Least Sum of Absolute Residuals Orbit Determination

A statistical orbit determination approach that minimizes the sum of absolute errors incurred by the vector measurements is developed. An iterative linear program is derived for the differential corrections associated with the best estimated epoch state to minimize the sum of the absolute errors. It is shown that in the presence of redundant measurements, the minimum one-norm solution rejects outlier measurements. An estimate of the variance of the estimated epoch state is also derived. The epoch state and associated covariance estimates are verified using Monte Carlo simulations for representative orbit determination examples.