Growth curve models in signal processing applications.

摘要

As a powerful statistical tool, the growth-curve (GC) model is attracting increasing attentions in various areas. In this dissertation, we study several variations of the growth-curve model, and discuss their applications to the emerging multiple-input multiple-output (MIMO) radar system.; We first study the statistical properties of two estimators for the regression coefficient matrix in the GC model, i.e., the maximum likelihood (ML) and Capon methods. We derive the closed-form expression of the Cramer-Rao bound (CRB) for the unknown regression coefficient matrix, and then analyze the bias properties and mean-squared errors (MSEs) of the two estimators. We show that the multivariate ML estimator is unbiased whereas the multivariate Capon estimator is biased downward for finite data samples. Both estimators are asymptotically statistically efficient when the number of data samples is large.; Next, we consider a variation of the GC model, referred to as the diagonal growth-curve (DGC) model, where the regression matrix is constrained to be diagonal. A closed-form approximate maximum likelihood (AML) estimator for this model is derived based on the maximum likelihood principle. We analyze the statistical properties of this method theoretically and show that the AML estimate is unbiased and asymptotically statistically efficient for a large number of data samples. Via several numerical examples in array signal processing and spectral analysis, we also show that the proposed AML estimator can achieve better estimation accuracy and exhibit greater robustness than the best existing methods.; Then we consider a general growth-curve model, referred to as the block diagonal growth-curve (BDGC) model, where the unknown regression coefficient matrix is constrained to be block-diagonal, and which can unify the GC and DGC models. We proposed a closed-form approximate maximum likelihood (AML) estimator for the block-diagonal constrained matrix, which is proved to be unbiased and asymptotically statistically efficient for a large data sample number. Several applications of this model in signal processing are then presented.; Finally, we consider a multiple-input multiple-output (MIMO) radar system with a general antenna configuration, i.e., both the transmitter and receiver have multiple well-separated subarrays with each subarray containing closely-spaced antennas. Hence, both the coherent processing gain and the spatial diversity gain can be achieved by the system simultaneously. We introduce several spatial spectral estimators, including Capon and APES, for target detection and parameter estimation. We also provide a generalized likelihood ratio test (GLRT) and a conditional generalized likelihood ratio test (cCLRT) for the system. Based on GLRT and iGLRT, we then propose an iterative GLRT (iGLRT) procedure for target detection and parameter estimation. Via several numerical examples, we show that iGLRT can provide excellent detection and estimation performance at a low computational cost.