Robust recursive subspace and adaptive eigen-decomposition algorithms with applications

Abstract

Subspace-based approaches have received much attention in various engineering fields due to their ability to separate the signal information in a lower dimensional subspace from the undesirable noise in the noise subspace. They have found many signal processing applications including frequency estimation, system identification, source localization, and factor analysis, etc. Most subspace methods rely on conventional singular value decomposition or eigenvalue decomposition methods of batch input samples for subspace estimation. To reduce the arithmetic complexity especially for online applications, a number of recursive algorithms have also been proposed.

Signal subspace estimation from real world data is still challenging as data samples may be corrupted by Gaussian as well as non-Gaussian noise with impulsive characteristics. Moreover, the underlying signal subspace may be time-varying with an unknown signal dimension.

This thesis proposes novel robust recursive subspace and adaptive eigen-decomposition algorithms to address these important issues.

First, the problems of subspace tracking in direction-of-arrival (DOA) and frequency estimation with measurements corrupted by non-Gaussian impulsive noise are considered. Specifically, a new recursive robust subspace tracking-based estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm for online estimation based on robust M-estimate function is developed to suppress the adverse effect of possible impulsive outliers. Moreover, variable forgetting factor (FF) and regularization schemes are proposed to adapt to the time-varying environments and reduce the estimation variance during signal fading. Simulation and experimental results on synthetic, stimulated wind turbine and electric arc furnace data show that the proposed approach outperforms the conventional methods both in stationary and non-stationary environments.

To address the issue of noisy observation, a new extended instrumentation variable (EIV)-based subspace tracking algorithm is developed for online system identification in spatially colored noise. Moreover, variable FF, a new smoothly clipped absolute deviation (SCAD) regularization and a bi-iteration-based schemes are incorporated for improving the convergence speed and performing online automatic model order selection, respectively. Simulation results show that the proposed algorithms offer improved convergence speed and steady state performance and it also provides an online estimate of the system parameters and model order.

To further investigate the problem of adaptive dimension reduction, a new recursive dynamic factor analysis algorithm is developed for the imputation of missing data in wireless sensor networks (WSNs). Specifically, a new discrete Fourier transform (DFT)-based multiple deflation technique is proposed for tracking the variable subspace dimension. By exploring the correlation between measurements in the factor analysis model, missing data are effectively imputed. Simulation results using real WSN datasets show that the proposed algorithm is able to achieve better accuracy than other conventional approaches.

Finally, the problem of recursive EIV estimation under linear constraints and color noise is investigated via the development of a new recursive linearly constrained minimum variance beamformer based on the EIV method for planar radial coprime arrays under spatially colored noise. A matrix factorization method is proposed to incorporate multiple linear constraints to the recursive EIV problem for recursive beamforming. Simulation results show that the proposed beamformer outperforms the conventional beamformer in the resolution and suppression of interferences under various scenarios.