The Method of Least Squares and Optimal Filtering Theory
Abstract
The correspondence between the well-known method of least squares and the more recent optimal filtering theory of Kalman is demonstrated. It shows that via a simple lemma on matrix inversion, most of the results in linear filtering and prediction theory can be easily derived. The connection of the least square method with the so-called Duality Principle in optimal control theory is also discussed. This connection places in evidence the mathematical similarities between problems of control and problems of prediction. The Memorandum concludes with a proposed application for orbit determination of a 24-hour satellite using the techniques described. This application is concerned with computing corrections to the satellite's orbital parameters based on noisy observations of azimuth and elevation angles by improving an initial orbital parameter estimation through additional observations. The orbital parameter corrections may then be used as the input to an orbit transfer process or to refine a preliminary orbit.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1962
- Accession Number
- AD0286742
Entities
People
- Y. C. Ho
Organizations
- RAND Corporation