Mixed integer estimation and validation for next generation GNSS

The coming decade will bring a proliferation of Global Navigation Satellite Systems (GNSS) that are likely to revolutionize society in the same way as the mobile phone has done. The promise of a broader multifrequency, multisignal GNSS "system of systems" has the potential of enabling a much wider range of demanding applications compared to the current GPS-only situation. In order to achieve the highest accuracies, one must exploit the unique properties of the received carrier signals. These properties include the multi-satellite system tracking, the mm-level measurement precision, the frequency diversity, and the integer ambiguities of the carrier phases. Successful exploitation of these properties results in an accuracy improvement of the estimated GNSS parameters of two orders of magnitude. The theory that underpins this ultraprecise GNSS parameter estimation and validation is the theory of integer inference. This theory is the topic of the present chapter.