Singular Perturbation for Non-Linear Filter Densities.
Abstract
For discrete periodic sensors and multi-dimensional white noise sources, with the source covariance matrix proportional to a scalar source noise parameter > o, the one-step predictor and the filter conditional densities are represented by a power series in the source noise parameter. Let n be an integer and 1/delta be the sampling rate. Then the coefficients of the power series at time n delta are differential operators acting on the conditional filter density at time (n-1) delta. A set of difference equations is derived which relates the jth coefficient of the series at time n delta to the k, k=o, 1, ..., j, coefficients of the series at time (n-1) delta. This difference equation is applied to a phase demodulator sensor with a one-dimensional Brownian motion source. For j=1, the Fourier transform of the difference equation is computed, and is shown to be identical to one obtained for this filtering system by other methods. The difference equation is used to derive a series solution for a phase demodulator which senses the first integral of Brownian motion. A sub-optimal filter is constructed from the Fourier transform of the difference equation. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1975
- Accession Number
- ADA015867
Entities
People
- Richard Ralph Tye
Organizations
- University of Southern California