Tracking on intensity-modulated sensor data streams

Abstract

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.

Multitarget Tracking of Distributed Targets Using Histogram-PMHT

“…, x T k }, the value of X(k) that maximizes the auxiliary function Q kX for each target k is efficiently solved by a recursive Kalman smoothing filter, even when there are truncated cells and the measurement covariance matrices R = {R tk } are to be estimated. The details of this result are omitted here, but the filter steps are listed explicitly in [1,10,11] for the linear Gaussian case and constant background noise.…”

“…The strong target has an SNR (peak signal to nominal noise power, in a beam) of +4.5 dB, while the weak target has an SNR of −1.5 dB. These SNRs reflect the use of an exponentially distributed beam intensity with mean value determined by the mixture model (10). The simulated mixture assumed a uniform noise distribution and Gaussian target distributions with means given by the true target bearings and standard deviations ρ tk = ρ k = 5°for the strong target and ρ tk = ρ k = 10°for the weak target.…”

“…A physical interpretation of component π tk G k (τ ; X t ) is that π tk represents the fraction of the total power due to the target k and G k (τ ; X t ) models the cell-tocell variations of target k, where k = 0 corresponds to the background noise. The parametric form (10) assumes that a target's power level may be spread across more than one cell of the sensor display.…”

“…Among references [4][5][6][7][8][9], only Luginbuhl [8] and Luginbuhl and Willett [9] considered the important problem of linking successive histograms using a dynamical model. This paper expands upon previous presentations of the H-PMHT algorithm [10,11] and provides a complete description of the H-PMHT method. The incomplete-and complete-data densities are formulated in Sections 2 and 3, respectively.…”

Multiple target tracking from images using the maximum likelihood HPMHT

“…This was extended and became a dynamic target tracker (the general frequency modulation tracker, or GFMT) making use of PMHT ideas in [11,12]. This was rebranded the histogram PMHT (HPMHT, which seems to have stuck as a monicker better than GFMT) in [18], and was augmented to have a "data dependent prior" and to extended such that unseen histogram values (from dead bins or at band edges) could be incorporated in a natural way. The data dependent prior is perhaps an artifact but a necessary one: a weakness of the GFMT is that each histogram (or spectral) "count" is treated as an observation, with the result that the effect of the (the target motion model) becomes asymptotically too small.…”