Crossing-point estimation for sampled random signals

We consider the problem of estimating the crossing points of a known carrier signal with a Gaussian random process, given uniformly-spaced, noisy samples of the random process. We derive the maximum a-posteriori (MAP) estimator for the problem, along with the Cramer-Rao bound (CRB) on estimator variance. We also derive an alternate, computationally efficient estimator using a minimum mean-squared error (MMSE) approach, and show that this MMSE estimator approximates the MAP estimator in the high-SNR regime. Simulations show that both MMSE and MAP estimators approach the CRB and outperform alternative estimators based on inverse linear and Lagrange interpolating polynomials.