In a multi-target multi-measurement environment, knowledge of the measuresnent-Lo-trk assignments is typally unavailable to the traking algorithm. In this r, a strictly probabiIist apoah to the measiwesnag-so-trk assignment problem is taken. Measurements are it assigned to tracks as in traditional multi-hypothesis tracking (Mill) algoriihms instead, the prObability that eh measurement belongs to eh track is estimated using a maximum Iikeiihond (ML) algorithm derived by the method of Expectafion-Maximization (EM). These measurement-to-trk probability estimates arc intrinsic to the multi-target tracker called the probabilistic multi-hypothesis trking (PMWF) algorithm. Unlike MHT algorithms, the PMHT algorithm does zt maintain explicit hypothesis lists. The PMHT algorithm is computatkxially practical because it requires neither enumaation of measurement-to-trk assignments nor pruning.

A maximum likelihood method is presented for training probabilistic neural networks (PNN's) using a Gaussian kernel, or Parzen window. The proposed training algorithm enables general nonlinear discrimination and is a generalization of Fisher's method for linear discrimination. Important features of maximum likelihood training for PNN's are: 1) it economizes the well known Parzen window estimator while preserving feedforward NN architecture, 2) it utilizes class pooling to generalize classes represented by small training sets, 3) it gives smooth discriminant boundaries that often are "piece-wise flat" for statistical robustness, 4) it is very fast computationally compared to backpropagation, and 5) it is numerically stable. The effectiveness of the proposed maximum likelihood training algorithm is assessed using nonparametric statistical methods to define tolerance intervals on PNN classification performance.

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Absfrucf-Conventional trackers are point trackers. Tracking energy on a field of sensor cells requires windowing, thresholding, and interpolating to arrive at data points to feed the tracker. This scheme poses problems when tracking energy that is distributed across many cells. Such signals are sometimes termed "over-resolved.'' It has been suggested that tracking could be improved by decreasing the resolution of the signal processor, so that the cells are large enough to encompass the bulk of the energy, and better match the point tracker assumptions. Larger arrays provide greater resolution at lower frequencies, with the potential for improved detection and classification performance, but in direct conflict with tracking "over-resolved" signals. These issues are addressed by the histogram-based probabilistic multi-hypothesis tracking (PMHT) method discussed in this paper, which provides a means for modeling and tracking signals that may be spread across many sensor cells. This paper will focus on the initial development and testing of this algorithm for one-dimensional sensor data. Elements of the signal model, theory, and algorithm will be presented along with two frequency domain examples.

The track repulsion effect induces track swapping in difficult target-crossing scenarios. This paper provides a simple analytical model for the probability of successful tracking in this setting. The model provides a means to quantify the degree-of-difficulty in target-crossing scenarios. We analyze model-based performance predictions for a range of scenario parameters. Additionally, we provide simulation results with a multi-hypothesis tracker that confirm the increased performance challenge in crossing target settings as the ambiguity persists longer, i.e. as the targets cross more slowly.

Sometimes radar targets cross and become unresolved; this is a concern, but with a reasonable track depth and an appropriate merged-measurement model the concern is considerably mitigated. Sonar targets, however, can become merged (in the same beam) for considerably longer, particularly with bearing-only measurements. In such cases the crossing times can be 100 scans long, and no reasonable depth exists for an multi-frame tracker that can "see" both ends of the merged period. Further, there is a demonstrable tendency for estimated targets to repel each other as they are being tracked. In this paper we explore the hypothesis-oriented multi-hypothesis tracker (HO-MHT), an MHT approach that uses the new "rollout" optimization insight and the to give an appropriate and cost-effective means to rank hypotheses, and also the PMHT tracker that operates on batches of scans with linear computational complexity in most quantities. We show results in terms of estimation error (RMSE), consistency (NEES) and computational effort in both linear and beam-space tracking scenarios.

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