On Estimating a Counter From Its Noisy Successive Instances

We consider the problem of estimating the initial state of an L-bit counter given noisy soft decision data corresponding to consecutive instances of this counter. This is relevant to a GPS L1C receiver, and we present a novel low-complexity bit iterative technique involving linear combining of data across the multiple instances. We show that this significantly improves the ability of an autonomous receiver to decode time from the GPS signal. We also propose a solution to a related problem that finds application in a GPS L2C receiver in which the data corresponding to successive instances of the counter are convolutionally encoded. Simulations show that our solutions perform very close to the optimal estimator at a fraction of the computational cost.