Optimum Position Estimation Using Multiple-Frequency Omega

The maximum-likelihood estimator of the line of position (LOP) resulting from K frequencies received from each of two Omega stations for high SNR is derived. The estimator takes advantage of interfrequency correlation of phase uncertainties by modeling them as resulting from phase velocity uncertainties which are jointly Gaussian with known covariance. The utilization of Omega for search and rescue systems is examined. For this application, the result of increasing the size of the unambiguous lanes of Omega by addition of a fourth frequency to the present three-frequency format is examined. The results of Monte Carlo simulation, performed for several easily implemented fourth frequencies, are presented. The simulation results illustrate the extent to which lane errors can be expected as a function of various fourth frequencies, phase velocity uncertainties, and SNR.