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.
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.
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