Roy L. Streit

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.

A comparison of the JPDAF and PMHT tracking algorithms

Here we analyze the tracking characteristics of a new data-association/tracking algorithm proposed by Streit and Luginbuhl, the probabilistic multi-hypothesis tracker (PMHT). The algorithm uses a recursive method (known amongst statisticians as the expectation-maximization or EM method) to compute in an optimal way the associations between the measurements and targets. Until now, no comparative performance analysis has been done. We compare the performance of this new scheme to that of a commonly used tracking algorithm, the joint probabilistic data association filter (JPDAF).

Multitarget Tracking of Distributed Targets Using Histogram-PMHT

Abstract Streit, R. L., Graham, M. L., and Walsh, M. J., Multitarget Tracking of Distributed Targets Using Histogram-PMHT, Digital Signal Processing 12 (2002) 394–404 The expectation-maximization method is applied to derive a stable tracking algorithm that uses the entire display (image) as its input data, completely avoiding peak picking and other data compression steps required to produce traditional point measurements. The algorithm links a histogram interpretation of the intensity data with the tracking method of probabilistic multihypothesis tracking (PMHT) and is thus referred to as H-PMHT. An example of H-PMHT applied to tracking in bearing on a passive sonar broadband display is provided.

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

Direct data fusion using the PMHT

We analyze the tracking characteristics of a new data-association/tracking algorithm proposed by Streit-Luginbuhl, the probabilistic multi-hypothesis tracking (PMHT) algorithm, in a multisensor environment. Given that in the formulation of the algorithm there is no constraint on the number of measurements originated per target, it is a natural candidate for direct fusion in the multi-sensor case, where a combined frame (assuming synchronicity among the sensors) may have more than one target-originated measurement. In this paper we compare the performance of this new algorithm to that of a commonly used multisensor tracking algorithm: the joint probabilistic data association filter with a centralized estimation-to-estimation fusion.

Tracking with distributed sets of proximity sensors using geometric invariants

We propose a new approach to forming an estimate of a target track in a distributed sensor system using very limited sensor information. This approach uses a central fusion system that collects only the peak energy information from each sensor and assumes that the energy attenuates as a power law in range from the source. A geometrical invariance property of the proximity of the distributed sensors relative to a target track is used to generate potential target track paths. Numerical simulation examples are presented to illustrate the practicality of the technique.

Probabilistic multi-hypothesis tracking in a multi-sensor, multi-target environment

In this paper the probabilistic multi-hypothesis tracking (PMHT) algorithm, a data fusion algorithm developed by Streit and Luginbuhl (1995), is extended to handle multiple sensors. In addition, performance of multi-target tracking algorithms is discussed in terms of the Cramer-Rao lower bound (CRLB) criterion that is computed from the marginalized measurement PMHT log-likelihood function. Simulation results for one set of scenarios are presented and an initialization procedure for the bearings only measurement case is recommended.

Hidden Gauss-Markov models for signal classification

Continuous-state hidden Markov models (CS-HMMs) are developed as a tool for signal classification. Analogs of the Baum (1972), Viterbi (1962), and Baum-Welch algorithms are formulated for this class of models. The CS-HMM algorithms are then specialized to hidden Gauss-Markov models (HGMMs) with linear Gaussian state-transition and output densities. A new Gaussian refactorization lemma is used to show that the Baum and Viterbi algorithms for HGMMs are implemented by two different formulations of the fixed-interval Kalman smoother. The measurement likelihoods obtained from the forward pass of the HGMM Baum algorithm and from the Kalman-filter innovation sequence are shown to be equal. A direct link between the Baum-Welch training algorithm and an existing expectation-maximization (EM) algorithm for Gaussian models is demonstrated. A new expression for the cross covariance between time-adjacent states in HGMMs is derived from the off-diagonal block of the conditional joint covariance matrix. A parameter invariance structure is noted for the HGMM likelihood function. CS-HMMs and HGMMs are extended to incorporate mixture densities for the a priori density of the initial state. Application of HGMMs to signal classification is demonstrated with a three-class test simulation.

Tracking, Association, and Classification: A Combined PMHT Approach

Abstract Davey, S., Gray, D., and Streit, R., Tracking, Association, and Classification: A Combined PMHT Approach, Digital Signal Processing12 (2002) 372–382 When tracking more than one object, a key problem is that of associating measurements with particular tracks. Recently, powerful statistical approaches such as probabilistic multihypothesis tracking (PMHT) and probabilistic least squares tracking have been proposed to solve the problem of measurement to track association. However, in practice other information may often be available, typically classification measurements from automatic target recognition algorithms, which help associate certain measurements with particular tracks. An extension to the Bayesian PMHT approach which allows noisy classification measurements to be incorporated in the tracking and association process is derived. Some example results are given to illustrate the performance improvement that can result from this approach.