Joint Detection and Super-Resolution Estimation of Multipath Signal Parameters Using Incremental Automatic Relevance Determination

Abstract

The presented work investigates a sparse Bayesian incremental automatic relevance determination (IARD) algorithm in the context of multipath parameter estimation in a super-resolution regime. The corresponding estimation problem is highly nonlinear and, in general, requires an estimation of the number of multipath components. In the IARD approach individual multipath components are processed sequentially, which permits a tractable convergence analysis of the corresponding inference expressions. This leads to a simple condition, termed here a pruning condition, that determines if a multipath component is "sparsified" or retained in the model, thus permitting a fast and adaptive realization of the estimation algorithm. Yet previous experiments demonstrated that IARD fails to select the correct number of components when the parameters entering nonlinearly the multipath model are also estimated. To understand this effect, an analysis of the statistical structure of the pruning condition is proposed. It is shown that the corresponding test statistic in the pruning condition follows an extreme value distribution. As a result, the standard IARD algorithm implements a statistical test with a very high probability of false alarm. This leads to insertion of estimation artifacts and underestimation of signal sparsity. Moreover, the probability of false alarm worsens as the number of measured signal samples grows. Based on the developed statistical interpretation of the IARD, an optimal adjustment of the pruning condition is proposed. This permits a reliable and efficient removal of estimation artifacts and joint estimation of signal parameters, as well as optimal model order selection within a sparse Bayesian learning framework.