Hugh L. Kennedy

Controlling track coalescence with scaled Joint Probabilistic Data Association

Track coalescence is undesirable when estimating the states of multiple manoeuvring targets, with a less-than-unity probability of detection, in clutter. Simple and compound forms of coalescence are defined and discussed. Simple coalescence is when two or more identical tracks follow a single target; compound coalescence is when two or more identical tracks follow the midpoint (or centroid) of two or more targets. It is shown that the incidence of compound track coalescence in joint probabilistic data association (JPDA) may be reduced using a scaling factor to favour the most likely association hypothesis. This prevents multiple hypothesis equivalence when tracking closely-spaced or crossing targets. The performance of the scaled JPDA (SJPDA) algorithm is compared with probabilistic data association (PDA) and JPDA using real and simulated data. Larger scaling factors decrease the likelihood and duration of compound track coalescence; however, they also increase the likelihood of track divergence on clutter or other targets. A value of unity corresponds to JPDA. The optimal value may be chosen to suit the application. A factor of two was found to give good results in the test data.

Recursive Digital Filters With Tunable Lag and Lead Characteristics for Proportional-Differential Control

Regression analysis using orthogonal polynomials in the time domain is used to derive a digital filter with an infinite impulse response that satisfies maximally flat design constraints near dc. The low-frequency phase, and high-frequency gain, may be adjusted for lead or lag compensation of plant dynamics. Simulated design examples are used to show how the compensating filter may be intuitively tuned for the desired closed-loop response. It is shown that the second-order instantiation of the compensating filter reduces to a proportional-differential plus filter controller, with improved noise attenuation; closed-form expressions for the filter coefficients, as a function of two design parameters, are provided.

Clutter-based Test Statistics for Automatic Track Initiation

Abstract Two test statistics based on clutter characteristics are derived. A tentative track is confirmed when the track-is-on- clutter hypothesis is rejected. A constant and known false track rate results when the assumptions of the null hypothesis are true. The first test statistic is based on the clutter density. A high probability of target detection is resulted when the expected distance to the nearest target peak is less than the expected distance to the nearest clutter peak. The second test statistic is based on the clutter amplitude. A high probability of target detection is resulted when the expected amplitude of the target peak is greater than the expected amplitude of clutter peaks. The behavior of the clutter-based test statistics is compared with the target visibility method, using simulated data. All track initiation methods are applied using a track updater based on probabilistic data association (PDA), extended to incorporate peak amplitude information, which is available.

Multidimensional Digital Filters for Point-Target Detection in Cluttered Infrared Scenes

Abstract. A three-dimensional (3-D) spatiotemporal prediction-error filter (PEF) is used to enhance foreground/background contrast in (real and simulated) sensor image sequences. Relative velocity is utilized to extract point targets that would otherwise be indistinguishable with spatial frequency alone. An optical-flow field is generated using local estimates of the 3-D autocorrelation function via the application of the fast Fourier transform (FFT) and inverse FFT. Velocity estimates are then used to tune in a background-whitening PEF that is matched to the motion and texture of the local background. Finite impulse response (FIR) filters are designed and implemented in the frequency domain. An analytical expression for the frequency response of velocity-tuned FIR filters, of odd or even dimension with an arbitrary delay in each dimension, is derived.

Powerful Test Statistic for Track Management in Clutter

A test statistic, which does not require prior knowledge of pd, is proposed to support automatic track confirmation and termination decisions in a multiple hypotheses tracker (MHT). Use of gamma distributions yields a linear log-likelihood ratio (LLR) with constant parameters derived from target and clutter models. The proposed LLR results in a higher probability of true track confirmation (i.e., the statistical power of the test) for a given probability of false track confirmation than does the reference MHT implementation and more uniform confirmation statistics.

Maximally Flat IIR Smoothers With Repeated Poles and a Prescribed Delay

The problem of optimal high-frequency noise suppression and low-frequency signal transmission in sampled sensor systems is considered in this paper. Low-delay digital filters with linear phase and unity magnitude at the dc limit (i.e., maximally flat) are of particular interest. Savitzky-Golay smoothers with an infinite impulse response (IIR) are introduced and their properties are explored. The filter coefficients are derived via regression analysis using orthogonal Laguerre polynomials in the time domain. A generalized form with a shape parameter included in the error-weighting function is proposed. This extension may be used to further reduce the white noise gain of the filter. A design process that determines the optimal position of the repeated real poles, either to minimize the white noise gain, or to maximize the high-frequency attenuation, for a specified low-frequency group delay, is discussed. An alternative process for the design of a generic class of maximally flat repeated-pole filters is also presented. This allows colored noise to be handled and/or additional frequency-domain constraints, such as Nyquist flatness, to be applied.

Improved IIR Low-Pass Smoothers and Differentiators with Tunable Delay

Regression analysis using orthogonal polynomials in the time domain is used to derive closed-form expressions for causal and non-causal filters with an infinite impulse response (IIR) and a maximally-flat magnitude and delay response. The phase response of the resulting low-order smoothers and differentiators, with low-pass characteristics, may be tuned to yield the desired delay in the pass band or for zero gain at the Nyquist frequency. The filter response is improved when the shape of the exponential weighting function is modified and discrete associated Laguerre polynomials are used in the analysis. As an illustrative example, the derivative filters are used to generate an optical-flow field and to detect moving ground targets, in real video data collected from an airborne platform with an electro-optic sensor.

Fusion of possibly biased location estimates using Gaussian mixture models

A probabilistic framework for fusing location estimates, which may be biased and inconsistent, is presented. The proposed method, involving Gaussian mixture models (GMMs), utilizes prior information regarding the sensor bias, firstly, to reduce errors in the fused location estimate, and secondly, to produce a fused covariance matrix that better reflects the expected location error. Simulations are used to evaluate performance, relative to other techniques, such as the covariance union (CU) method. A passive geolocation application involving an airborne electronic support (ES) system is considered.

Detecting and Tracking Moving Objects in Sequences of Color Images

A statistical change detector, implemented as a zero-latency finite-memory filter, is used to identify anomalies in temporal pixel statistics. An F-distributed test statistic is computed for each pixel and used in a hypothesis test. The tracker, with automatic track initiation and termination, uses a low-complexity pairwise joint probabilistic data association (JPDA) algorithm, which has been restricted to consider clusters (sub-problems) containing no more than two tracks. The track state and clutter model are augmented to include color. The detector and tracker are used to process sample video data.

Digital Filter Designs for Recursive Frequency Analysis

Digital filters for recursively computing the discrete Fourier transform (DFT) and estimating the frequency spectrum of sampled signals are examined, with an emphasis on magnitude-response and numerical stability. In this tutorial-style treatment, existing recursive techniques are reviewed, explained and compared within a coherent framework; some fresh insights are provided and new enhancements/modifications are proposed. It is shown that the replacement of resonators by (non-recursive) modulators in sliding DFT (SDFT) analyzers with either a finite impulse response (FIR), or an infinite impulse response (IIR), does improve performance somewhat; however stability is not guaranteed, as the cancellation of marginally stable poles by zeros is still involved. The FIR deadbeat observer is shown to be more reliable than the SDFT methods, an IIR variant is presented, and ways of fine-tuning its response are discussed. A novel technique for stabilizing IIR SDFT analyzers with a fading memory, so that all poles are inside the unit circle, is also derived. Slepian and sum-of-cosine windows are adapted to improve the frequency responses for the various FIR and IIR DFT methods.