Spectra using data distribution and covariance modelling

The autoregressive and Prony methods for spectral estimation do not make full use of the statistics of the additive noise. These statistics are included in the following as constraints on the solution. The finite number of data samples imposes a limit on the resolution thus making it possible to approximate random signals by a set of deterministic signals which can be modelled in terms of a finite set of time-invariant parameters, θ. The non-Toeplitz covariance calculated from the data is modelled here using the θ parameters. Statistical constraints and covariance modelling are combined to produce non-linear methods for spectral estimation. The resulting higher resolution requires high computational complexity; this can often be substantially reduced by using knowledge-based techniques.