Novel recursive instrumental variable algorithms for sensor arrays and related applications

Abstract

Sensor array processing has broad applications including radar, communication, and underwater acoustics. Many algorithms have been proposed to estimate the bearings of multiple narrowband signals from measurements of an array of sensors. Subspace-based approaches have drawn much attention recently due to their ability to resolve closely spaced arrival angles for low signal-to-noise ratios as well as its computational simplicity. Unfortunately, subspace-based approaches used in the above-mentioned applications may suffer from various problems such as unknown statistics of underlying signals, Gaussian or even correlated interference or noise, low signal to noise ratio environment, slowly time-varying or sharp change system channel, etc. All these problems will degrade the performance of subspace-based algorithms. This work aims to propose some novel subspace-based algorithms with applications to tackle these problems. In certain applications, these unknown statistics (or signal subspace) of underlying signals to be estimated is time-varying and the system is contaminated by Gaussian noise. Hence we propose a new local polynomial modeling (LPM) based variable forgetting factor (VFF) and variable regularized (VR) projection approximation subspace tracking (PAST) algorithm to tackle these problems. The subspace to be estimated is modeled as a local polynomial model so that a new locally optimal forgetting factor (LOFF) can be obtained by minimizing the resulting mean square deviation of the RLS algorithm. An l2-regularization term is also incorporated into the LOFF-PAST algorithm to reduce the estimation variance of the subspace during signal fading. Simulation results are carried out to demonstrate the superiorities of the proposed algorithm. Many least squares (LS) based subspace tracking algorithms assume that the noise is spatially white. Consequently, the estimates may be biased by non-uniform noises. We further proposed a new square-root extended instrumental variable (IV) PAST algorithm with VFF and VR to solve this problem. A new LPM based VFF is first developed by minimizing the mean square deviation (MSD) of the EIV linear model and the IV-PAST algorithm. A new variable l2 regularization term is also derived to reduce the variance of the estimator. A square-root version of the algorithm is then proposed to improve the numerical stability of the algorithm and avoid the problem of loss of positive-definiteness of the inverse covariance matrix. Simulations show that the proposed algorithm yields improved performance over the conventional algorithms. As the conventional LS method can become biased when the linear model is correlated with input noise. We finally propose a new VFF QR decomposition-based recursive least squares (RLS) algorithm with bias compensation (VFF-QRRLS-BC) for system identification with input noise. Particularly, a new VFF scheme is proposed to improve the convergence speed and steady-state mean squares error (MSE) of the RLS-based bias compensation. A new method for recursive estimation of the additive noise variance is also proposed for reliable bias compensation. A self-calibration scheme is further proposed to improve the steady-state MSE due to finite sample effect. An efficient linear array architecture is proposed for the realization of this algorithm. The good performances demonstrate the advantages of the proposed VFF-QRRLS-BC algorithm.