A novel efficient estimator for three-dimensional bearings-only source localisation with unknown sensor altitude and systematic measurement errors

A novel two-stage profile maximum likelihood estimator is proposed to estimate the source location and the systematic errors jointly, with the aim of addressing the problem of source localisation using angle-only measurements from a single sensor with unknown sensor altitude and systematic measurement errors. The proposed two-stage profile maximum likelihood estimator algorithm is capable of decoupling the azimuth and elevation angle measurements while transforming the original maximum likelihood optimisation problem into two sub-problems, that is, two-dimensional-projected maximum likelihood estimator and relative altitude maximum likelihood estimator. In terms of the two-dimensional-projected maximum likelihood estimator, an algorithm combining pseudo-linear estimating and Kalman filtering is proposed to generate an initial estimate. Subsequently, a Gauss–Newton iterative method is developed to estimate the two-dimensional-projected target location and the azimuth systematic error jointly. The relative height maximum likelihood estimator is initialised using a pseudo-linear estimator. Next, a Gauss–Newton iterative algorithm is adopted to estimate the elevation systematic error and the relative height. As indicated by the result of the simulation studies, the proposed algorithm exhibits an estimation performance close to the Cramér–Rao lower bound with unknown sensor altitude and systematic measurement errors.