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Maximum likelihood training of probabilistic neural networks

A maximum likelihood method is presented for training probabilistic neural networks (PNNs) using a Gaussian kernel, or Parzen window. The proposed training algorithm enables general nonlinear discrimination and is a generalization of Fishers method for linear discrimination. Important features of maximum likelihood training for PNNs 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.

Training of homoscedastic hidden Markov models for automatic speech recognition

A method for training a speech recognizer in a speech recognition system is described. The method of the present invention comprises the steps of providing a data base containing acoustic speech units, generating a homoscedastic hidden Markov model from the acoustic speech units in the data base, and loading the homoscedastic hidden Markov model into the speech recognizer. The hidden Markov model loaded into the speech recognizer has a single covariance matrix which represents the tied covariance matrix of every Gaussian probability density function PDF for every state of every hidden Markov model structure in the homoscedastic hidden Markov model.

Maximum likelihood method for probabilistic multihypothesis tracking

In a multi-target multi-measurement environment, knowledge of the measurement-to-track assignments is typically unavailable to the tracking algorithm. In this paper, a strictly probabilistic approach to the measurement-to-track assignment problem is taken. Measurements are not assigned to tracks as in traditional multi-hypothesis tracking (MHT) algorithms; instead, the probability that each measurement belongs to each track is estimated using a maximum likelihood algorithm derived by the method of Expectation-Maximization. These measurement-to-track probability estimates are intrinsic to the multi-target tracker called the probabilistic multi-hypothesis tracking (PMHT) algorithm. Unlike MHT algorithms, the PMHT algorithm does not maintain explicit hypothesis lists. The PMHT algorithm is computationally practical because it requires neither enumeration of measurement-to-track assignments nor pruning.

Track before Detect Algorithms

1 Surface Radar, Thales Nederland B.V. Haaksbergerstraat 49, 7554 PA Hengelo, The Netherlands 2NURC, NATO Research Centre, Viale S. Bartolomeo 400, 19126 La Spezia, Italy 3German Defence Establishment (FGAN-FKIE), Neuenahrer Strasse 20, 53343 Wachtberg, Germany 4Naval Undersea Warfare Center, 1176 Howell Street, Newport, RI 02841-1708, USA 5Metron Inc., 11911 Freedom Drive, Suite 800, Reston, VA 20190, USA

Estimating the parameters of general frequency modulated signals

A general frequency modulated (GFM) signal characterizes the vibrations produced by compressors, turbines, propellers, gears, and other rotating machines in a dynamic environment. A GFM signal is defined as the composition of a real or complex, periodic, or almost-periodic carrier function with a real, differentiable modulation function. A GFM signal therefore contains sinusoids whose frequencies are (possibly nonintegral) multiples of a fundamental; to distinguish a GFM signal from a set of unrelated sinusoids, it is necessary to track them as a group. This paper develops the general frequency modulation tracker (GFMT) for one or more GFM signals in noise using the expectation/conditional maximization (ECM) algorithm that is an extension of the expectation-maximization (EM) algorithm. Three advantages of this approach are that the ratios (harmonic numbers) of the carrier functions do not need to be known a priori, that the parameters of multiple signals are estimated simultaneously, and that the GFMT algorithm exploits knowledge of the noise spectrum so that a separate normalization procedure is not required. Several simulated examples are presented to illustrate the algorithms performance.

Tracking on intensity-modulated sensor data streams

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, which provides a means for modeling and tracking signals that may be spread across many sensor cells. This paper focuses on the initial development and testing of this algorithm for one-dimensional sensor data. Elements of the signal model, theory, and algorithm are presented along with two frequency domain examples.

Tracking a general, frequency modulated signal in noise

A general, frequency modulated (GFM) signal characterizes the vibrations produced by compressors, turbines, propellers, gears and other rotating machines in a dynamic environment. A GFM signal is defined as the composition of a real or complex, periodic or almost periodic function (the carrier) with a real, differentiable function (the modulation). The paper develops a frequency domain tracking algorithm for a GFM signal in noise using the expectation-maximization (EM) algorithm. The primary advantage of this approach is the ratios (harmonic numbers) of the carrier function do not need to be known a priori. The tracking algorithm exploits knowledge of the noise spectrum so that a separate normalization procedure is not required. The noise spectrum is incorporated into the tracking algorithm in essentially the same way that a clutter or noise model is incorporated into the probabilistic multi-hypothesis tracking algorithm (PMHT). Consequently, the GFM signal tracking algorithm presented in this paper is a PMHT-style algorithm. The algorithms performance is compared to two other algorithms from the literature using Monte Carlo trials and a simulated signal.

Converting Bearings-OnlyMeasurements to Cartesian Coordinates

The lack of range information for passive measurements complicates sensor registration, requires one to address the arctangent functions singularities, and prevents one from applying existing polar to Cartesian conversion mappings. Consequently, a coordinate conversion method is developed for passive measurements using an integral representation. In addition, the existing coordinate conversion methods are shown to differ only by a constant multiplying each converted measurement and in the eigenvalues of the corresponding covariance matrix.

Extreme-value analysis for mlML-PMHT, Part 2: target trackability

The Maximum Likelihood Probabilistic Multi-Hypothesis Tracker (ML-PMHT) can be used as a powerful multisensor, low-observable, multitarget active tracker. It is a non-Bayesian algorithm that uses a generalized likelihood ratio test (GLRT) to differentiate between clutter and targets. We use a new method, initially developed to obtain the probability density function (pdf) of the maximum point in the ML-PMHT log-likelihood ratio (LLR) due to clutter, to now develop a pdf for the maximum value of the ML-PMHT LLR caused by a target. With expressions for the pdfs of the maximum points caused by both clutter (developed in a companion article) and a target, we can, for a given set of tracking parameters (signal-to-noise ratio, search volume, target measurement probability of detection, etc.), develop ML-PMHT tracker operating characteristic curves, similar to receiver operating characteristic curves for a detector. Since ML-PMHT can be thought of as an optimal algorithm in the sense that, as long as the target and the environment match the algorithms assumptions, all the information from all the available measurements can be used, and no approximations are necessary to get the algorithm to function, the analysis presented in this paper offers for the first time part of the answer to the fundamental question: Can a particular target be tracked?

MHT tracking for crossing sonar targets

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.