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Assessing Probability of Correct Ambiguity Resolution in the Presence of Time-Correlated Errors

To meet their accuracy requirements, many applications require the resolution of the carrier phase ambiguities to their integer values. However, the process of ambiguity resolution is ultimately based on statisti- cal values and therefore has an associated probability of being performed correctly. This paper develops a method of computing the probability of correctly fixing the ambiguities in the presence of time correlated errors. A new Kalman filter for use in the presence of time correlated observations is reviewed and adapted for carrier phase GPS applications. In terms of correlated errors, consideration is specifically given to ionosphere, zenith troposphere, and multipath effects; all modeled as first-order Gauss-Markov processes. Simulated results, based on the covariance matrix of the float ambiguities, are used to provide theoretical bounds on the probability of correct fix using several levels of observation error variances and time correlations. Results indicate that increased correlation of observations reduces the ability to resolve ambiguities suggesting that if observation cor- relation is ignored, overly optimistic probabilities of correct ambiguity resolution will be obtained.