Kristine L. Bell

Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking

This article reviews Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking by Harry L. Van Trees, Kristine L. Bell , Piscataway, New Jersey, 2007. 951 pp.

A Bayesian approach to robust adaptive beamforming

111.00 (paperback), ISBN: 0470120959

A recursive least squares implementation for LCMP beamforming under quadratic constraint

An adaptive beamformer that is robust to uncertainty in source direction-of-arrival (DOA) is derived using a Bayesian approach. The DOA is assumed to be a discrete random variable with a known a priori probability density function (PDF) that reflects the level of uncertainty in the source DOA. The resulting beamformer is a weighted sum of minimum variance distortionless response (MVDR) beamformers pointed at a set of candidate DOAs, where the relative contribution of each MVDR beamformer is determined from the a posteriori PDF of the DOA conditioned on previously observed data. A simple approximation to the a posteriori PDF results in a straightforward implementation. Performance of the approximate Bayesian beamformer is compared with linearly constrained minimum variance (LCMV) beamformers and data-driven approaches that attempt to estimate signal characteristics or the steering vector from the data.

Extended Ziv-Zakai lower bound for vector parameter estimation

Quadratic constraints on the weight vector of an adaptive linearly constrained minimum power (LCMP) beamformer can improve robustness to pointing errors and to random perturbations in sensor parameters. We propose a technique for implementing a quadratic inequality constraint with recursive least squares (RLS) updating. A variable diagonal loading term is added at each step, where the amount of loading has a closed-form solution. Simulations under different scenarios demonstrate that this algorithm has better interference suppression than both the RLS beamformer with no quadratic constraint and the RLS beamformer using the scaled projection technique, as well as faster convergence than LMS beamformers.

Array self-calibration with large sensor position errors

The Bayesian Ziv-Zakai bound on the mean square error (MSE) in estimating a uniformly distributed continuous random variable is extended for arbitrarily distributed continuous random vectors and for distortion functions other than MSE. The extended bound is evaluated for some representative problems in time-delay and bearing estimation. The resulting bounds have simple closed-form expressions, and closely predict the simulated performance of the maximum-likelihood estimator in all regions of operation.

Robust constrained linear receivers for CDMA wireless systems

Self-calibration algorithms estimate both source directions-of-arrival (DOAs) and perturbed array response vector parameters, such as sensor locations. Calibration errors are usually assumed to be small and a first order approximation to the perturbed array response vector is often used to simplify the estimation procedure. In this paper, we develop a new procedure that does not rely on the small error assumption. It has better performance for large estimation errors, and when used to initialize the Weiss and Friedlander (1991) MUSIC-based iterative technique, we see significant improvement over existing techniques for both small and large errors.

A bound on mean-square estimation error with background parameter mismatch

For code-division multiple access (CDMA) communication systems, many constrained linear receivers have been developed to suppress multiple access interference. The linearly constrained formulations are generally sensitive to multipath fading and other types of signal mismatch. We develop robust linear receivers by exploring appropriate constraints. Multiple linear constraints are exploited to preserve the output energy that is scattered in multipath channels. In addition, a quadratic inequality constraint on the weight vector norm is used to improve robustness with respect to imprecise signal modeling. These constraints can be applied to the minimum output energy (MOE) detector to mitigate the signal mismatch problem and to the decision directed minimum mean square error (MMSE) detector to prevent error propagation and eliminate the need for training sequences at startup. Adaptive implementations for the proposed detectors are presented using recursive least square (RLS) updating in both the direct form and the partitioned linear interface canceller (PLIC) structure. Simulations are performed in a multipath propagation environment to illustrate the performance of the proposed detectors.

A recursive least squares implementation for adaptive beamforming under quadratic constraint

In typical parameter estimation problems, the signal observation is a function of the parameter set to be estimated as well as some background (environmental/system) parameters assumed known. The assumed background could differ from the true one, leading to biased estimates even at high signal-to-noise ratio (SNR). To analyze this background mismatch problem, a Ziv-Zakai-type lower bound on the mean-square error (MSE) is developed based on the mismatched likelihood ratio test (MLRT). At high SNR, the bound incorporates the increase in MSE due to estimation bias; at low SNR, it includes the threshold effect due to estimation ambiguity. The kernel of the bounds evaluation is the error probability associated with the MLRT. A closed-form expression for this error probability is derived under a random signal model typical of the bearing estimation/passive source localization problem. The mismatch is then analyzed in terms of the related ambiguity functions. Examples of bearing estimation with system (array shape) mismatch demonstrate that the developed bound describes the simulations of the maximum-likelihood estimate well, including the sidelobe-introduced threshold behavior and the bias at high SNR.

Maximum likelihood approach to joint array detection/estimation

Quadratic constraints on the weight vector of an adaptive linearly constrained minimum power (LCMP) beamformer can improve robustness to pointing errors and to random perturbations in sensor parameters. In this paper, we propose a technique for implementing a quadratic inequality constraint with recursive least squares (RLS) updating. A variable diagonal loading term is added at each step, where the amount of loading is found from the solution to a quadratic equation. Simulations under different scenarios demonstrate that this algorithm outperforms both the RLS beamformer with no quadratic constraint, and the RLS beamformer using the scaled projection technique.

A unified method for measurement and tracking of contacts from an array of sensors

The problem of detecting the number of (possibly correlated) narrowband sources of energy and estimating the direction of arrival (DOA) of each detected source using data received by an array of sensors is investigated. A combined detection and estimation approach based on the likelihood function (LF) is used. The approach is motivated by detection theoretic considerations instead of information theoretic criteria and uses maximum likelihood (ML) signal-to-noise ratio (SNR) estimates of hypothesized sources as detection statistics rather than maximizing the LF with a penalty function. Performance comparisons are made to unstructured and structured techniques based on Akaike information theoretic criteria (AIC), minimum description length (MDL), and Bayesian predictive density (BPD) approaches as well as the minimum variance distortionless response (MVDR) approach. An important feature that distinguishes this approach is the ability to trade off detection and false alarm performance, which is not possible with the other LF-based approaches, while achieving performance levels comparable to or exceeding the LF-based and MVDR approaches.