Tracking of crossing targets with imaging sensors

The authors present an algorithm for the tracking of crossing targets using the centroid measurement and the centroid offset measurement of the distributed image formed by the targets. The measurements are obtained by a forward-looking infrared (FLIR) imaging sensor. The joint probabilistic data association merged-measurement coupled filter (JPDAMCF) is used for state estimation which performs filtering in a coupled manner for the targets with common measurements. Two filters are examined: one assuming the displacement noise white and the other one modeling it correctly as autocorrelated. The latter is shown to yield substantially better performance. The proposed algorithm demonstrates the usefulness of the JPDAMCF for tracking crossing targets in combination with the models for the centroid and offset measurements. Even though the centroid offset measurement requires more computations and a more complex model for estimation, it yields significantly better results if the filter accounts for its colored measurement noise     

Comments on `Comparison of two-sensor tracking methods based onstate vector fusion and measurement fusion' by J. Roecker et al

As shown in the above named work (ibid., vol.24, p.447-9, July, 1988), the improvement in the centralized scheme over the decentralized one was shown to be about 6-8%. The reason is briefly described     

Joint probabilistic data association for autonomous navigation

A new autonomous navigation scheme based on the joint probabilistic data association (JPDA) approach that processes landmark detections in the field of view (FOV) of an on-board sensor is developed. These detections-some true, some false-are associated to a set of stored landmarks and used to update the state of the vehicle. The results obtained from Monte Carlo simulations prove the ability of this navigation filter to perform in very high false alarm environments. In the different environmental conditions tested in the simulations, the performance of the JPDA navigation filter (JPDANF) is very close to that of the filter based on perfect data association. The very efficient cluster decomposition algorithm presented for the purpose of the navigation problem can also be used in many multitarget tracking applications     

DOA estimation using one-bit quantized measurements

The effects 1-bit quantization of the input samples has on the direction-of-arrival (DOA) estimation accuracy are considered. The signal model assumes a single stochastic Gaussian point source that is embedded in white Gaussian noise (WGN). The inherent limitations governed by the extreme clipping of the input data are analyzed using the Cramer-Rao bound (CRB) that is derived for a two-sensor array. In addition, several estimators for the I-bit estimation are discussed. Numerical and analytical analyses of the estimation error reveal weak dependency on signal-to-noise ratio (SNR) with singular behavior of the estimation error in certain DOA angles.     

Detection threshold selection for tracking performance optimization

A technique for the evaluation of the track loss probability and the estimation error during track maintenance in clutter has been developed recently by the authors. This work overcomes the limitation of an earlier technique that does not handle the transient process of tracking divergence. Track loss, being a “runaway” phenomenon, clearly requires transient evaluation capability. The new technique provides, without the need for expensive Monte Carlo simulations, the probability that a hack is maintained in the presence of all sources of uncertainty encountered In a tracking process. This technique is of a hybrid nature; it involves explicit probabilistic accounting of both the continuous and the discrete uncertainties. Here it is demonstrated how this technique can be used for the selection of the detection threshold to optimize the overall performance of a detection-trading system     

Bias compensation and tracking with monopulse radars in the presence of multi path

The problem of tracking targets in the presence of reflections from sea or ground is addressed. Both types of reflections (specular and diffuse) are considered. Specular reflection causes large peak errors followed by an approximately constant bias in the monopulse ratio, while diffuse reflection has random variations which on the average generate a bias in the monopulse ratio. Expressions for the average error (bias) in the monopulse ratio due to specular and diffuse reflections and the corresponding variance in the presence of noise in the radar channels are derived. A maximum maneuver-based filter and a multiple model estimator are used for tracking. Simulation results for five scenarios, typical of sea skimmers, with Swerling III fluctuating radar cross sections (RCSs) indicate the significance and efficiency of the technique developed in this paper-a 65% reduction of the rms error in the target height estimate.     

Coordinate Conversion and Tracking for Very Long Range Radars

The problem of tracking with very long range radars is studied in this paper. First, the measurement conversion from a radar's r-u-v coordinate system to the Cartesian coordinate system is discussed. Although the nonlinearity of this coordinate transformation appears insignificant based on the evaluation of the bias of the converted measurements, it is shown that this nonlinearity can cause significant covariance inconsistency in the conventionally converted measurements (CM1). Since data association depends critically on filter consistency, this issue is very important. Following this, it is shown that a suitably corrected conversion (CM2) eliminates the inconsistency. Then, initialized with the converted measurements (using CM2), four Cartesian filters are evaluated. It is shown that, among these filters, the converted measurement Kalman filter with second order Taylor expansion (CM2KF) is the only one that is consistent for very long range tracking scenarios. Another two approaches, the range-direction-cosine extended Kalman filter (ruvEKF) and the unscented Kalman filter (UKF) are also evaluated and shown to suffer from consistency problems. However, the CM2KF has the disadvantage of reduced accuracy in the range direction. To fix this problem, a consistency-based modification for the standard extended Kalman filter (E1KF) is proposed. This leads to a new filtering approach, designated as measurement covariance adaptive extended Kalman filter (MCAEKF). For very long range tracking scenarios, the MCAEKF is shown to produce consistent filtering results and be able to avoid the loss of accuracy in the range direction. It is also shown that the MCAEKF meets the posterior Carmer-Rao lower bound for the scenarios considered.     

Radar power multiplier for acquisition of low observables using anESA radar

In this paper the acquisition of a low observable (LO) incoming tactical ballistic missile using the measurements from a surface based electronically scanned array (ESA) radar is presented. We present a batch maximum likelihood (ML) estimator to acquire the missile while it is exo-atmospheric. The proposed estimator, which combines ML estimation with the probabilistic data association (PDA) approach resulting in the ML-PDA algorithm to handle false alarms, also uses target features. The use of features facilitates target acquisition under low signal-to-noise ratio (SNR) conditions. Typically, ESA radars operate at 13-20 dB, whereas the new estimator is shown to be effective even at 4 dB SNR (in a resolution cell, at the end of the signal processing chain) for a Swerling III fluctuating target, which represents a significant counter-stealth capability. That is, this algorithm acts as an effective “power multiplier” for the radar by about an order of magnitude. An approximate Cramer-Rao lower bound (CRLB), quantifying the attainable estimation accuracies and shown to be met by the proposed estimator, is derived as well     

Applications of level crossing theory to target intervisibility: to be seen or not to be seen?

Here we discuss intervisibility (the existence of an unobstructed line of sight (LOS) between two points) accounting for the vertical and horizontal errors in the estimated locations of both points as well as elevation errors in the database of the terrain that could obstruct the LOS between these points. The errors are first simply treated as a "white" noise sequence: we assume no correlation between the intervisibility at two different times, and the probability of an instantaneous intervisibility event is in this case developed. This is useful; but perhaps of greater concern is whether or not a target remains visible long enough and/or often enough that its motion can be tracked? Consequently, we present a second treatment in which the errors are stochastic processes of a certain bandwidth, and both the probability density function (pdf) of an intervisibility interval and the average number of intervisibility intervals over a certain time period are developed.