The Modified Ambiguity Function Approach with regularization for instantaneous precise GNSS positioning

Abstract

Abstract The Modified Ambiguity Function Approach (MAFA) implicitly conducts the search procedure of carrier phase GNSS integer ambiguity resolution (IAR) in the coordinate domain using the integer least squares (ILS) principle, i.e. MAFA-ILS. One of the still open scientific problems is an accurate definition of the search region, especially in the context of instantaneous IAR. In doing so, the float solution results, which encompass float position (FP) and its variance-covariance (VC) matrix, must be improved as these are necessary for defining the search region. For this reason, the ambiguity parameters are separately regularized, and then the baseline parameters are conditioned on regularized float ambiguities. The conditional-regularized estimation is thus designed, obtaining the regularized FP (RFP) and its VC-matrix. This solution is promising because its accuracy is enhanced in the sense of mean squared error (MSE) thanks to the improved precision at the cost of regularized bias. The optimal regularization parameter (RP) values obtained for ambiguity parameters balance the contributions of improved precision and bias in the regularized float baseline solution’s MSE. Therefore, the regularized search region is defined accurately in the coordinate domain to contain such approximate coordinates that more frequently give the correct ILS solution. It also contains fewer MAFA-ILS candidates, improving the search procedure’s numerical efficiency. The regularized ILS estimator performs well with the presence of bias, increasing the probability of correct IAR in the coordinate domain.