Requiring Observer Acceleration,” Ser. No. 10/419193, hereinafter referred to as “inventor&#39;s co-pending application” filed on even date herewith and incorporated by reference by its entirety into the instant specification. The method described in the aforementioned patent application avoids the observability constraint. That is, obtaining emitter range, speed and heading does not require the observer to fly a dogleg course, or otherwise accelerate. The described method obtains emitter range by estimating speed in two ways: (1) using platform and mission identification to estimate a discrete target speed; and (2) obtaining speed from bearing rates-of-change, but as a function of unknown range. Equating the functionality speed with the discrete speed determines emitter range. 
     The above-described approach performs well for many critical emitters. However, a large data base covering the performance of all platforms encountered is required in order to accurately estimate emitter speed. Usually, associating signal pulse parameters with target kinematics requires an artificial intelligence or expert system implementation. And even with an extensive data base and sophisticated logic, the track generated for a subset of emitters can be ambiguous because several discrete speeds are equally likely. This speed-ambiguity arises from a one-to-several radar-to-platform mapping, and also a one-to-several radar-mode to mission mapping. Breaking or reducing the ambiguities requires the use of elevation measurements. 
     For many installations, it is desirable to utilize aspects of the speed, heading and range estimation method disclosed in the inventor&#39;s co-pending application, but with only a simple generic platform database and simple logic. It is also desirable to not require an elevation array in order to break ambiguities. But, the simple data base and logic mean there will be many more speed ambiguities, and, even for one discrete speed, significant uncertainty about its correct value. Thus, while a complex implementation can achieve accuracies for many emitters of 5%, a simple implementation has errors typically at least three times greater than the complex implementation. 
     Thus, a need exists for a method which removes the vulnerability of a tactical aircraft associated with the observability maneuver, and makes the use of TMA for tactical aircraft practical. Another need is for a method using bearings-only TMA, without elevation measurements to resolve speed ambiguities and identify an emitter. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The present invention is illustrated by way of example, and not by limitation, in the figures of the accompanying drawings, wherein elements having the same reference numeral designations represent like elements throughout and wherein: 
     FIG. 1 a  graphically depicts a prior art lead-lag observer maneuver; 
     FIG. 1 b  depicts a prior art lag-lead maneuver; 
     FIG. 2 is a top level flow chart depicting the steps of performing the method according to an embodiment of the invention; 
     FIG. 3 a  is a detailed block diagram of a preferred implementation of the observer maneuver determination and TMA estimator initialization aspect of the present invention; 
     FIG. 3 b  is a detailed block diagram of a preferred implementation of the TMA track estimation aspect of the present invention; 
     FIG. 4 a  is a graph depicting the performance of an embodiment of the present invention using a lead-lag maneuver; and 
     FIG. 4 b  is a graph depicting the performance for a lag-lead maneuver in the FIG. 4 a  scenario, and graphically depicts the enhancement of lag-lead performance over that of conventional TMA so the initial convergence is comparable to lead-lag. 
    
    
     SUMMARY AND OBJECTS OF THE PRESENT INVENTION 
     It is thus an object of the present invention to combine TMA, which requires multiple data collection legs, and the single-leg track estimation approach described in inventor&#39;s co-pending application, in a manner overcoming the deficiencies in both and improving the performance of each. 
     The present invention utilizes TMA to resolve single-leg track speed estimate ambiguities, and particularly those arising from simplified implementations of inventor&#39;s co-pending application. Thus, the invention also improves the radar-platform-mission identification over that intrinsically obtainable in suboptimal implementations of inventor&#39;s co-pending application. In a sense, the invention deduces the mission from speed, rather than deducing speed from the mission, as performed in inventor&#39;s copending application. 
     The present invention requires the observer accelerations, typically heading changes, of conventional bearings-only passive ranging. The present invention eliminates the current shortcomings in the TMA maneuver because before maneuvering the observer knows the possible approximate speeds and headings of the target. Therefore, the present invention minimizes the vulnerability of the observer when executing the necessary TMA accelerations, and further allows the observer to exploit the optimal heading change results of McCabe. 
     It is another object of the present invention to provide a method which removes the vulnerability of a tactical aircraft associated with the observability maneuver, and makes possible the use of TMA for tactical aircraft. 
     Thus, it is another object of the present invention to enhance TMA estimator performance, and in particular lag-lead performance, by insuring the correct initialization of the estimator&#39;s state and error covariance, by at least one of the track estimates made using the method of the inventor&#39;s co-pending application, because inventor&#39;s co-pending application provides a mechanism for generating the most accurate a priori information available. 
     Still another object of the present invention is to reduce the amount of data collection required to obtain accurate track and the number of maneuvers that should be performed. 
     The present invention assures rapid convergence not only because the optimal maneuver is utilized, but also because the estimator a priori error statistics accurately match the initial state estimate provided by the filter algorithm. T. Nishimura, in “On the A Priori Information in Sequential Estimation,”  IEEE Transaction on Automatic Control , vol. AC-11, pp. 197-204, April 1966, has shown this is essential for optimal filter performance in the sense of most rapid convergence to an estimate having the smallest possible error. The difference in lead-lag and lag-lead performance for conventional TMA estimators is that lead-lag more quickly damps out a priori error. 
     Because the invention provides TMA the most rapid possible convergence to the emitter track both by optimal maneuver, and optimal estimator initialization, an accurate range estimate can be obtained at the very start of the second data collection leg. Thus, the invention reduces the overall amount of data collection required to obtain an accurate track, and the number of maneuvers that must be performed. 
     The present invention allows the use of a simplified implementation of the method of inventor&#39;s co-pending application. It uses bearings-only TMA, rather than elevation measurements, to resolve the speed ambiguities, and so does not require an elevation array. 
     The present invention also provides a means to utilize McCabe&#39;s results in optimizing TMA performance. Track estimates generated by the method of inventor&#39;s copending application initialize the bearings-only TMA estimator. The initial track estimates predict the relative observer-emitter positions after the data collection legs, eliminating the vulnerability due to uncertainty in observer-emitter geometry during the required maneuver. The initial track estimates also enhance the estimator convergence performance for lag-lead maneuvers so that performance rivals that of lead-lag. 
     Thus, by not only removing the potential vulnerability of the observability maneuver but also enhancing the performance of the lag-lead intercept, the invention makes the use of TMA for tactical aircraft much more practical and robust. 
     In accordance with the above objects and features, a method aspect according to an embodiment of the present invention describes a method of estimating target range and heading based on bearing measurements. One or more target characteristics are measured and a set of parameters characterizing a set of potential target signal sources is generated based thereon. Based on the set of potential target characterization parameters and a target data base, a most probable set of targets is identified and the mode of operation of the target and the corresponding target set are associated with a set of target kinematic regimes. A performance data base is used to: (1) derive from the set of target kinematic regimes a specific speed or discrete set of speeds best adapted to a set of all possible target missions, (2) generate from the target characteristic measurements one or more target bearings, (3) estimate from the one or more target bearings the target speed as a continuous function of target range, and (4) determine the target range consistent therewith by comparing the continuous target speed with the specific speed or the discrete set of speeds derived from the performance data base. 
     DESCRIPTION OF PREFERRED EMBODIMENTS 
     A logic flow chart of an embodiment of the present invention is depicted in FIG.  2 . Process steps  200  through  205  occur prior to the observability maneuver in step  210 . 
     Steps  200 - 205  are similar to the steps described in the inventor&#39;s copending application with a key difference. Unlike the aforementioned disclosure, the signal parameters extracted in step  200  are not required to uniquely or nearly uniquely identify the platform type in step  201 . Hence, a large set of speeds may be obtained in step  202 . Typically, the set may contain over twenty discrete speeds. Process steps  203  and  204  estimate speed as a function of unknown range and heading. These steps may be implemented as described in the aforementioned disclosure. Comparing this single continuous speed with each discrete speed from step  201  generates (step  205 ) a set of range and velocities consistent with each discrete speed. 
     As part of the ID emitting platform process (Step  201 ), an error for the discrete speed estimate is determined. The discrete speed estimate error is obtained from the performance data used to produce the speed estimate. Using the discrete speed estimate error, step  205  determines the variance in the range, speed and heading estimates, and the estimate cross correlations. The variance and cross correlation estimates form the elements of an a priori error covariance matrix used to initialize the TMA track estimator in step  207 . The range, speed, and heading estimates are also used to generate an initial state set in the process at step  207 . 
     Determining the best maneuver at step  206  is complicated by the fact that step  202  generally produces multiple speed estimates; however, the emitter headings generated from the speeds in step  205  cluster into a small number of sets relative to the optimum lead lag maneuver. In most cases, there will be only two sets and they will have the following important property: the lead-lag maneuver for one set results in a lag-lead maneuver for the other. Thus, even if the optimal maneuver is not correctly flown, the emitter track will be generated using the second best maneuver. The most common reason for not flying the lead-lag against the emitter is the misassignment of speed probability in step  202 ; however, self-defense is another key reason. Emitter identification in step  201  may provide signals at step  208  representing the ID of a threat that contravenes the most likely cluster determined from steps  202  and  205 . Thus, based on information  208  from the ID emitting platform step  201 , the observer can choose to fly a track minimizing vulnerability or resulting in an intercept rather than optimizing data collection. 
     Because there are a set of initial conditions, rather than just one initial condition as in conventional TMA, tracking filter initialization (step  207 ) requires establishing a track estimator for each initial state and initial a priori error variance estimate. The observability maneuver (step  210 ) is performed after step  206 . After the observability maneuver (step  210 ) is performed, the correctly initialized filter is determined (step  211 ) using the estimators from step  207  and the observability maneuver  210 . This determination exploits the performance characteristics described by the Nishimura reference. The actual mechanism used depends on the specific estimator implementation, but is generally based on the innovations or residual whitening property of optimal estimators, as described by Kailath, “An Innovations Approach to Least Squares Estimation-Part I: Linear Filtering in Additive White Noise,”  IEEE Trans. on Automatic Control , Vol. AC-13, No.6, December 1968. 
     In parallel with track determination, bearing data collection continues and is stored in step  209 . After step  210 , the optimum maneuver is performed, and the correct filter is determined at step  211 . The correct initial estimator state determination is fed back (step  212 ) to the platform identification process  201 , and the unique, correct platform is determined. Initial estimator state determination (step  211 ) typically uses all available bearing data from step  209  from the start of data collection to the current time. There may be data buffer size limitations preventing the storage of all data from the initial detection to current time. Emitter tracking at step  213  continues as bearing measurements are made. Using the estimator properties elucidated by the Kailath reference, step  214  determines whether another maneuver is required. Another maneuver may be required if step  205  failed to produce an a priori state consistent with the initial error variance estimate, or the maneuver requirement generated in step  206  did not result in a lead-lag maneuver. A determination of no further maneuver required, causes the process flow to continue to perform track estimation at step  216  until the required track fidelity is met. 
     The preceding description of the present invention shows there are two steps which require further discussion: step  206 , Determine Optimal Observer Maneuver; and step  211 , Determine Correct Initialization. 
     FIGS. 3 a  and  3   b  are block diagrams of a portion of an embodiment of the present invention. FIG. 3 a  depicts the detailed implementation of steps  200  through  207 , while FIG. 3 b  depicts a preferred implementation of the TMA track portion of the invention (steps  208  through  216 ). Because both the derived range, speed and heading estimates in step  205  (FIG. 2) and track estimate performed in steps  211  and  213  require accurate bearing rates of change, the preferred sensor  300  (FIG. 3 a ) is a short-baseline/long-baseline interferometer (SBI/LBI) as described in Kaplan, U.S. Pat. No. 4,734,702, “Passive Ranging Method and Apparatus.” The long baseline interferometer provides excellent bearing resolution, and supports very accurate bearing rate-of-change measurements. 
     Step  301  involves conventional Electronic Surveillance Measures (ESM) parameter extraction. The SBI phase measurement ambiguities are resolved, and bearing estimates derived from the extracted ESM parameters and used to resolve the LBI utilizing the method described by Kaplan. The combined SBI/LBI bearing estimates stored at step  329  (FIG. 3 b ) are input to step  303  to estimate the first and second derivatives with respect to time. The continuous speed function is generated from the relative heading vector in step  304 , as described in the co-pending application. 
     Step  305  is a subset of the process used to generate the discrete speed in the copending application. In particular, the platform identification determined at step  306  is not unique, as indicated by the multiple outputs (reference numeral  307 ), and the radar mode step  308 , rather than radar model, is identified. Therefore, unlike the implementation in the copending application, radar identification is typically not available for platform identification, and even the mode ID may not be unique, as indicated by the multiple outputs (reference numeral  309 ) from step  308 . Also, a flight envelope data base  311  and a power curve data base  312  are generic, and not specific to a particular aircraft. Thus, steps  311  and  312  refine the coarse speed estimates from step  310 , but the result  313  is a set of discrete speeds. Note that set  313  can be larger than the set initially generated in step  310 . The discrete speeds are compared with the continuous speed function in step  314 , and a set of range, speed, and heading triads output to the initial state generator  315 . 
     The initial state generator  315  transforms the range, speed, and heading triads, bearing measurements, and rate calculations to the particular state used by the estimator. The preferred state elements are modified polar coordinates  316 . The modified polar coordinates are bearing or azimuth a, azimuth rate {dot over (a)}, range rate divided by range {dot over (r)}/r, and inverse range 1/r. The modified polar state elements are desirable to use because, except for the last inverse range state element, all elements in the state vector are observable before the first maneuver. If elevation measurements arc available, elevation and elevation rate may be added to this state vector. 
     A preferred embodiment of the present invention is implemented such that elevation measurements are not required. At the longer distances of interest when performing passive TMA, aircraft are predominantly found in a ±5° elevation wedge relative to the level plane at the observer. Also, changes in relative altitude do not generate significant changes in elevation, except for close-in emitters and therefore the present invention does not benefit significantly from elevation measurements, in direct distinction to the invention of the copending application, where elevation measurements may play a crucial role. 
     The a priori error variance associated with the initial state vector  316  is determined by the uncertainty in the range, speed, and heading triad estimate and in the bearing measurements, and the particular transformations used to generate the state vector  316 . The uncertainty in the bearing measurement is a function of the signal-to-noise ratio and system calibration errors and is straightforward to determine. Errors in the triad estimate are predicated on the correct data base elements  311  and  312  being used to generate the discrete speed seed. For incorrect speeds, the error estimate can be proportionately wrong. Determined by the set of speed estimates  313 ,the set of initial states is shown schematically as candidate ranges and velocities  318 . Only one of the range-velocity pairs shown generates the correct initial state in the set of state vectors  316  generated in step  315 . The error variance is computed for each state vector  316  assuming the speed associated with that state is correct. 
     As is readily understood from the Nishimura reference, the potentially huge discrepancy between initial state and initial error variance estimate is disadvantageous for conventional TMA implementations. However, in the present invention the discrepancy is actually a benefit because the incorrect state is more easily detectable in the state hypothesis test  317 , FIG. 3 b . The state hypothesis test  317 , and a most probable initial state determination step  319 , implement step  211 , FIG. 2, Determine Correct Initial State. The implementation is performed by computing likelihood weights (step  323 ) according to the method described by Magill, “Optimal Adaptive Estimation of Sampled Stochastic Processes,”  IEEE Trans. Automatic Control , AC-10, vol.4, 1965. Each likelihood weight is based on an initial range and velocity represented conceptually by candidate ranges and velocities  318 FIG. 3 b  as, for example a range and velocity pair  325 , range r i  and velocity v i , i.e. speed and heading along an initial line of bearing  324 . The initial values each determine a separate tracking filter in set  322 . For example, (r i , v i )  325  is associated with a TMA tracker i  326 . 
     In the probability weight computation step  323 , the consistency, of the bearing predictions based on the estimator state, or equivalently the estimated range and velocity, is compared with the measured bearing utilizing a Bayes rule calculation (see, for example,  Bayesian Inference and Maximum Entropy Methods in Science and Engineering : 20 th International Workshop , Ali Mohammad-Djafari (Editor), American Institute of Physics, July 2001). 
     The Bayes rule calculation uses the error variance associated with the TMA tracker  322 . Ultimately, this error variance is associated with the initial error. Hence for probability weight  327 , which uses state and error variance estimates from tracker  1326 , the probability weight  327  has an assigned likelihood of the initialization  325 . 
     Thus, the resulting likelihood functions in effect assign probabilities to the range-velocity pairs shown in range and velocity candidates  318 FIG. 3 a  and FIG. 3 b . Each of the range-velocity pairs is assumed equally probable initially. The likelihoods are revised over time, as bearing measurements  329  are processed by each estimator. After several iterations, and after the observability maneuver (step  210  of FIG.  2 ), the initialization range-vclocity pairs located proximate the correct state value generate a subset of Bayes weights, or likelihoods, approaching  1 . The Bayes weights are utilized in step  319  to determine the correct estimator initialization. Step  319  determines the number of bearing measurements required to generate the requisite confidence that the weight values correctly reflect the relative fidelity of the initial state estimates  316 . The initial range-velocity state  325  found in process  319  is used to determine which TMA estimator of the TMA estimator set  322  correctly matches the emitter track. The single tracking filter of set  322  associated with the correct initialization is typically used for future calculations. The bank of tracking filters could be used and the single estimate from the Baysian weighted sum of the outputs generated; however, this approach is cumbersome once the correct initialize set is known. Thus, after sufficient bearing measurement iterations have generated the most probable Bayesian weight (as determined by comparing the Baysian weight to a predetermined threshold value), the single tracking filter is used in step  213 , FIG.  2 . However, an alternative approach would use the Bayesian weighted estimate of all the tracking filter state outputs. The weighted sum, or alternately the single filter iteration, is performed in a generate best current track estimate step  320 . Step  320  calculation determines a current state estimate  321  developed from the initial track estimate  328  using the bearing measurement sequence  329 . The Bayesian weights  317  are also provided to the platform ID step  201  (FIG.  2 ). Generally, one weight is significantly closer to 1 than the others, so uniquely determining the correct platform is straightforward. 
     An embodiment of the present invention in the form shown in FIG. 3 a  and FIG. 3 b  was implemented in a simulation. The target was a 10 GHz emitter at 100 nmi initially with a speed of 600 knots, heading 45° and altitude of 28,000 feet. The observer was flying at 480 knots due north at 31,000 feet. The LBI baseline was 200 inches, and signal SNR, after pulse averaging, was 25 dB. The sample rate was 1 Hz. The number of range-velocity pairs  325  (FIG. 3 b ) generated was  11 , but the clustering in process  314  resulted in only three initial state vectors  316  required. 
     FIG. 4 a  is a graph depicting the range error versus time performance for the observer performing a lead-lag maneuver with a 30° heading change between constant velocity data collection legs. The first leg was 6 seconds, followed by a standard rate 3° per second turn. The correctly initialized TMA estimator converged ( 402 , FIG. 4 a ) after four bearing updates following the heading change. The filter was selected in  319 FIG. 3 b , by a threshold test. The threshold was set at 0.9, and a correct likelihood value of 0.98. 
     FIG. 4 b  is a graph depicting the range error versus time performance for the same scenario, but for the observer performing a lag-lead maneuver. Unlike conventional TMA implementations, the hypothesis test implemented here resulted in TMA convergence even faster than for lead-lag. Convergence ( 400 FIG. 4 b ) actually occurred during the standard rate turn. This demonstrates that one of the main objects of the invention, to render lag-lead maneuver as effective as lead-lag maneuver by utilizing the initialization set  318  and hypothesis test  317 , was met. 
     However, it is important to note that lead-lag estimates of speed and heading are generally better than lag-lead. The target heading had random heading fluctuations with a correlation time of approximately 5 seconds, and standard deviation of about 3 degrees. The lead-lag long time straight leg performance  403  (FIG. 4 a ) indicates the tracking filter was able to continually refine the heading and speed estimate. However, the lag-lead estimates grew in error  401  (FIG. 4 b ) because of the inability to refine target velocity. This indicates additional observer maneuvers may be required for lag-lead when undertaking long term surveillance, but not in short-time tactical situations. It is precisely in such short-time tactical situations, involving emitter interception, that lag-lead maneuvers are most useful. 
     It will be readily seen by one of ordinary skill in the art that the present invention fulfills all of the objects set forth above. After reading the foregoing specification, one of ordinary skill be able to affect various changes, substitutions of equivalents and various other aspect of the invention as broadly disclosed herein. It is therefore intended that the protection granted hereon be limited only by the definition contained in the appended claims and equivalents thereof.