Integer Parameter Estimation in Linear Models with Applications to GPS

A. Hassibi and S. P. Boyd

IEEE Transactions on Signal Processing, 46(11):2938-2952, November 1998.
Shorter version in Proceedings of IEEE Conference on Decision and Control, 3:3245-3251, December 1996.

We consider parameter estimation in linear models when some of the parameters are known to be integers. Such problems arise, for example, in positioning using phase measurements in the global positioning system (GPS). Given a linear model, we address two problems: The problem of estimating the parameters and the problem of verifying the parameter estimates. Finding maximum likelihood estimates and verifying them (under Gaussian measurement noise) are very difficult in theory (NP-hard). However, by using a polynomial-time algorithm (LLL algorithm) both of these problems can be solved efficiently in practice. Simulation results are given that are based on a GPS setup.