Maximum likelihood coordinate registration for over-the-horizon radar

Over-the-horizon radar exploits the refractive and multipath nature of high-frequency propagation through the ionosphere to achieve wide-area surveillance. The coordinate registration process converts the group delays and azimuths (i.e., slant coordinates) from a set of multipath target returns to an estimate of its location (i.e., ground coordinates). This is performed by associating the target returns with ray modes determined using a computational electromagnetic propagation model. Not surprisingly, errors in the estimates of down-range ionosphere parameters can seriously degrade the accuracy of the target location estimate. The coordinate registration method presented is designed to achieve improved accuracy by employing a statistical model for uncertainties in the ionosphere. Modeling down-range ionospheric parameters as random variables with known statistics facilitates maximum likelihood (ML) target location estimation, which is more robust to errors in the measured ionospheric conditions. The statistics of down-range ionospheric parameters can be determined using current and historical soundings of the ionosphere. ML target localization consists of determining the most likely target ground coordinates over an ensemble of ionospheric conditions consistent with the data. For greater computational efficiency, the likelihood function is approximated by a hidden Markov model (HMM) for the probability of a sequence of observed slant coordinates given a hypothesized target location. The parameters of the HMM are determined via Monte Carlo execution of a ray tracing propagation model for random realizations of the ionosphere. A simulation study performed using a random ionospheric model derived from ionogram measurements made at Wallops Island suggests that the ML method can potentially achieve average absolute miss distances as much as five times better than a conventional coordinate registration technique.