Optimal Position Estimate from a Stars Fix with Correlated Errors

Abstract

This paper concerns the estimate of a ship's position from a sequence of measurements of 3, 4 or 5 altitudes of stars or planets. The measurement errors are assumed to be mutually correlated. This correlation is mainly caused by the appearance of so-called systematic errors. It is the main intention of this paper to dispense with the policy of pre-separation of these systematic errors. Instead, the equal contribution of some partial errors to the total measuring errors is fully accounted for by the formation of the covariance matrix, which corresponds with the vector of measurement errors. The algorithm produces a position estimate with a bias-free estimation error, meaning that the estimate and the error are stochastically independent. The resulting covariance matrix of the position error has a minimal trace.