W.D. Blair

Fixed-interval smoothing for Markovian switching systems

A suboptimal approach to the fixed-interval smoothing problem for Markovian switching systems is examined. A smoothing algorithm is developed that uses two multiple-model filters, where one of the filters propagates in the forward-time direction and the other one propagates in the backward-time direction. A backward-time filtering algorithm based on the interacting multiple model concept is also developed. Results from a simulation example are given to illustrate the performance of the smoothing algorithm with respect to that of filtering. The example involves radar tracking of a Mach 1 aircraft.

On the optimality of two-stage state estimation in the presence of random bias

Sufficient conditions for the optimality of a two-stage state estimator in the presence of random bias are derived. Under an algebraic constraint on the correlation between the state and bias process noises, the optimal estimate of the system state can be obtained as a linear combination of the output of the first stage (a bias-free filter) and the second stage (a bias filter). Because the algebraic constraint is restrictive in practice, the results indirectly indicate that for most practical systems the proposed solution to the two-stage estimation problem will be suboptimal. >

Benchmark problem for beam pointing control of phased array radar against maneuvering targets in the presence of ECM and false alarms

This paper extends an earlier benchmark problem for beam pointing control of a phased array radar to include the effects of false alarms and ECM. Multiple waveforms are included in the benchmark problem so that the radar energy can be coordinated with the tracking algorithm. The ECM includes a standoff jammer broadcasting wideband noise and targets attempting range gate pull off. The paper presents the radar model, the ECM techniques, the target scenarios, and performance criteria for the benchmark problem.

A two-stage Kalman estimator for state estimation in the presence of random bias and for tracking maneuvering targets

The authors provide the optimal solution of a two-stage estimation problem in the presence of random bias. Under an algebraic constraint, the optimal estimate of the system state can be obtained as a linear combination of the output of the first stage (a bias-free filter) and the second stage (a bias filter). The results presented provide a basis for assessing the suboptimality of a two-stage estimator when used for a specific system. By treating the bias vector as a target acceleration, the two-state Kalman estimator can be used for tracking maneuvering targets.<<ETX>>

Two-Stage Alpha-Beta-Gamma Estimator For Tracking Maneuvering Targets

The two-stage Alpha-Beta-Gamma Estimator is proposed as an alternative to adaptive gain versions of the Alpha-Beta and Alpha-Beta-Gamma filters for tracking maneuvering targets. The purpose of this paper is to accomplish constant gain, variable dimension filtering with a two-stage Alpha-Beta-Gamma Estimator which is derived from a two-stage Kalman estimator. The noise variance reduction matrix and steady-state error covariance matrix are given as a function of the steady-state gains. A procedure for filter parameter selection is also given along with techniques for maneuver response and gain scheduled initialization.

One-step fixed-lag smoothers for Markovian switching systems

Suboptimal approaches to the one-step fixed-lag smoothing problem for Markovian switching systems are examined in this paper. Two different methods for obtaining suboptimal smoothed estimates are given, where the methods differ by the sampling period upon which the state of the system is conditioned. For n models, the first method requires n/sup 2/ predictions and residual evaluations, while the second method requires n residual evaluations. Simulation results are presented to compare the performances of the two smoothers.

Tracking constant speed targets using a kinematic constraint

The tracking of constant speed, maneuvering targets is addressed through the use of a kinematic constraint. The trajectory of any constant speed target must satisfy the kinematic constraint A.V=0, where A and V are the target acceleration and velocity, respectively. The kinematic constraint is included in the filtering process is a pseudomeasurement. The formulation derived for the constraint equation provides significantly better tracking performance than the original formulation. The rationale for formulation given is discussed and the improvement in tracking performance achieved demonstrated through simulation results.<<ETX>>

Discrimination of target and RGPO echoes using frequency diversity

Range gate pull off (RGPO) is a deceptive electronic counter measure (ECM) that targets perform to cause the radar to break its track on the target. Targets performing RGPO utilize digital radio frequency memory (DRFM) to store the radar pulse and repeat the pulse at the radar with a controlled delay, so that the radar receives signals from the actual target and a false target. The use of frequency diversity in the discrimination of actual target echoes from the RGPO echoes is considered. The amplitudes of the target echoes are considered to be Rayleigh distributed, while the amplitude the RGPO echoes are considered to be fixed across the frequencies. Estimators of the amplitude parameters for Rayleigh and fixed-amplitude targets are presented along with algorithms for discriminating between fixed-amplitude and Rayleigh targets. The performance of the discrimination algorithms are illustrated through the results of Monte Carlo simulations.

Estimation and discrimination for Swerling targets

The radar cross section (RCS) of most targets is sensitive to the aspect angle of the target with respect to the radar and fluctuates from pulse-to-pulse or scan-to-scan. The RCS fluctuations are typically characterized as one of four Swerling types. Examining the receiver operating characteristic (ROCs) curves for detection of Swerling targets shows that Swerling targets of type 3 and 4 can be detected with similar probabilities at lower transmitted energy than that required by Swerling targets of type 1 or 2. Thus, effective discrimination between Swerling types can be used to improved the utilization of radar resources by coordinating the waveform type and duration with the target type. Since waveforms with frequency diversity that induces pulse-to-pulse fluctuations are of interest, parameter estimation and discrimination for Swerling targets of types 2 and 4 are considered in the paper. Maximum Likelihood (ML) estimation of the amplitude parameters (i.e., SNR) is developed for both Swerling types, and techniques for discriminating between Swerling 2 and Swerling 4 targets are discussed.

Detection of multiple unresolved Rayleigh targets using quadrature monopulse measurements

When the returns from two or more targets interfere (i.e., the signals are not resolved in the frequency or time domains) in an amplitude comparison monopulse radar system, the direction of arrival estimate indicated by the monopulse ratio can wander far beyond the angular separation of the targets. The failure to detect the presence of the interference can be catastrophic to the performance of the tracking algorithm. The detection of the presence of unresolved Rayleigh targets is considered in the paper. A Neyman-Pearson detection algorithm is developed with density functions that are conditioned on the measured amplitude of the target echoes, which will be shown to define the statistics of each measured monopulse ratio. The algorithm uses both the in-phase and quadrature portions of the monopulse ratios. Receiver operating characteristic curves are given along with simulation results that illustrate the application of the algorithm.