Over‐the‐horizon radar target localization using a hidden Markov model estimated from ionosonde data

Uncertainty about the downrange ionospheric conditions is a well-known source of localization errors in over-the-horizon radar. Statistical modeling of ionospheric parameters has recently been proposed in order to derive a maximum likelihood (ML) localization method which is more robust to ionospheric variability. Maximum likelihood coordinate registration 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. In previous work, estimation of the HMM parameters was achieved assuming that the statistics of the underlying ionosphere were known precisely. This paper addresses the problem of estimating the parameters of the HMM from contemporaneous ionospheric sounder measurements. The approach taken here is to treat the plasma frequency profile as a homogeneous random process over the region around the midpoint between the radar and the dwell illumination region. In particular, spatial sampling of a three-dimensional (3-D) ionospheric model, fitted to ionosonde measurements, is used to generate quasi 2-D plasma frequency profile realizations. Estimates of the hidden Markov model parameters are then obtained by using smoothed bootstrap Monte Carlo resampling. A comparison of ML localization and conventional methods, using full 3-D ionospheric modeling and 2-D ray tracing, are given using real data from a known target at a ground range of 2192 km. Results for over 250 radar dwells indicate that the ML localization technique achieves better than a factor of 2 improvement over conventional methods.