Interacting multiple model tracking with target amplitude feature

A recursive tracking algorithm is presented which uses the strength of target returns to improve track formation performance and track maintenance through target maneuvers in a cluttered environment. This technique combines the interacting multiple model (IMM) approach with a generalized probabilistic data association (PDA), which uses the measured return amplitude in conjunction with probabilistic models for the target and clutter returns. Key tracking decisions can be made automatically by assessing the probabilities of target models to provide rapid and accurate decisions for both true track acceptance and false track dismissal in track formation. It also provides the ability to accurately continue tracking through coordinated turn target maneuvers     

An interacting multiple model approach for target tracking withglint noise

The application of the interacting multiple model (IMM) estimation approach to the problem of target tracking when the measurements are perturbed by glint noise is considered. The IMM is a very effective approach when the system has discrete uncertainties in the dynamic or measurement model as well as continuous uncertainties. It is shown that this method performs better than the “score function” method. It is also shown that the IMM method performs robustly when the exact prior information of the glint noise is not available     

A recursive multiple model approach to noise identification

Correct knowledge of noise statistics is essential for an estimator or controller to have reliable performance. In practice, however, the noise statistics are unknown or not known perfectly and thus need to be identified. Previous work on noise identification is limited to stationary noise and noise with slowly varying statistics only. An approach is presented here that is valid for nonstationary noise with rapidly or slowly varying statistics as well as stationary noise. This approach is based on the estimation with multiple hybrid system models. As one of the most cost-effective estimation schemes for hybrid system, the interacting multiple model (IMM) algorithm is used in this approach. The IMM algorithm has two desirable properties: it is recursive and has fixed computational requirements per cycle. The proposed approach is evaluated via a number of representative examples by both Monte Carlo simulations and a nonsimulation technique of performance prediction developed by the authors recently. The application of the proposed approach to failure detection is also illustrated     

Tracking in clutter with nearest neighbor filters: analysis andperformance

The measurement that is “closest” to the predicted target measurement is known as the “nearest neighbor” (NN) measurement in tracking. A common method currently in wide use for tracking in clutter is the so-called NN filter, which uses only the NN measurement as if it were the true one. The purpose of this work is two fold. First, the following theoretical results are derived: the a priori probabilities of all three data association events (updates with correct measurement, with incorrect measurement, and no update), the probability density functions (pdfs) of the NN measurement conditioned on the association events, and the one-step-ahead prediction of the matrix mean square error (MSE) conditioned on the association events. Secondly, a technique for prediction without recourse to expensive Monte Carlo simulations of the performance of tracking in clutter with the NN filter is presented. It can quantify the dynamic process of tracking divergence as well as the steady-state performance. The technique is a new development along the line of the recently developed general approach to the performance prediction of algorithm with both continuous and discrete uncertainties     

Track segment association, fine-step IMM and initialization with Doppler for improved track performance

In this work we present a new track segment association technique to improve track continuity in large-scale target tracking problems where track breakages are common. A representative airborne early warning (AEW) system scenario, which is a challenging environment due to highly maneuvering targets, close target formations, large measurement errors, long sampling intervals, and low detection probabilities, provides the motivation for the new technique. Previously, a tracker using the interacting multiple model (IMM) estimator combined with an assignment algorithm was shown to be more reliable than a conventional Kalman filter based approach in tracking similar targets but it still yielded track breakages due to the difficult environment. In order to combine the broken track segments and improve track continuity, a new track segment association algorithm using a discrete optimization approach is presented. Simulation results show that track segment association yields significant improvements in mean track life as well as in position, speed, and course rms errors. Also presented is a modified one-point initialization technique with range rate measurements, which are typically ignored by other initialization techniques, and a fine-step IMM estimator, which improves performance in the presence of long revisit intervals. Another aspect that is investigated is the benefit of "deep" (multiframe or N-dimensional, with N > 2) association, which is shown to yield significant benefit in reducing the number of false tracks.     

Angle estimation for two unresolved targets with monopulse radar

Most present-day radar systems use monopulse techniques to extract angular measurements of sunbeam accuracy. The familiar "monopulse ratio" is a very effective means to derive the angle of a single target within a radar beam. For the simultaneous estimation of the angles of two closely-spaced targets, a modification on the monopulse ratio was derived in (Blair and Pearce, 2001), while (Sinha et al., 2002) presented a maximum likelihood (ML) technique via numerical search. In this paper it is shown that the ML solution can in fact be found explicitly, and the numerical search of ((Sinha et al., 2002) is unnecessary. However, the ML solution requires the signal to noise ratio (SNR) for each target to be known, and hence we generalize it so it requires only the relative SNR. Several versions of expectation maximization (EM) joint angle estimators are also derived, these differing in the degree to which prior information on SNR and on beam pattern are assumed. The performances of the different direction-of-arrival (DOA) estimators for unresolved targets are studied via Monte Carlo, and it is found that most have similar performance: this is remarkable since the use of prior information (SNR, relative SNR, beam pattern) varies widely between them. There is, however, considerable performance variability as a function of the two targets' off-boresight angles. A simple combined technique that fuses the results from different approaches is thus proposed, and it performs well uniformly.     

Exact multisensor dynamic bias estimation with local tracks

An exact solution is provided for the multiple sensor bias estimation problem based on local tracks. It is shown that the sensor bias estimates can be obtained dynamically using the outputs of the local (biased) state estimators. This is accomplished by manipulating the local state estimates such that they yield pseudomeasurements of the sensor biases with additive noises that are zero-mean, white, and with easily calculated covariances. These results allow evaluation of the Cramer-Rao lower bound (CRLB) on the covariance of the sensor bias estimates, i.e., a quantification of the available information about the sensor biases in any scenario. Monte Carlo simulations show that this method has significant improvement in performance with reduced rms errors of 70% compared with commonly used decoupled Kalman filter. Furthermore, the new method is shown to be statistically efficient, i.e., it meets the CRLB. The extension of the new technique for dynamically varying sensor biases is also presented.     

Ballistic missile track initiation from satellite observations

An algorithm is presented to initiate tracks of a ballistic missile in the initial exoatmospheric phase, using line of sight (LOS) measurements from one or more moving platforms (typically satellites). The major feature of this problem is the poor target motion observability which results in a very ill-conditioned estimation problem. The Gauss-Newton iterative least squares minimization algorithm for estimating the state of a nonlinear deterministic system with nonlinear noisy measurements has been previously applied to the problem of angles-only orbit determination using more than three observations. A major shortcoming of this approach is that convergence of the algorithm depends strongly on the initial guess. By using the more sophisticated Levenberg-Marquardt method in place of the simpler Gauss-Newton algorithm and by developing robust new methods for obtaining the initial guess in both single and multiple satellite scenarios, the above mentioned difficulties have been overcome. In addition, an expression for the Cramer-Rao lower bound (CRLB) on the error covariance matrix of the estimate is derived. We also incorporate additional partial information as an extra pseudomeasurement and determine a modified maximum likelihood (ML) estimate of the target state and the associated bound on the covariance matrix. In most practical situations, probabilistic models of the target altitude and/or speed at the initial point constitute the most useful additional information. Monte Carlo simulation studies on some typical scenarios were performed, and the results indicate that the estimation errors are commensurate with the theoretical lower bounds, thus illustrating that the proposed estimators are efficient