Model based processing of signals: a state space approach

This paper is a tutorial on linear, state space, model-based methods for certain nonlinear estimation problems commonly encountered in signal and data analysis. A prototypical problem that is studied is that of estimating the frequencies of multiple, superimposed sinusoids from a short record of noise-corrupted data. The approach expounded however, is applicable to a vast range of nonlinear signal analysis problems and applications in direction finding and damped sinusoid retrieval are dealt with in some detail. The benefits that result from using a state space description of the signal are highlighted in this paper. It is shown that state space models provide an elegant tool for exposing the structure present in the problem. The approach also allows for robust parameterization of the model with respect to finite precision errors. The robustness of the parameter set is complemented by the availability of numerically robust tools to estimate the parameters. The resulting algorithms are compatible with multiprocessor implementations