Estimation of Relative Satellite Position Using Transformed Differential Carrier-Phase GPS Measurements

Abstract

Techniques for applying differential carrier-phase global positioning systems to satellite formation clusters with large (approximately 100 km or more) baselines are described. Because satellites in the cluster may move relative to each other, it is imperative that the carrier-phase ambiguities be resolved quickly and accurately. We propose a transformation of the m-vector carrier-phase measurement equations that restricts the geometric nonlinearities to a one-dimensional subspace and an almost universal linearization of the position state and integer ambiguities in the remaining m - 1 dimensional subspace. We then show that all of the measurement equations can be processed with an unscented Kalman filter to quickly compute very accurate floating-point valued estimates of the system state and error covariance. By an integer-preserving transformation found in the least-squares ambiguity decorrelation adjustment method, the number of possible hypotheses for the double-differenced wide-lane ambiguity candidates can be reduced. For the hypotheses set applying a multiple hypothesis Wald sequential probability test, using a specially conditioned form of the transformed global positioning system measurements, quickly and almost optimally determines the correct value of the carrier-phase double-differenced ambiguity. Once the double-differenced wide-lane ambiguities are obtained, the L 1 double-differenced ambiguities are resolved by using L 1 and L 2 carrier-phase measurements based on wide-lane integers in the unscented Kalman filter, then using the least-squares ambiguity decorrelation adjustment method for determining the hypotheses, followed by the multiple hypothesis Wald sequential probability test for resolving the L 1 double-differenced ambiguities. Finally, using the L 1 carrier-phase measurements, the unscented Kalman filter produces the relative position estimates. These techniques are then demonstrated on a simulation of a formation of two satellites in low Earth orbits.