An introduction to deterministic modelling

This paper outlines some of signal analysis methods based on deterministic data models. These models assume the data consists of a small number of deterministic components embedded in noise. As with all model based signal processing the performance of the methods described herein critically depends upon the accuracy of the underlying model. If the model chosen is appropriate for the data measured then excellent results can be obtained. However, use of an inappropriate model can, at best, be suboptimal and possibly produce misleading results. It is concluded that, for the problem of estimating the frequencies of sinusoidal signals in white noise, there is a wide variety of methods available (only a very limited subset have been dealt with herein). The Fourier transform gives near optimal results if only one sinusoid is present or if the signals are well separated. In other circumstances probably the most desirable method is that of maximum likelihood, however, the required non-linear optimisation is tedious. The iterative formulation of this method offers a more feasible approach and should be considered. The eigen based methods, such as MUSIC, offer a more palatable alternative, by sacrificing some performance to reduce the problem to one dimension