Abstract:

In this paper, recursive filters are formulated for the mixed-integer GNSS receiver estimation problem, where the integer variables come from the ambiguities in the carrier-phase measurements. Insights from the linear setting illustrate pitfalls in designing optimal recursive filters, motivating a relaxation of the original optimization problem and a departure from conventional methods. A set of filters are developed for sequential nonlinear mixed-integer estimation based on statistical linearization, entertaining two estimate densities and taking the time-evolution of the ambiguities into account by adapting the process noise covariance based on a statistical model. Numerical examples illustrate the efficacy of the proposed algorithms.