Combination of Land-Based and Satellite-Based OTH Geolocations Using Differentiable Exact Penalty Method

In civil or military applications, a transmitter on Earth may utilize different means of communications. A typical example is the naval craft, which often radiates very high frequency signals received by a satellite system and high frequency signals received by land-based observers. This article concentrates on the combination of land-based and satellite-based over-the-horizon (OTH) geolocations. A quadratic constrained weighted least-squares optimization model for the combined geolocation is established and a differentiable exact penalty solution is developed to locate the OTH transmitter in an iterative manner, which is shown to have robust convergence performance. Theoretical analysis is presented, which involves the Cramér–Rao bound for combined geolocation under the constraint of ellipsoidal Earth model and the closed-form expression of mean square error for the proposed method. Numerical examples are provided to validate our theoretical analysis and illustrate that the proposed method outperforms other geolocation methods in a wide range of scenarios.