Orbit determination: Statistical methods

The problem of finding a satellite trajectory from position and/or velocity measurements taken at a given instant in time is examined. A trajectory evolution model including a random vector which represents measurement error is presented. Assuming an iterative approach, the problem is linearized using a previous orbital position estimation. The least squares method is considered in terms of the linear model, approximation in Euclidean space, and for the calculation power of a minimum variance estimator and a maximum likelihood estimator. The Kalman method is then studied and aspects of Bayesian statistics and calculation using a discrete Kalman filter are shown. In application, algorithms based on both least squares and Kalman methods are developed for orbit determination.