Dynamic Dictionary Algorithms for Model Order and Parameter Estimation

TLDR: It is demonstrated that dictionary-based estimation methods are capable of parameter estimation performance comparable to the Cramér-Rao lower bound and to traditional ML-based model estimation over a wide range of signal-to-noise ratios.

Abstract: In this paper, we present and evaluate dynamic dictionary-based estimation methods for joint model order and parameter estimation. In dictionary-based estimation, a continuous parameter space is discretized, and vector-valued dictionary elements are formed for specific parameter values. A linear combination of a subset of dictionary elements is used to represent the model, where the number of elements used is the estimated model order, and the parameters corresponding to the selected elements are the parameter estimates. In static-based methods, the dictionary is fixed; while in the dynamic methods proposed here, the parameter sampling, and hence the dictionary, adapt to the data. We propose two dynamic dictionary-based estimation algorithms in which the dictionary elements are dynamically adjusted to improve parameter estimation performance. We examine the performance of both static and dynamic algorithms in terms of probability of correct model order selection and the root mean-squared error of parameter estimates. We show that dynamic dictionary methods overcome the problem of estimation bias induced by quantization effects in static dictionary-based estimation, and we demonstrate that dictionary-based estimation methods are capable of parameter estimation performance comparable to the Cramer-Rao lower bound and to traditional ML-based model estimation over a wide range of signal-to-noise ratios.