Satellite Orbital Parameter Refinement

Abstract

Simulation studies have many limitations, but one of their indisputable advantages is that they enable us to make a comparison between supposed results and the truth. Starting from simulated radar observations, orbital parameters for six near-earth satellites were derived. Tracking was done using expanding- and fading-memory a-ß-? filters based on the orthogonal polynomials of Legendre and Laguerre. These also served as pre-processors for the estimation and refinement of the orbital parameters by three algorithms:

· Gauss-Newton (1809) (known to astronomers as differential correction and to statisticians as non-linear regression)

· Bayes-Swerling (1958)

· Kalman-Bucy (1960)

Keplerians were obtained together with their errors and covariance matrices, making it possible to compare accuracy as well as statistical consistency by use of the Chi-squared metric. Execution times of the three estimation algorithms as well as the polynomial trackers were also studied. In most cases Kalman and Swerling give estimates that are acceptable although differential correction almost always gives estimates that are more accurate, sometimes substantially so. In many situations Kalman and Swerling have problems of consistency between the errors and their covariance matrices (as evidenced by out of bounds Chi-square values), while differential correction almost never does ".

The talk should be of all interest to those PhD students and engineers who are interested in orbit (and attitude estimation), Kalman filtering, applications of GPS etc.