SOME DESIGN CONSIDERATIONS FOR DIGITAL TRACKING FILTERS.
Abstract
The problem of how best to operate on sampled data to smooth and predict a polynomial corrupted by noise has received much attention. Finite memory and recursive filters have been studied. In this paper the weighting sequences for both are derived in the same notation, by designing the filters according to the criterion of minimizing the square error weighted by a function of the age of the data. When the age-weighting function is truncated, the filters become finite memory; when the age-weighting function is exponentially decaying, recursive filters result. Expressions are then derived in this uniform notation for the random error due to white measurement noise; and the systematic error, which arises because the actual track is assumed to be a higher order polynomial than the model. The random error increases with the model order m and decreases with the memory length, while the reverse is true for the systematic error. Thus numerical evaluation of these expressions provides some basis for the choice of memory length, model order, and filter type for the filtering of polynomials. The results of some explicit calculations are given for finite memory and recursive filters, one-step-ahead prediction, cubic actual track, and linear and quadratic models. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1967
- Accession Number
- AD0664486
Entities
People
- Kenneth Steiglitz
Organizations
- Institute for Defense Analyses