In a wireless sensor network the nodes collect independent observations about a nonrandom parameter theta to be estimated, and deliver informations to a fusion center (FC) by transmitting suitable waveforms through a common Multiple Access Channel (MAC). The FC implements some appropriate fusion rule and outputs the final estimate of theta. We introduce a new access/estimation scheme, here referred to as LBMA (Likelihood Based Multiple Access), and prove it to be asymptotically efficient in the limit of increasingly large number of sensors n, when the used bandwidth W is allowed to scale as n-to-the-alpha, 0.5

Conceptual and practical encoding/decoding, aimed at accurately reproducing remotely collected observations, has been heavily investigated since the pioneering works by Shannon about source coding. However, when the goal is not to reproduce the observables, but making inference about an embedded parameter and the scenario consists of many unconnected remote nodes, the landscape is less certain. We consider a multiterminal system designed for efficiently estimating a random parameter according to the MMSE criterion. The analysis is limited to scalar quantizers followed by a joint entropy encoder, and it is performed in the high-resolution regime where the problem can be easier mathematically tackled. Focus is made on the peculiarities deriving from the estimation task, as opposed to that of reconstruction, as well as on the multiterminal, as opposite to centralized, character of the inference. The general form of the optimal nonuniform quantizer is derived and examples are given.

Prognostics, which refers to the inference of an expected time-to-failure for a system, is made difficult by the need to track and predict the trajectories of real-valued system parameters over essentially unbounded domains, and by the need to prescribe a subset of these domains in which an alarm should be raised. In this paper we propose an idea, one whereby these problems are avoided: instead of physical system or sensor parameters, a vector corresponding to the failure probabilities of the system’s sensors (which of course are bounded within the unit hypercube) is tracked. With the help of a system diagnosis model, the corresponding the fault signatures can be identified as terminal states for these probability vectors. To perform the tracking, Kalman filters and interacting multiple model (IMM) estimators are implemented for each sensor. The work that has been completed thus far shows promising results in both large and small-scale systems, with the impending failures being detected quickly and the prediction of the time until this failure occurs being determined accurately.

It has recently been found that via jointly processing multiple (sum, azimuth- and elevation-difference) matched filter samples it is possible to extract and localize several (more than two) targets spaced more closely than the classical interpretation of radar resolution. This paper derives the Cramer-Rao lower bound (CRLB) for sampled monopulse radar data. It is worthwhile to know the limits of such procedures; and in addition to its role in delivering the measurement accuracies required by a target tracker, the CRLB reveals an estimator's efficiency. We interrogate the CRLB expressions for cases of interest. Of particular interest are the CRLB's implications on the number of targets localizable: assuming a sampling-period equal to a rectangular pulse's length, five targets can be isolated between two matched filter samples given the target's SNRs are known. This reduced to three targets when the SNRs are not known, but the number of targets increases back to five (and beyond) when a dithered boresight strategy is used. Further insight to the impact of pulse shape and of the benefits of over-sampling are given.

We present two procedures for validating candidate target tracks obtained using the Maximum Likelihood Probabilistic Data Association (ML-PDA) algorithm. The ML-PDA, developed for Very Low Observable (VLO) target tracking, always provides a track estimate that must then be validated or rejected by comparing the value of the Log Likelihood Ratio (LLR) at the track estimate to a threshold. Using extreme value theory, we show that in the absence of a target the LLR at the track estimate obeys approximately a Gumbel distribution rather than the Gaussian distribution previously ascribed to it in the literature. The optimal off-line track validation procedure relies on extensive off-line simulations to obtain a set of track validation thresholds that are then used by the tracking system. The real-time procedure, which is suboptimal, uses the data set that produced the track estimate to also determine the track validation threshold. The performance of these two procedures is investigated through simulation of two active sonar tracking scenarios by comparing the false track and true track acceptance probabilities. These techniques have potential for use in a broader class of maximum likelihood estimation problems with similar structure.

Optical Doppler tomography is a valuable functional extension of optical coherence tomography OCT that can be used to study subsurface blood flows of biological tissues. We propose a novel frequency estimation technique that uses an adaptive notch filter ANF to track the depth-resolved Doppler frequency. This new technique is a minimal-parameter filter and works in the time domain without the need of Fourier transformation. Therefore, the algorithm has a computationally efficient structure that may be well suited for implementation in real-time ODT systems. Our simulations and imaging results also demonstrate that this filter has good performance in terms of noise robustness and estimation accuracy compared with existing estimation algorithms.

We look at the simple scenario where multiple sensors make conditionally independent observations of a binary source and process the measurement data using a function U(x) before forwarding them to a fusion center via a Gaussian multiaccess channel. Subject to a total power constraint, we obtain the optimal U(x) that maximizes the deflection; the latter can also be interpreted as the output signal-to-noise ratio for an equivalent binary detection problem. The shape of the optimal function only depends on the probability density function of the observation noise, which we assume symmetric around zero, while the height is scaled by the allowed transmission power. We emphasize that the optimal function herein is derived for an arbitrary distribution of the observation noise. It reduces to a tanh function when the observation noise is additive Gaussian, which has been studied in the literature.

A network of sensors polled by a mobile agent (the SENMA paradigm) is used for detection purposes, with both the remote nodes and the mobile agent implementing Wald's sequential tests. When polled, each remote node transmits its local decision (if any) to the agent, and two network/agent communication schemes are considered. One of these is designed with specific care to the network's energy consumption. In both cases, collisions over the common communication channel are precluded by the sequentiality of the sensors' query. The system performances in terms of average decision time, error probability, and network energy consumption are derived in exact analytical form. A tradeoff exists between the amount and the reliability of the information that the rover may collect: at optimality, the decentralized system overcomes a single supernode by orders of magnitude in terms of decision time, while only 30% of the sensors encountered by the mobile agent spend energy to reveal themselves. The remaining sensors contribute to the detection process by their silence.

We investigate the design of simple noncooperative quantizers for distributed estimation of a common random variable. It is assumed that there is a budget of aggregate rate, a criterion of Fisher information and a large population of sensors. It is further assumed that sensor quantizers are uniform, and that rate is determined by the entropy of the outputs of these. The key question asked is whether it is better to quantize a relatively few sensors finely or as many as possible coarsely.

For the case of a single resolved target, monopulse-based radar sub-beam angle and sub-bin range measurements carry errors that are approximately Gaussian with known covariances, and hence a tracker that uses them can be Kalman-based. However, the errors accruing from extracting measurements for multiple unresolved targets are not Gaussian. We therefore submit that to track such targets it is worth the effort to apply a nonlinear (non-Kalman) filter. Specifically, in this paper we propose a particle filter that operates directly on the monopulse sum/difference data for two unresolved targets. Significant performance improvements are seen versus a scheme in which signal processing (measurement extraction from the monopulse data) and tracking (target state estimation from the extracted measurements) are separated.

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 un-managed 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 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 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: (i) the target has a high process noise; and/or (ii) the false alarm density is high; and/or (iii) the probability of detection is high.

In a recent paper we showed that a network of unconnected and completely DOA-blind sensors (“beepers”) is able within the SENMA architecture (unlabeled polling performed by a mobile agent) to perform DOA estimation quite effectively. The idea is that the mobile agent collects the periodic emissions of the polled sensors, with the time origin of such emissions being the passage of the acoustic wavefront. Depending on the relative orientation between the acoustic wavefront and the field of view of the mobile agent, the impinging times over different sensors are more or less clustered, and so are the recorded emissions. On this basis the DOA may be inferred. Here two new estimators are proposed. One method (support-based) exploits the maximum spread between recorded times, is simple to implement and its performance, measured in terms of mean square error, is improved significantly versus that proposed in the older paper. In fact, the support-based estimator achieves performance close to that of the maximum-likelihood estimator – also investigated here – indicating that the support-based structure is perhaps suitable for tasks that involve cheap robust designs, such as sea/ground surveillance and sniper location.

In the world full of diverse, distributed and uncertain information sources, how to use information to increase analysis efficiencies, collaborate more effectively, make better decisions, and respond more quickly to new threats or opportunities have become key issues in many areas. One such area is counter-terrorism. In this paper, a collaboration scheme for information integration among multiple agencies (and/or various divisions within a single agency) is designed using hierarchical and hybrid Bayesian networks (HHBNs). In this scheme, raw information is represented by transactions (such as communication, travel, financing), and information entities to be integrated are modeled as random variables (such as an event occurs, an effect exists, or an action is undertaken). Each random variable has certain states with probabilities assigned to them. Hierarchical is in terms of the model structure and hybrid stems from our usage of both general Bayesian networks (BNs) and hidden Markov models (HMMs, a special form of dynamic BNs). The general Bayesian networks are adopted in the top (decision) layer to address global assessment for a specific question (e.g., “Is target A under terrorist threat?” in the context of counterterrorism). HMMs function in the bottom (observation) layer to report processed evidence to the upper layer BN based on the local information available to a particular agency or a division. A software tool, termed the adaptive safety analysis and monitoring (ASAM) system, is developed to implement HHBNs for information integration either in a centralized or in a distributed fashion. As an example, a terrorist attack scenario gleaned from open sources is modeled and analyzed to illustrate the functionality of the proposed framework.

We develop optimal probability loading for parallel binary channels, subject to a constraint on the total probability of sending “1”s. The distinctions from the water-filling power loading for parallel Gaussian channels, particularly the latter’s “dropping” of poor quality channels, are highlighted. The only binary input binary output channel that is never dropped is the Z-channel.

When employed to detect a transient change between known iid populations, Page’s test is easy to implement and provides reliable performance. However, its application to unknown transient changes is less clear. A Page test can be thought of as a repeated sequential test, and here we propose that each sequential test use a time-varying threshold. The idea is that short signals are detected quickly before post-termination data has a chance to refute them; and that evidence for a long signal is allowed to build, rather than being summarily discarded too early.

Following the SENMA concept, we consider a wireless network of very dumb and cheap sensors, polled by a travelling “rover”. Sensors are randomly placed and isotropic: individually they have no ability to resolve the direction of arrival (DOA) of an acoustic wave. However, they do observe the wavefront at different times. We assume that the communication load must be as limited as possible, so that these times cannot be communicated to the rover. Notwithstanding the lack of transmission of arrival times and the lack of DOA resolution ability of the individual sensors, DOA estimation is possible, simple, and asymptotic efficiency becomes closely approximated after a reasonable number of rover snapshots. Key features are the directionality of the rover antenna, the area it surveys, and the average number of sensors inside that area, as accorded a Poisson distribution.

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 multi-frame (N-D) assignment algorithm.

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 of an intervisibility interval and the average number of intervisibility intervals over a certain time period are developed.

Many practical multi-sensor tracking systems are based on some form of track fusion, in which local track estimates and their associated covariances are shared among sensors. Communication load is a significant concern, and the goal of this paper is to propose an architecture for low-bandwidth track fusion. The scheme involves intelligent scalar and vector quantization of the local state estimates and of the associated estimation error covariance matrices. Simulation studies indicate that the communication saving can be quite significant, with only minor degradation of track accuracy.

If several closely-spaced targets fall within the same radar beam and between two adjacent matched filter samples in range, monopulse information from both of these samples can and should be used for estimation, both of angle and of range (i.e., estimation of the range to sub-bin accuracy). Similarly, if several closely-spaced targets fall within the same radar beam and among three matched filter samples in range, monopulse information from all of these samples should be used for the estimation of the angles and ranges of these targets. Here, a model is established and a maximum likelihood (ML) extractor is developed. The limits of the number of targets that can be estimated are given for both case A, where the targets are in a beam and in a range “slot” between the centers of two adjacent resolution cells (that is, from detections in two adjacent matched filter samples), and case B, where the targets are in two or more adjacent slots (among three or more adjacent samples). A minimum description length (MDL) criterion is used to detect the number of targets between the matched filter samples, and simulations support the theory.

Quantization for estimation is explored for the case that it must be performed jointly with data association; that is, the case in which measurements are of uncertain origin. Data association requires some sort of gating of distributed observations, and a censoring strategy is proposed. Several quantization philosophies are explored, specifically uniform quantization, uniform quantization with measurement exchangeability incorporated (the “type” method), and uniform quantization of sorted measurements. The second scheme uses less bandwidth than the third. But it is shown, perhaps surprisingly, that the third preserves more information that may be useful for estimation; and a simple procedure for optimal fused estimation based on this third scheme is given. Interestingly, when compared in terms of ratedistortion curve, the schemes two and three perform similarly; their censored versions offer further improvement in performances due to the uncertain-origin property of the measurements.

The PMHT (probabilistic multi-hypothesis 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.

The Probabilistic Multiple Hypothesis Tracker (PMHT) uses the Expectation-Maximization (EM) algorithm to solve the measurement-origin uncertainty problem. Here we explore some of its variants for maneuvering targets and in particular discuss the Multiple Model PMHT. We apply this PMHT to the six “typical” tracking scenarios given in the second benchmark problem from Blair et al. [6]. The manner in which the PMHT is used to track the targets and to manage radar allocation is discussed, and the results compared to those of the IMM/PDAF and IMM/MHT. The PMHT works well: its performance lies between those of the IMM/PDAF and IMM/MHT both in terms of tracking performance and computational load.

A new complex sphere decoding algorithm is presented for signal detection in V-BLAST systems, which has a computational cost that is significantly lower than that of the original complex sphere decoder (SD) for a wide range of SNRs. Simulation results on a 64-QAM system with 23 transmit and 23 receive antennas at an SNR per bit of 24 dB show that the new sphere decoding algorithm obtains the ML solution with an average cost that is at least 6 times lower than that of the original complex SD. Further, the new algorithm also shows robustness with respect to the initial choice of sphere radius.

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 in this paper. 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 terms of detection probability and estimation accuracy.

The Probabilistic Data Association (PDA) method for multiuser detection over synchronous CDMA channels is extended to the signal detection problem in V-BLAST systems where it is generalized for the case of complex modulation. Computer simulations show that the algorithm has an error probability that is significantly lower than that of the V-BLAST optimal order detector and has a computational complexity of O(8n_T^3), where n_T is the number of transmit antennas.

In this paper, we compare the complexity and efficiency of several methods used for multi-user detection in a synchronous CDMA system. Various methods are discussed, including decision feedback (DF) detection, group decision feedback (GDF) detection, coordinate descent, quadratic programming with constraints, space alternating generalized EM (SAGE) detection, TABU search, a Boltzmann machine detector, semi-definite relaxation, Probabilistic Data Association (PDA), branch and bound and the sphere decoding method. The efficiencies of the algorithms, defined as the probability of group detection error divided by the number of floating point computations, are compared under various situations. Of particular interest is the appearance of an "efficient frontier" of algorithms, primarily composed of DF detector, GDF detector, PDA detector, the branch and bound optimal algorithm and the sphere decoding method. The efficient frontier is the convex hull of algorithms as plotted on probability-of-error versus computational-demands axes: algorithms not on this efficient frontier can be considered dominated by those that are.

We present an approach for the joint segmentation and classification of a time series. The segmentation is on the basis of a menu of possible statistical models: each of these must be describable in terms of a sufficient statistic, but there is no need for these sufficient statistics to be the same, and these can be as complex (for example, cepstral features or autoregressive coefficients) as fits. All that is needed is the PDF (probability density function) of each sufficient statistic under its own assumed model --- presumably this comes from training data, and it is particularly appealing that there is no need at all for a *joint* statistical characterization of all the statistics. There is similarly no need for an a-priori specification of the number of sections, as the approach uses an appropriate penalization of an over-zealous segmentation. The scheme has two stages. In stage one, rough segmentations are implemented sequentially using a piecewise GLR (generalized likelihood ratio); in the second stage, the results from the first stage (both forward and backward) are refined. The computational burden is remarkably small, approximately linear with the length of the time series, and the method is nicely accurate in terms both of discovered number of segments and of segmentation accuracy. A hybrid of the approach with one based on Gibbs sampling is also presented; this combination is somewhat slower but considerably more accurate.

A fast optimal algorithm based on the branch and bound (BBD) method is proposed for the joint detection of binary symbols of K users in a synchronous Code-Division Multiple Access (CDMA) channel with Gaussian noise. Relationships between the proposed algorithms (depth-first BBD and fast BBD) and both the decorrelating decision feedback (DF) detector and sphere decoding (SD) algorithm are clearly drawn. It turns out that decorrelating DF detector corresponds to a "one-pass" depth-first BBD; sphere decoding is in fact a type of depth-first BBD, but one that can be improved considerably via tight upper bounds and user ordering as in the fast BBD. A fast "any-time" sub-optimal algorithm is also available by simply picking the "current-best" solution in the BBD method. Theoretical results are given on the computational complexity and the performance of the "current-best" sub-optimal solution.

A common model for sonar clutter is that of the transmitted signal convolved with a colored Gaussian process relating to the sea-bottom profile. Rather surprisingly, this noise becomes strongly non-Gaussian if there are multiple realizations and if a realistic random phase is introduced --- the univariate statistics remain Gaussian, but the joint probability density function (pdf) is not. In this short paper we explore this behavior and we develop optimal detection statistics for a "two-look" situation. It turns out that the gains over a naive assumption of Gaussianity can be substantial.

A general frequency modulated (GFM) signal characterizes the vibrations produced by compressors, turbines, propellers, gears and other rotating machines in a dynamic environment. A GFM signal is defined as the composition of a real or complex, periodic or almost-periodic carrier function with a real, differentiable modulation function. A GFM therefore contains sinusoids whose frequencies are (possibly non-integral) multiples of a fundamental; to distinguish a GFM from a set of unrelated sinusoids it is necessary to track them as a group. This paper develops the general frequency modulation tracker (GFMT) for one or more GFM signals in noise using the expectation/conditional maximization (ECM) algorithm which is an extension of the expectation-maximization (EM) algorithm. Three advantages of this approach are that the ratios (harmonic numbers) of the carrier functions do not need to be known a priori, that the parameters of multiple signals are estimated simultaneously, and that the GFMT algorithm exploits knowledge of the noise spectrum so that a separate normalization procedure is not required. Several simulated examples are presented to illustrate the algorithm's performance.

The Probabilistic Data Association (PDA) method is extended to multiuser detection over symbol asynchronous Code-Division Multiple Access (CDMA) communication channels. PDA achieves near-optimal performance with O(K^3) computational complexity in synchronous CDMA where K is the number of users. In this paper, a direct extension of the PDA method to an asynchronous system is firstly presented by viewing the asynchronous CDMA as a large synchronous one. Then, a sliding window processing is proposed, to avoid considering the entire data. Computer simulations show that the probability of group detection error of the proposed PDA method is very close to the performance lower bound provided by an ideal clairvoyant optimal detector. While the computational complexity of the PDA method is O(K^3) in synchronous CDMA where K is the number of users, it is only marginally increased to O([h/s]K^3) per time frame in asynchronous CDMA where h and s are the width and the sliding rate of the processing window, respectively. Due to the outstanding performance of the PDA detector in heavily-overloaded asynchronous systems, it is also proposed to use asynchronous transmission deliberately even when synchronous transmission is possible -- asynchronous is better than synchronous!

A strategy for user ordering and time labeling for a decision feedback detector in asynchronous Code-Division Multiple Access communications is discussed. Ordering and labeling would at first appear to be of a complexity exponential in K, the number of users. Surprisingly, optimal sequencing requires only O(K^4) operations, and is needed only once per packet: it is thus a cheap way to obtain an often marked improvement in performance, compared to power-ordering and chronological labeling.

In this paper a method of classification referred to as the Bayesian Data Reduction Algorithm is developed. The algorithm is based on the assumption that the discrete symbol probabilities of each class are a priori uniformly Dirichlet distributed, and it employs a "greedy" approach (similar to a backward sequential feature search) for reducing irrelevant features from the training data of each class. Notice that reducing irrelevant features is synonymous here with selecting those features that provide best classification performance; the metric for making data reducing decisions is an analytic formula for the probability of error conditioned on the training data. To illustrate its performance the Bayesian Data Reduction Algorithm is applied both to simulated and to real data, and it is also compared to other classification methods. Further, the algorithm is extended to deal with the problem of missing features in the data. Results demonstrate that the Bayesian Data Reduction Algorithm performs well despite its relative simplicity. This is significant because the Bayesian Data Reduction Algorithm differs from many other classifiers: as opposed to adjusting the model to obtain a "best fit" for the data, the data, through its quantization, is itself adjusted.

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 sequential group detection technique is studied in this paper. The computational complexity of a Group For important classification tasks there may already be extant an arsenal of classification tools, these representing previous attempts and best efforts at solution. Many times these are useful classifiers; and although the fact that all base their decisions on the same observations implies that their decisions are strongly dependent, there is often some benefit from fusing them to a better corporate decision. However, these classifiers are often of a black-box nature, and there is no precise way to model their joint statistical behavior such that the fused decision can be optimal. Nonetheless one can consider this fusion as of building a meta-classifier, based on data vectors whose elements are the individual legacy classifier decisions. The Bayesian data reduction algorithm (BDRA) imposes a uniform prior probability mass function on discrete symbol probabilities, and thereby can predict its own probability of error performance as conditioned upon its training data. It turns out that this prior probability implies a very appropriate penalty on models whose complexity is not supported by the training data: the BDRA can select a best subset of its input features, by which is meant that the fused decision may best use only a subset of legacy classifier outputs. In this paper the BDRA is applied to such decision-fusion, and is compared favorably to a number of other expert-mixing approaches. Parameters varied include the number of relevant legacy classifiers (some may have been poorly designed, and ought to be discounted automatically), the numbers of training data and classes, and the dependence between legacy classifiers -- a fusion approach should reject redundant decisions.

The sequential group detection technique is studied in this paper. The computational complexity of a Group Decision Feedback Detector (GDFD) is exponential in the largest size of the groups; thus instead of using the partition of users as design parameters, choosing the "maximum group size" is more reasonable in practice. Given the maximum group size, a grouping algorithm is proposed. It is shown that the proposed grouping algorithm maximizes the Asymptotic Symmetric Energy (ASE) of the multiuser detection system. Furthermore, based on a set of lower bounds on Asymptotic Group Symmetric Energy (AGSE) of the group decision feedback detector, it is shown that the proposed grouping algorithm, in fact, maximizes the AGSE lower bound for every group of users. Together with a fast computational method based on branch-and-bound, the theoretical analysis of the grouping algorithm enables the offline estimation of the computational cost and the performance of GDFD. Simulation results on both small and large size problems are presented to verify the theoretical results. All the results in this paper can be applied to the Decision Feedback Detector (DFD) by simply setting the maximum group size to 1.

Two new algorithms are presented for the segmentation of a white Gaussian-distributed time series having unknown but piecewise-constant variances. The first "Sequential/MDL" idea includes a rough parsing via the GLR, a penalization of segmentations having too many parts via MDL, and an optional refinement stage. The second "Gibbs Sampling" approach is Bayesian, and develops a Monte Carlo estimator. From simulation it appears that both schemes are very accurate in terms of their segmentation; but that the Sequential/MDL approach is orders of magnitude lower in its computational needs. The Gibbs approach can, however, be useful and efficient as a final post-processing step. Both approaches (and a hybrid) are compared to several algorithms from the literature.

It is often required to detect a long weak signal in Gaussian noise, and frequently the exact form of that signal is parametrized, but not known. A bank of matched filters provides an appropriate detector. However, in some practical applications there are very many matched filters and most are quite long. The consequent computational needs may render the classical bank-of-filters approach infeasibly expensive. One example, and our original motivation, is the detection of chirp gravitational waves by an earth-based interferometer. In this paper we provide a computational approach to this problem via sequential testing. Since the sequential tests to be used are not for constant signals, we develop the theory in terms of average sample number (ASN) for this case. Specifically, we propose two easily-calculable expressions for the ASN, one a bound and the other an approximation. The sequential approach does yield moderate computational savings. But we find that by pre-processing the data using short/medium FFT's, and an appropriate sorting of these FFT outputs such that the most informative samples are entered to a sequential test first, quite high numerical efficiency can be realized. The idea is simple, but appears to be quite successful: examples are presented in which the computational load is reduced by several orders of magnitude. The FFT is an example of an energy-agglomerating transform, but of course there are many others. The point here is that the transform need not match the sought signal exactly, in the sense that all energy becomes confined to a single sample: it is enough that the energy becomes concentrated, and the more concentrated the better.

To detect a purely harmonic signal it is difficult to beat an FFT. However, when the signal is very long and weak, Parker and White have shown that a sequential probability ratio test (SPRT) operating on magnitude-square FFT data is far more efficient. Indeed, both from a numerical-error perspective and in terms of robustness against a deviation from a precisely tonal signal, the block-FFT/SPRT idea is very appealing. Here the approach is extended to the case that the frequency is unknown, and expressions are developed for performance both in terms of detection and of average sample number. The approach is applicable to a large number of practical problems; but particular attention is paid to the continuous gravitational wave example. The computational savings as compared to a fixed test vary as a function of signal strength, block length, bandwidth and operating point; but gains of a factor of two are easy. That these gains are not more exciting relates mostly to the underlying FFT structure: although it is useful that many SPRT's "end early", it is difficult to take advantage of that with an efficient FFT algorithm.

The Probabilistic Data Association (PDA) method for multiuser detection in synchronous Code-Division Multiple Access (CDMA) communication channels is extended to asynchronous CDMA, where a Kalman filter or smoother is employed to track the correlated noise arising from the outputs of a decorrelator. The estimates from the tracker, coupled with an iterative PDA, result in impressively low bit error rates. Computer simulations show that the new scheme significantly outperforms the best Decision Feedback detector. The algorithm has the order of K-cubed complexity per time frame, where K is the number of users.

The 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 PDAF; and since the implementation of the PDAF is less intense numerically the PMHT has been having a hard time finding acceptance. In this paper the PMHT's problems of nonadaptivity, narcissism, and over-hospitality to clutter are elicited. 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, this paper's "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 MSE) track, then there are a number of versions for which this is available. In terms of lost tracks there is no clearly preferable PMHT, although several variants (e.g. convergence-aided via measurement-variance inflation, maneuvering, and homothetic) offer performance similar to that of the PDAF; also, in very adverse tracking situations, the PMHT is preferable. We further hope that our demonstration of the facility by which a new model "idea" is turned into a working algorithm is encouraging to other researchers.

The conventional approach for tracking system design is to treat the sensor and tracking subsystems as completely independent units. However, the two subsystems can be designed jointly to improve system (tracking) performance. It is known that different radar signal waveforms result in very different resolution cell shapes (for example, a rectangle versus an eccentric parallelogram) in the range/range-rate space, and that there are corresponding differences in overall tracking performance. In this paper we develop a framework for the analysis of this performance. An imperfect detection process, false alarms, target dynamics, and the matched filter sampling grid are all accounted for, using the Markov chain approach of Li and Bar-Shalom. The role of the grid is stressed, and it is seen that the measurement-extraction process from contiguous radar "hits" is very important. A number of conclusions are given, perhaps the most interesting of which is the corroboration in the new measurement space of Fitzgerald's result for delay-only (i.e. range) measurements, that a linear FM upsweep offers very good tracking performance.

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 simulational performance of the HT detector are obtained and compared to 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 FFTs) and increasing the FFT length can reduce the minimum detectable frequency slope with nearly no additional computation.

The use of active sonar in shallow water results in received echoes that may be considerably spread in time compared to the resolution of the transmitted waveform. The duration and structure of the spreading and the time of occurrence of the received echo are unknown without accurate knowledge of the environment and a priori information on the location and reflection properties of the target. A sequential detector based on the Page test is proposed for the detection of time-spread active sonar echoes. The detector also provides estimates of the starting and stopping times of the received echo. This signal segmentation is crucial to allow further processing such as more accurate range and bearing localization, depth localization, or classification. The detector is designed to exploit the time spreading of the received echo and is tuned as a function of range to the expected signal-to-noise ratio (SNR) as determined by the transmitted signal power, transmission loss, approximate target strength, and the estimated noise background level. The theoretical false alarm and detection performance of the proposed detector, the standard Page test, and the conventional thresholded matched filter detector are compared as a function of range, echo duration, SNR, and the mismatch between the actual and assumed SNR. The proposed detector and the standard Page test are seen to perform better than the conventional thresholded matched filter detector as soon as the received echo is minimally spread in time. The use of the proposed detector and the standard Page test in active sonar is illustrated with reverberation data containing target-like echoes from geological features, where it was seen that the proposed detector was able to suppress reverberation generated false alarms that were detected by the standard Page test.

Detecting signals that are long, weak, and narrowband is a well known and important problem in signal processing, and has among many applications those in industrial process monitoring, radar and sonar. Such signals may be composed of dense sets of lightly-modulated tones or be true narrowband processes; in fact, which form they have will be shown to be moot as regards detection. An {\em ad hoc} scheme is developed: its stages include the DFT, a multiresolution decomposition in the frequency domain, and a 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 CFAR operation in both prewhitened and unwhitened cases, and to the detection of multi-band signals. As regards the last, it is discovered that there is little loss from over-estimating the number of bands.

Recently, a power-law statistic operating on DFT data has emerged as a basis for a remarkably robust detector of transient signals having unknown structure, location and strength. In this paper we offer a number of improvements to Nuttall's original power-law detector. Specifically, the power-law detector requires that its data be pre-normalized and spectrally white; a CFAR and self-whitening version is developed and analyzed. Further, it is noted that transient signals tend to be contiguous both in temporal and frequency senses, and consequently new power-law detectors in the frequency and the wavelet domains are given. The resulting detectors offer exceptional performance and are extremely easy to implement. There are no parameters to tune: they may be considered "plug-in" solutions to the transient detection problem, and are "all-purpose" in that they make minimal assumptions on the structure of the transient signal save of some degree of agglomeration of energy in time and/or frequency.

A Probabilistic Data Association (PDA) method is proposed in this paper for multiuser detection over synchronous Code Division Multiple Access (CDMA) communication channels. PDA models the undecided user signals as binary random variables. By approximating the Inter-User Interference (IUI) as Gaussian noise with an appropriately elevated covariance matrix, the probability associated with each user signal is iteratively updated. Computer simulations show that the system usually converges within 3-4 iterations, and the resulting probability of error is very close to that of the optimal Maximum Likelihood (ML) detector. Further modifications are also presented to significantly reduce the computational cost.

In many estimation situations measurements are of uncertain origin. This is best exemplified by the target-tracking situation in which at each scan (of a radar, sonar, or electro-optical sensor) a number of measurements are obtained, and it is not known which, if any, of these is target-originated. The source of extraneous measurements can be false alarms - especially in low-SNR situations that force the detector at the end of the signal processing chain to operate with a reduced threshold - or spurious targets. In several earlier papers the surprising observation was made that the Cramer-Rao lower bound (CRLB) for the estimation of a fixed parameter vector (e.g., initial position and velocity) that characterizes the target motion, for the special case of multidimensional measurements in the presence of additive white Gaussian noise, is simply a multiple of that for the case with no uncertainty. That is, there is a scalar information-reduction factor; this is particularly useful as it allows comparison in terms of a scalar. In this paper we explore this result to determine how wide the class of such problems is. It turns out to include many non-Gaussian situations. Simulations corroborate the analysis.

This paper addresses the quickest detection of superimposed hidden Markov model (HMM) transient signals. 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.

Existing detection systems generally are operated using a fixed threshold, optimized to the Neyman-Pearson criterion. An alternative is Bayes detection, in which the threshold varies according to the ratio of prior probabilities. In a recursive target tracker such as the probabilistic data association filter (PDAF) such priors are available in the form of a predicted location and associated covariance; but the information is not at present made available to the detector. Put another way, in a standard detection/tracking implementation information flows only one way, from detector to tracker. Here we explore the idea of two-way information flow, in which the tracker instructs the detector where to look for a target, and the detector returns what it has found. More specifically, we show that the Bayesian detection threshold is lowered in the vicinity of the predicted measurement, and we explain the appropriate modification to the PDAF. The implementation is simple, and the performance is remarkably good.

An artificial neural network (ANN) approach is proposed for the detection of workpiece "burn", the undesirable change in metallurgical properties of the material produced by overly-aggressive or otherwise inappropriate grinding. The grinding Acoustic Emission (AE) signals for 52100 bearing steel were collected and digested to extract feature vectors which appear to be suitable for ANN processing. Two feature vectors are represented, one concerning the band-power, the kurtosis and the skew, and the other the autoregressive (AR) coefficients. The result (burn or no-burn) of the signals was identified based on hardness and profile tests after grinding. Then 10 burn, 10 no-burn and 10 noise-only signals were used to train a radial basis NN employing either of the feature vectors as the input. The trained NN works remarkably well for burn detection. Other signal processing approaches are also discussed. Among them, the CFAR power-law and the Mean-Value Deviance (MVD) prove useful.

Most results about quantized detection rely strongly on an assumption of independence among random variables. With this assumption removed, little is known. Thus, in this paper, Bayes-optimal binary quantization for the detection of a shift in mean in a pair of dependent Gaussian random variables is studied. This is arguably the simplest meaningful problem one could consider. If results and rules are to be found, they ought to make themselves plain in this problem. For certain problem parametrizations (meaning: the signals and correlation coefficient) optimal quantization is achievable via a single threshold applied to each observation -- the same as under independence. In other cases one observation is best ignored, or is quantized with two thresholds; neither behavior is seen under independence. Further, and again in distinction from the case of independence, it is seen that in certain situations an XOR fusion rule is optimal, and in these cases the implied decision rule is bizarre. The analysis is extended to the multivariate Gaussian problem.

This paper addresses quickest detection of transient signals which can be represented as hidden Markov (HMM), 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.

We present a simulational study of several different statistics applied to the detection of unknown low-SNR transient signals in white Gaussian noise. The results suggest that relatively-unsophisticated tests based on temporal localization of power, such as the Page test and a test based on a new statistic due to Nuttall, give reliable results.