Ll-CFAR: a flexible and robust alternative

A new family of constant false alarm rate (CFAR) processors is introduced. An Ll-CFAR forms its noise power estimate by linearly filtering ranked samples from the reference set; the weights of this combination, however, depend not only on the rank, but also on the relative proximity of the sample to the cell under test. From the class of Ll-CFARs may be chosen members which effectively censor spurious targets; members which exhibit impressive control of false alarm in the presence of a clutter edge; and members which are robust against both such inhomogeneities. While the design of such schemes is involved, their implementation is not significantly more burdensome than that of plain ordered statistic CFAR (OS-CFAR). After a discussion of the stochastic training of Ll-CFAR, the performance is thoroughly assessed under the most commonly encountered instances of environmental conditions, and compared with those of classical CFAR techniques     

Angle estimation for two unresolved targets with monopulse radar

Most present-day radar systems use monopulse techniques to extract angular measurements of sunbeam accuracy. The familiar "monopulse ratio" is a very effective means to derive the angle of a single target within a radar beam. For the simultaneous estimation of the angles of two closely-spaced targets, a modification on the monopulse ratio was derived in (Blair and Pearce, 2001), while (Sinha et al., 2002) presented a maximum likelihood (ML) technique via numerical search. In this paper it is shown that the ML solution can in fact be found explicitly, and the numerical search of ((Sinha et al., 2002) is unnecessary. However, the ML solution requires the signal to noise ratio (SNR) for each target to be known, and hence we generalize it so it requires only the relative SNR. Several versions of expectation maximization (EM) joint angle estimators are also derived, these differing in the degree to which prior information on SNR and on beam pattern are assumed. The performances of the different direction-of-arrival (DOA) estimators for unresolved targets are studied via Monte Carlo, and it is found that most have similar performance: this is remarkable since the use of prior information (SNR, relative SNR, beam pattern) varies widely between them. There is, however, considerable performance variability as a function of the two targets' off-boresight angles. A simple combined technique that fuses the results from different approaches is thus proposed, and it performs well uniformly.     

Detection of long-duration narrowband processes

Detecting long, weak signals that are narrowband but of unknown frequency structure is an important signal processing challenge, with many applications in remote sensing and process monitoring. An ad hoc scheme is developed. Its stages include the discrete Fourier transform (DFT), a multiresolution decomposition in the frequency domain, and a generalized likelihood ratio test (GLRT). The computational load is light, and the performance is remarkably good. This is so not just in the original narrowband situation, but also, due to an inherent adaptivity to the data, in the detection of signals that are relatively broadband in nature. Generalizations are given to constant false alarm rate (CFAR) operation in both prewhitened and unwhitened cases, and to the detection of multiband signals. As regards the last, it is discovered that there is little loss from overestimating the number of bands     

PMHT: problems and some solutions

The probabilistic multihypothesis tracker (PMHT) is a target tracking algorithm of considerable theoretical elegance. In practice, its performance turns out to be at best similar to that of the probabilistic data association filter (PDAF); and since the implementation of the PDAF is less intense numerically the PMHT has been having a hard time finding acceptance. The PMHT's problems of nonadaptivity, narcissism, and over-hospitality to clutter are elicited in this work. The PMHT's main selling-point is its flexible and easily modifiable model, which we use to develop the "homothetic" PMHT; maneuver-based PMHTs, including those with separate and joint homothetic measurement models; a modified PMHT whose measurement/target association model is more similar to that of the PDAF; and PMHTs with eccentric and/or estimated measurement models. Ideally, "bottom line" would be a version of the PMHT with clear advantages over existing trackers. If the goal is of an accurate (in terms of mean square error (MSE)) track, then there are a number of versions for which this is available.     

Practical Fusion of Quantized Measurements via Particle Filtering

Most treatments of decentralized estimation rely on some form of track fusion, in which local track estimates and their associated covariances are communicated. This implies a great deal of communication; and it was recently proposed that by an intelligent quantization directly of measurements, the communication needs could be considerably cut. However, several issues were not discussed. The first of these is that estimation with quantized measurements requires an update with a non-Gaussian distribution, reflecting the uncertainty within the quantization "bin."; In general this would be a difficult task for dynamic estimation, but Markov-chain Monte-Carlo (MCMC, and specifically here particle filtering) techniques appear quite appropriate since the resulting system is, in essence, a nonlinear filter. The second issue is that in a realistic sensor network it is to be expected that measurements should arrive out-of-sequence. Again, a particle filter is appropriate, since the recent literature has reported particle filter modifications that accommodate nonlinear-filter updates based on new past measurements, with the need to refilter obviated. We show results that indicate a compander/particle-filter combination is a natural fit, and specifically that quite good performance is achievable with only 2-3 bits per dimension per observation. The third issue is that intelligent quantization requires that both sensor and fuser share an understanding of the quantization rule. In dynamic estimation this is a problem since both quantizer and fuser are working with only partial information; if measurements arrive out-of-sequence the problem is compounded. We therefore suggest architectures, and comment on their suitabilities for the task. A scheme based on delta-modulation appears to be promising.     

Superimposed HMM transient detection via target tracking ideas

The quickest detection of superimposed hidden Markov model (HMM) transient signals is addressed. It is assumed that a known HMM is always extant but at an unknown time a second known HMM may also be present, and overlapped with the previous. Two approaches are proposed. The first treats the superimposed HMMs as a unit with an expanded state space, thus converting the problem of detecting superimposed HMMs into detection of a change in HMM, this being readily solved using a previously proposed procedure. Such an approach, though excellent in terms of performance, is not suitable for the superposition of multiple HMMs with large state dimensions due to computational complexity. A second detection scheme (based on multiple target tracking ideas) with much lower computational needs but little loss in terms of performance, is therefore developed     

Dynamic Cramer-Rao bound for target tracking in clutter

Recently, there have been several new results for an old topic, the Cramer-Rao lower bound (CRLB). Specifically, it has been shown that for a wide class of parameter estimation problems (e.g. for objects with deterministic dynamics) the matrix CRLB, with both measurement origin uncertainty (i.e., in the presence of false alarms or random clutter) and measurement noise, is simply that without measurement origin uncertainty times a scalar information reduction factor (IRF). Conversely, there has arisen a neat expression for the CRLB for state estimation of a stochastic dynamic nonlinear system (i.e., objects with a stochastic motion); but this is only valid without measurement origin uncertainty. The present paper can be considered a marriage of the two topics: the clever Riccati-like form from the latter is preserved, but it includes the IRF from the former. The effects of plant and observation dynamics on the CRLB are explored. Further, the CRLB is compared via simulation to two common target tracking algorithms, the probabilistic data association filter (PDAF) and the multiframe (N-D) assignment algorithm.     

Uniform versus nonuniform sampling when tracking in clutter

Many target tracking subsystems have the ability to schedule their own data rates; essentially they can "order" new information whenever they need it, and the cost is in terms of the sensor resource. But among the unmanaged schemes, uniform sampling, in which a new measurement is requested periodically and regularly, is the most commonly-used sampling scheme; deliberately nonuniform schemes are seldom given serious consideration. In this paper, however, we show that such schemes may have been discarded prematurely: a nonuniform sampling can have its benefits. Specifically, the nonuniform and uniform sampling schemes are compared for two kind of trackers: the probabilistic data association filter (PDAF), which updates its track based on a single scan of information at a time; and N-D assignment (an optimization-based implementation of the multi-hypothesis tracker (MHT)), in which the sliding window involves many scans of observations. We find that given the ground rule of maintenance of the same overall scan rate (i.e., the same sensor effort) uniform sampling is always optimal for the single-scan tracker in the sense of track life. However, nonuniform sampling can outperform uniform sampling if a more sophisticated multi-scan tracker is used, particularly when 1) the target has a high process noise, and/or 2) the false alarm density is high, and/or 3) the probability of detection is high.     

Applications of level crossing theory to target intervisibility: to be seen or not to be seen?

Here we discuss intervisibility (the existence of an unobstructed line of sight (LOS) between two points) accounting for the vertical and horizontal errors in the estimated locations of both points as well as elevation errors in the database of the terrain that could obstruct the LOS between these points. The errors are first simply treated as a "white" noise sequence: we assume no correlation between the intervisibility at two different times, and the probability of an instantaneous intervisibility event is in this case developed. This is useful; but perhaps of greater concern is whether or not a target remains visible long enough and/or often enough that its motion can be tracked? Consequently, we present a second treatment in which the errors are stochastic processes of a certain bandwidth, and both the probability density function (pdf) of an intervisibility interval and the average number of intervisibility intervals over a certain time period are developed.