Waveform fusion in sonar signal processing

In active sonar systems, proper selection of the transmitted waveform is critical for target detection and parameter estimation, especially with the existence of clutter (reverberation). Two commonly used waveforms (constant frequency (CF) and linear frequency modulated (LFM)) are studied. Their characteristics are complementary both with respect to their accuracies and their sensitivity to the blind zero-Doppler ridge. Several fusion schemes of the two kinds of waveforms are explored and fusion results are studied both analytically and from simulation. It is concluded that fusion of the information of different waveforms can be not only more robust, but in some cases outright preferable, in term of detection probability and estimation accuracy.     

Directed Subspace Search ML-PDA with Application to Active Sonar Tracking

The maximum likelihood probabilistic data association (ML-PDA) tracking algorithm is effective in tracking Very Low Observable targets (i.e., very low signal-to-noise ratio (SNR) targets in a high false alarm environment). However, the computational complexity associated with obtaining the track estimate in many cases has precluded its use in real-time scenarios. Previous ML-PDA implementations used a multi-pass grid (MPG) search to find the track estimate. Two alternate methods for finding the track estimate are presented-a genetic search and a newly developed directed subspace (DSS) search algorithm. Each algorithm is tested using active sonar scenarios in which an autonomous underwater vehicle searches for and tracks a target. Within each scenario, the problem parameters are varied to illustrate the relative performance of each search technique. Both the DSS search and the genetic algorithm are shown to be an order of magnitude more computationally efficient than the MPG search, making possible real-time implementation. In addition, the DSS search is shown to be the most effective technique at tracking a target at the lowest SNR levels-reliable tracking down to 5 dB (postprocessing SNR in a resolution cell) using a 5-frame sliding window is demonstrated, this being 6 dB better than the MPG search.     

The turbo PMHT

The PMHT (probabilistic multihypothesis tracker) uses "soft" a posteriori probability associations between measurements and targets. Its implementation is a straightforward iterative application of a Kalman smoother operating on "synthetic" (i.e., modified) measurements, and of recalculation of these synthetic measurements based on the current track estimate. In this correspondence, we first discuss the basic PMHT and some of the older PMHT variants that have been used to enhance convergence. We then introduce the new turbo PMHT, which is informed by the recent success of turbo decoding in the digital communication context. This new PMHT has performance substantially improved versus any of the previous versions.     

Detection of hidden Markov model transient signals

Addressed here is the quickest detection of transient signals which can be represented as hidden Markov models (HMMs), with the application of detection of transient signals. Relying on the fact that Page's test is equivalent to a repeated sequential probability ratio test (SPRT), we are able to devise a procedure analogous to Page's test for dependent observations. By using the so-called forward variable of an HMM, such a procedure is applied to the detection of a change in hidden Markov modeled observations, i.e., a switch from one HMM to another. Performance indices of Page's test, the average run length (ARL) under both hypotheses, are approximated and confirmed via simulation. Several important examples are investigated in depth to illustrate the advantages of the proposed scheme.     

Robust detection of small stochastic signals

We consider the problem of detecting a stochastic signal in white not-necessarily-Gaussian noise, using vector valued observations. The locally optimal detector is presented and its performance evaluated. The least-favorable signal spectrum and noise density (over specified classes) are found, and it is shown that the detector using these least-favorable assumptions is minimax robust. The class of spectra is that of any stochastic signal of specified power whose spectrum can be bounded from above and from below by two given positive functions. The class of densities is the ε-contamination model. We present examples of the performance achievable with the robust detector in one of these the spectral uncertainty class corresponds to the unknown Doppler shift of a radar return signal. It is demonstrated that the standard matched-filter's performance degradation with increasing Doppler shift can be avoided almost entirely through use of the robust processor     

Correlation between horizontal and vertical monopulse measurements

Many radar systems use the monopulse ratio to extract angle of arrival (AOA) measurements in both azimuth and elevation angles. The accuracies of each such measurement are reasonably well known: each measurement is, conditioned on the sum-signal return, Gaussian-distributed with calculable bias (relative to the true AOA), and variance. However, we note that the two monopulse ratios are functions of basic radar measurements that are not entirely independent, specifically in that the sum signal is common to both. The effect of this is that the monopulse ratios are dependent, and a simple explicit expression is given for their correlation; this is of considerable interest when the measurements are supplied to a tracking algorithm that requires a measurement covariance matrix. The system performance improvement when this is taken into account is quantified: while it makes little difference for a tracking radar with small pointing errors, there are more substantial gains when a target is allowed to stray within the beam, as with a rotating (track-while-scan) radar or when a single radar dwell interrogates two or more targets at different ranges. But in any case, the correct covariance expression is so simple that there is little reason not to use it. We additionally derive the Cramer-Rao lower bound (CRLB) on joint azimuth/elevation angle estimation and discover that it differs only slightly from the covariance matrix corresponding to the individual monopulse ratios. Hence, using the individual monopulse ratios and their simple joint accuracy expression is an adequate and quick approximation of the optimal maximum likelihood procedure for single resolved targets.     

The case for like-sensor predetection fusion

There has been a great deal of theoretical study into decentralized detection networks composed of similar (often identical), independent sensors, and this has produced a number of satisfying theoretical results. At this point it is perhaps worth asking whether or not there is a great deal of point to such study-certainly two sensors can provide twice the illumination of one, but what does this really translate to in terms of performance? We take as our metric the ground area covered with a specified Neyman-Pearson detection performance. To be fair, the comparison will be of a multisensor network to a single-sensor system where both have the same aggregate transmitter power. The situations examined are by no means exhaustive but are, we believe, representative. Is there a case? The answer, as might be expected, is “sometimes.” When the statistical situation is well behaved there is very little benefit to a fused system; however, when the environment is hostile the gains can be significant. We see, depending on the situation, gains from colocation, gains from separation, optimal gains from operation at a “fusion range,” and sometimes no gains at all     

Predetection fusion: resolution cell grid effects

If members of a suite of sensors from which fusion is to be carried out are not colocated, it is unreasonable to assume that they share a common resolution cell grid; this is generally ignored in the data fusion community. We explore the effects of such “noncoincidence”, and we find that what at first seems to be a problem can in fact be exploited. The idea is that a target is known to be confined to an intersection of overlapping resolution cells, and this overlap is generally small. We examine noncoincidence from two viewpoints: tracking and detection. With respect to tracking our analysis is first static, by which is meant that we establish the decrease in measurement error; and then dynamic, meaning that the overall effect in the tracking problem is quantified. The detection viewpoint considers noncoincidence as it has impact on a predetection fusion system. Specifically, the role of the fusion rule is examined, and the use of noncoincidence to improve detection performance (rather than that of tracking) is explored     

Local SNR considerations in decentralized CFAR detection

We consider the decentralized detection problem, involving N sensors and a central processor, in which the sensors transmit unquantized data to the fusion center. Assuming a homogeneous background for constant false-alarm rate (CFAR) analysis, we obtain the performances of the system for the Swerling I and Swerling III target models. We demonstrate that a simple nonparametric fusion rule at the central processor is sufficient for nearly optimum performance. The effect of the local signal-to-noise ratios (SNRs) on the performances of the optimum detector and two suboptimum detectors is also examined. Finally, we obtain a set of conditions, related to the SNRs, under which better performance may be obtained by using decentralized detection as compared with centralized detection     

Hough transform for long chirp detection

The online detection of a very long and weak chirp signal is studied. The signal has an extremely slowly decreasing frequency, and is corrupted by white Gaussian noise and possibly also by powerful tones. By exploring and comparing candidate methods, it is found that the Hough transform (HT) detector appears to be most suitable given constraints on computational load and detectability. The analytical and the simulational performance of the HT detector are obtained and compared with the analytical performance of the generalized likelihood ratio test (GLRT), which is assumed to be optimal. Applying a suitable threshold for the HT can increase speed dramatically while preserving performance. We have found that both dithering (taking varied frequency shifts for fast Fourier transforms (FFTs)) and increasing the FFT length can reduce the minimum detectable frequency slope with nearly no additional computation