Solutions to the Kalman Filter Wordlength Problem: Square Root and U-D Covariance Factorizations.
Abstract
This report presents the concept of square root filters and the closely related U-D covariance factorization filter as viable alternatives to conventional Kalman filters. For a modest increase in computational loading, one obtains optimal filter algorithms equivalent to the Kalman filter if infinite wordlength is assumed, but with vastly superior numerical characteristics with finite wordlength. These algorithms are at least as good as a solution to troublesome measurement update computations as implementing a Kalman filter in double precision, since the Kalman filter inherently involves unstable numerics. The filter algorithms are developed and presented in a form convenient for implementation. Of the covariance square root forms, the Carlson filter is more efficient than the Potter form computationally, and it also maintains triangularity of the square root matrices. The U-D covariance factorization filter is even more efficient, not requiring square root computations. In comparison, the inverse covariance square root filter is often considerably more burdensome, although it too becomes competitive if the measurement dimension is very large. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1977
- Accession Number
- ADA049704
Entities
People
- Peter S. Maybeck
Organizations
- Air Force Institute of Technology