Maximum Likelihood Processing Research Articles

Stochastic-basis matched-field processing

Matched-field processing (MFP) suffers serious degradation due to environmental mismatch between received acoustic-field vectors and modeled replica vectors. Physical reasons for degradation include uncertainty caused by incomplete descriptions of the parameters and fields necessary for correct specification of the acoustic waveguide (i.e., environmental uncertainty), and system uncertainty associated with incomplete knowledge of the array configuration, source depth, etc. Recent research in the theory of stochastic-basis expansions (polynomial chaos) provides a mathematically consistent way of incorporating both types of uncertainty into MFP. Such expansions are used efficiently to construct replica matrices that steer high-rank subspaces capable of capturing signals with uncertain wavefronts. When combined with cross-spectral density matrices, stochastic-basis steering matrices enable the design of new processors with properties not previously evaluated in a MFP context. A maximum likelihood processor is developed which incorporates environmental uncertainty through polynomial chaos expansions. The processor can be written as a Frobenius product between an estimated cross-spectral density matrix and the inverse of a stochastic-basis replica matrix. This talk will outline the theoretical foundation of stochastic-basis MFP, and illustrate the method with some simulations. [Work supported by the Office of Naval Research.]

Maximum-likelihood and other processors for incoherent and coherent matched-field localization

This paper develops a series of maximum-likelihood processors for matched-field source localization given various states of information regarding the frequency and time variation of source amplitude and phase, and compares these with existing approaches to coherent processing with incomplete source knowledge. The comparison involves elucidating each processor's approach to source spectral information within a unifying formulation, which provides a conceptual framework for classifying and comparing processors and explaining their relative performance, as quantified in a numerical study. The maximum-likelihood processors represent optimal estimators given the assumption of Gaussian noise, and are based on analytically maximizing the corresponding likelihood function over explicit unknown source spectral parameters. Cases considered include knowledge of the relative variation in source amplitude over time and/or frequency (e.g., a flat spectrum), and tracking the relative phase variation over time, as well as incoherent and coherent processing. Other approaches considered include the conventional (Bartlett) processor, cross-frequency incoherent processor, pair-wise processor, and coherent normalized processor. Processor performance is quantified as the probability of correct localization from Monte Carlo appraisal over a large number of random realizations of noise, source location, and environmental parameters. Processors are compared as a function of signal-to-noise ratio, number of frequencies, and number of sensors.

Array processing for signals with non-zero means in colored noise fields

Array processing in spatially correlated noise fields is a difficult problem which cannot be solved without constraining either the noise or the signals in various ways. In this paper we assume that the signals impinging on the array have non-zero means. We show that the problem of array processing in completely general spatially colored noise fields is solvable under the previous assumption. In fact we argue that the non-zero mean signal assumption probably is one of the simplest conditions which makes array processing in colored noise possible. We also present a maximum-likelihood (ML) methodology for signal detection and parameter estimation. The derivation of the ML processor under the aforementioned assumption is conceptually straightforward and its implementation is standard. We provide a statistical analysis of the ML signal parameter estimator along with an expression for the associated Cramer–Rao bound (CRB) matrix. Finally, we include some numerical examples to show the type of performance that can be achieved by the estimation and detection approach proposed in this paper.

Adaptive loading for OFDM/SDMA-based wireless networks

The two major obstacles toward high-capacity indoor wireless networks are distortion due to the indoor channel and the limited availability of bandwidth which necessitates a high spectral efficiency. A combined orthogonal-frequency division multiplexing/spatial-diversity multiple access (OFDM/SDMA) approach can effectively tackle both obstacles. The channel distortion due to multipath propagation is easily mitigated with OFDM while the bandwidth efficiency can be increased with the use of SDMA. In order to keep the network's cost acceptable, simplified SDMA processors are preferred over the exponentially complex optimal maximum-likelihood processors. However, these simplified processors perform significantly worse than the optimal ones in terms of average bit error rate (BER). In this paper, we show that by adapting the constellation sizes applied on the individual subcarriers to the channel conditions, the performance of OFDM/SDMA processors can be significantly enhanced. In the uplink, we derive simple closed-form equations for the optimal constellation sizes for both a simple linear minimum mean-square error (MMSE) detector and for a nonlinear MMSE decision feedback equalizer (DFE) detector. Furthermore, for each detector, we introduce a simplified loading algorithm which lowers the computational and signaling complexity substantially at a small performance penalty. In the downlink, we study the dual precoders of the uplink detectors, respectively, the linear MMSE precoder and the nonlinear Tomlinson-Harashima (TH) MMSE-based precoder. For both precoders, we derive expressions for the optimal and the simplified constellation sizes. Additionally, we show that in time-division duplexing systems, the constellation distribution of a set of dual detectors/precoders is identical for up- and downlink, which effectively halves the computational complexity of adaptive loading. In the fully loaded uplink, the proposed adaptive loading algorithm results in a gain of 9 dB for a BER=10/sup -3/ for the linear MMSE detector and a gain of 4.5 dB for the nonlinear MMSE-DFE detector. In the fully loaded downlink, a gain of 6.3 dB is achieved for the MMSE precoder and 5.5 dB for the TH-MMSE precoder.

Optimal target tracking on image sequences with a deterministic background

Until now, most optical pattern recognition filters have been designed to process one image at a time. However, in image sequences, successive frames are highly correlated, so that it is useful to take this correlation into account while designing the filter. We develop a target tracking processor following this method. The images are assumed to consist of a moving object appearing against a moving background. A model that takes into account two successive frames is designed. From this model we determine the maximum-likelihood processor for tracking the object from one frame to the next. Since this processor is based on correlation operations, it could be implemented on a hybrid optoelectronic system that makes use of the rapidity of optical correlation.

The multivalued Bartlett processor and source tracking

A matched-field processing algorithm based on the eigenvectors of the covariance matrix is developed for localization problems involving interference from multiple sources and ambient noise. Since the multivalued Bartlett processor is related to the Bartlett processor, it should be more robust in practice than eigenprocessors that are related to the maximum likelihood processor. This eigenprocessor also has the advantage that it provides well-defined estimates of the locations of multiple sources. An example involving moving sources and ambient noise illustrates that matched-field eigenprocessing requires source motion in order to be reliable when there are multiple sources.

Application of a maximum likelihood processor to acoustic backscatter for the estimation of seafloor roughness parameters

Maximum likelihood (ML) estimation is used to extract seafloor roughness parameters from records of acoustic backscatter. The method relies on the Helmholtz–Kirchhoff approximation under the assumption of a power-law roughness spectrum and on the statistical modeling of bottom reverberation. The result is a globally optimum, highly automated technique that is a useful tool in the context of seafloor classification via remote acoustic sensing. The general geometry of the Sea Beam bathymetric system is incorporated into the design of the ML processor in order to make it applicable to real acoustic data collected by this system. The processor is initially tested on simulated backscatter data and is shown to be very effective in estimating the seafloor parameters of interest. The simulated data are also used to study the effect of data averaging and normalization in the absence of system calibration information. The same estimation procedure is applied to real data collected over two central North Pacific seamounts, Horizon Guyot and Magellan Rise. The Horizon Guyot results are very close to estimates obtained through a curve-fitting procedure presented by de Moustier and Alexandrou [J. Acoust. Soc. Am. 90, 522–531 (1991)]. In the case of Magellan Rise, discrepancies are observed between the results of ML estimation and curve fitting.

A mode subspace approach for source localization in shallow water

Abstract Range and depth source localization in shallow water amounts to the estimation of the normal mode structure of the acoustic field. The new technique presented in this paper uses the spectral decomposition of the sample covariance matrix in order to estimate the mode subspace spanned by the normal modes that are significantly excited by the source. Simulation results obtained using realistic environments show that the technique's performance is always better than or equal to that of the generalized maximum likelihood processor.

Multisource detection using matched‐field processing and scientific visualization techniques

The matched‐field processor has the ability to provide good source location estimates for a single source in a given search volume. If the scenario is complicated by the presence of multiple sources, the detection/localization capability of the matched‐field processor will be degraded from the case where only a single source is present. The sensitivity of localization estimates to varying configurations (e.g., number of sources, source levels, spatial distribution) involving multiple sources are considered. The Bartlett and maximum likelihood processors have been applied, and new three‐dimensional visualization tools have been developed in order to address these issues. Simulated results are presented to illustrate the efficiency of the technique. [Work support by NRL.]

Adaptive realizations of the maximum likelihood processor for time delay estimation

This correspondence introduces an adaptive realization of the maximum likelihood (ML) processor for time delay estimation (TDE). Also presented is a modified ML processor, which requires less computations but still performs better than the other when implemented in an adaptive way. Widrow's least mean square (LMS) adaptive filter algorithm is used to implement the two methods. Simulation results comparing these processors with other existing adaptive TDE algorithms are also presented.

Delay estimation by expected value

The estimation of time delay between narrowband signals is discussed. A minimum mean square error (MMSE) estimator is used that utilizes the maximum likelihood (ML) window derived by Knapp and Carter in obtaining the required conditional probability density function from which the delay estimate is calculated. The results of simulations using a narrowband signal are presented which evaluate and compare the mean square error of the MMSE and ML processors. The MMSE estimator shows improvement over the ML estimator, particularly in regions below the threshold signal-to-noise ratio. Conditions for application of the MMSE processor are discussed as well as some important considerations for its implementation.

Optimum localization of multiple sources by passive arrays

The maximum likelihood (ML) estimator of the location of multiple sources and the corresponding Cramer-Rao lower bound on the error covariance matrix are derived. The derivation is carried out for the general case of correlated sources so that multipath propagation is included as a special case. It is shown that the ML processor consists of a bank of beam-formers, each focused to a different source, followed by a variable matrix-filter that is controlled by the assumed location of the sources. In the special case of uncorrelated sources and very low signal-to-noise ratio this processor reduces to an aggregate of ML processors for a single source with each processor matched to a different source. Iterative algorithms for the actual computation of the ML estimator are also presented.

Maximum-likelihood receiver for low-angle tracking radar. Part 1: The symmetric case

A new maximum-likelihood processor is described for estimating the elevation angle of a target in the combined presence of specular multipath and receiver noise, as encountered in a low-angle tracking-radar environment. The processor makes special use of the symmetry of the incident direct and specular multipath components with respect to the normal to the receiving array. The theory of the processor is supported by both computer simulation and experimental results. The effect of deviation from perfect symmetry is also examined.

Passive systems theory with narrow-band and linear constraints: Part II - Temporal diversity

This paper studies passive problems where the receiver extracts from the source radiated signature information concerning the parameters defining the relative source/receiver geometry. A model encompassing the fundamental global and local characteristics for passive positioning and navigation is presented. It considers narrow-band signals, imposes linear constraints on the geometry, and exhibits explicitly the symmetry between the space and time aspects. The analysis concentrates on questions of global geometry identifiability, emphasizing the passive global range acquisition. The maximum-likelihood processor is analyzed by studying the ambiguity structure associated with inhomogeneous passive narrowband tracking. Bounds on the global and local mean-square error performance are studied and tested via Monte Carlo simulations. By considering two limiting geometries, a distant and a close observer, simple approximate expressions for the mean-square errors are presented and compared to the exact bounds. Herein the study is restricted to stationary geometries where the source is located by an extended array (spatial diversity). Subsequent papers generalize the study to moving sources (temporal diversity) and to coupled geometries.

Seismic signal and noise processing

The character of seismic signals and noise is known on the basis of theoretical solutions of the elastic wave equation and from observations made at seismic stations and arrays. The design of these arrays depends on the correlation structure of the signals and noise, and on whether the goal is to separate mixed signals or to detect signals in noise., Advanced signal-processing techniques have been shown to be of practical importance in the mixed signal problem. Among techniques which have been developed beyond beamforming are three-dimensional frequency-wavenumber spectra, nonlinear three-component waveform filtering, maximum-likelihood processors using either a priori or measured signal and noise characteristics, and eigenvalue-eigenvector decompositions of mixed signals. Theory and examples will be given for each of these techniques.