Phillip L. Ainsleigh

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.

A B-wavelet-based noise-reduction algorithm

A wavelet-based method is introduced for removing structured noise (e.g., impulsive spikes or unwanted harmonic components) from data. For this type of noise, the time- and frequency-localization capabilities of wavelets provide better noise detection and less signal distortion than direct filtering of data. The procedure is applied to time-series data with impulsive noise and transfer-function data with multipath interference. The authors use a single set of scaling and wavelet bases that can effectively represent a wide range of signals, and then they perform noise reducing operations on the scaling and wavelet coefficients. Multiresolution analysis is introduced in order to describe the noise reduction algorithm.

Observations on oblique projectors and pseudoinverses

Oblique projectors (which were examined by Behrens and Scharf (see ibid., vol.42, no.6, p.1413-24, 1994)) are related to earlier work on oblique pseudoinverses and constrained least-squares methods and are reconsidered from the standpoint of orthogonal basis vectors and QR factorizations. Construction algorithms are presented that are numerically more stable than the normal-equations constructions previously used.

A Modified JPDA

This paper presents a coupled, joint probabilistic data association (JPDA) algorithm for multi-target tracking using a modified version of the standard measurement-to-track assignment model. The mutually exclusive nature of standard JPDA association events precludes any measurement being associated with more than one target in a given event. This constraint is relaxed here to allow a measurement to be assigned to multiple targets. All other JPDA assumptions are retained (i.e., no measurement can be simultaneously associated with target and clutter, and each track can claim at most one measurement). The computational requirements of the resulting algorithm grow linearly with the number of tracks. The recursive estimators for the coupled track means and covariance are derived and presented

Classification of nonstationary narrowband signals using segmented chirp features and hidden Gauss-Markov models

A method is provided for classifying finite-duration signals with narrow instantaneous bandwidth and dynamic instantaneous frequency (IF). In this method, events are partitioned into nonoverlapping segments, and each segment is modeled as a linear chirp, forming a piecewise-linear IF model. The start frequency, chirp rate, signal energy, and noise energy are estimated in each segment. The resulting sequences of frequency and rate features for each event are classified by evaluating their likelihood under the probability density function (PDF) corresponding to each narrowband class hypothesis. The class-conditional PDFs are approximated using continuous-state hidden Gauss-Markov models (HGMMs), whose parameters are estimated from labeled training data. Previous HGMM algorithms are extended by dynamically weighting the output covariance matrix by the ratio of the estimated signal and noise energies from each segment. This covariance weighting discounts spurious features from segments with low signal-to-noise ratio (SNR), making the algorithm more robust in the presence of dynamic noise levels and fading signals. The classification algorithm is applied in a simulated three-class cross-validation experiment, for which the algorithm exhibits percent correct classification greater than 97% as low as -7 dB SNR.

Accurate Likelihood Evaluation for Multiple Model PMHT Algorithms

A variety of authors have incorporated multiple target motion models into the probabilistic multi-hypothesis tracking (PMHT) algorithm using a discrete Markov chain to model the motion model switching process. However, in these papers the observed data likelihood function is not written down for this model, nor is it evaluated because all possible model assignment sequences must be considered over the PMHT batch. These two issues are addressed in this paper under the assumption that the Markov chain switching model affects the target state process but not the target measurement process: the observed data likelihood function for the PMHT algorithm is given along with a method for evaluating it. A closely related method of including multiple target motion models in the PMHT algorithm that results in a finite mixture distribution of motion models is described as well. In addition, it is shown that using multiple-model smoothing algorithms such as an IMM smoother to estimate the target states in a multiple model PMHT algorithm will not maximize the observed data likelihood function. Finally, it is shown that the MAP target state estimates for linear Gaussian targets with multiple motion models can be computed using a bank of Kalman smoothers. This result fills a gap in the existing literature.

Acoustic echo detection and arrival-time estimation using spectral tail energy

An algorithm is introduced for detecting signal and echo onsets and estimating their arrival times in multipath acoustic data. The algorithm accommodates superimposed narrow-band signals with continuous onsets, unknown envelopes, and arrival-time separations of less than one cycle at the dominant tonal frequency. It does not require the multipath components to be shifted and weighted replicas of each other or of a template signal. The separation of closely spaced signals is enabled by applying a prefilter that isolates spectral “tail” energy in which the onsets are discernible, and by operating on the filtered data using a matched-subspace detector that is conditioned on previously detected onsets. This algorithm has particular value for laboratory measurements, as it utilizes the high signal-to-noise ratios available in a laboratory to solve a previously intractable detection and estimation problem.

Characterization of transient wandering tones by dynamic modeling of fractional-Fourier features

A novel approach is presented for characterizing transient wandering tones. These signals are segmented and approximated as time series with piecewise linear instantaneous frequency and piecewise constant amplitude. Frequency rate, center frequency, and energy features are estimated in each segment of data using chirped autocorrelations and the fractional Fourier transform. These features are tracked across segments using linear dynamical models whose parameters are estimated using an expectation-maximization algorithm. A new cross-covariance estimator for adjacent states of the dynamical model is given. The feature extraction/tracking algorithm is used to characterize a measured marine-mammal vocalization. Application of the representation algorithm to signal classification is discussed.

A Modified PDAF Algorithm For Measurement Covariances that Vary within a Time Scan

This paper presents a modified version of the probabilistic data association filter (PDAF) algorithm for single target tracking which allows for measurement covariances to vary within, as well as between, time scans. This modification enhances the ability to track targets in situations where the measurement errors within a time scan are highly variable. The potential for improved tracking is demonstrated by comparing the performance of the modified and the standard algorithm in tracking simulated intensity detector measurements.

Performance of multiple-model filters and parameter-sensitivity analysis for likelihood evaluation with shock variance models

The performance of multiple-model filtering algorithms is examined for shock-variance models, which are a form of linear Gaussian switching models. The primary aim is to determine whether existing multiple-model filters are suitable for evaluating measurement likelihoods in classification applications, and under what conditions such classification models are viable. Simulation experiments are used to empirically examine the likelihood-evaluation performance of suboptimal merging and pruning algorithms as the number of state hypotheses per time step (i.e., algorithm order) increases. The second-order generalized pseudo-Bayes or (GPB(2)) algorithm is found to provide excellent performance relative to higher order GPB algorithms through order five. Likelihoods from fixed-size pruning (FSP) algorithms with increasing numbers of state hypotheses are used to validate the GPB likelihoods, and convergence of the FSP likelihoods to the GPB values is observed. These results suggest that GPB(2) is a reasonable approximation to the unrealizable optimal algorithm for classification. In all cases except very-low-noise situations, the interacting multiple model (IMM) algorithm is found to provide an adequate approximation to GPB(2). Sensitivity of likelihood estimates to certain model parameters is also investigated via a mismatch analysis. As a classification tool, the discrimination capabilities of the measurement likelihoods are tested using an idealized forced-choice experiment, both with ideal and with mismatched models