Stochastic assessment of GPS observations for LEO relative navigation

A more realistic stochastic model to GPS observations for LEO spacecraft relative navigation applications is formulated. This model considers the double-differencing introduced correlation between different channels, the correlation between different observation types, as well as temporal correlation of the measurements. The individual observation precision of each single channel is modelled using a predefined carrier-to-noise-power-density-ratio (C/N0) dependent model, which is more realistic than the usually used satellite elevation dependent model. This GPS observations stochastic model is presented in a form of covariance matrix which has been written as an unknown linear combination of known cofactor matrices. The coefficients of this linear combination are then assessed by an iterated reweighted least-squares variance component estimator. The efficiency of this estimator is investigated using data collected in a high-dynamics aircraft experiment and a zero-baseline experiment. Test results indicate that the precision of the estimated relative position and the randomness of the observation residuals are improved by applying the proposed stochastic model and assessment procedure.