Bearings-Only Localization with NLOS Reflected AoAs

Sensor networks enable the localization of a target (or source) of interest with spatially complementary observations. Current available physical measurements include received signal strength [1], time of arrival [11], angle of arrival (AoA) [6, 7, 10, 13, 19], and so forth. They can be individually or cooperatively utilized in target information extraction. In this paper, we concentrate on localizing a single target with distributed AoAs, specifically bearings-only localization. Bearings-only localization infers the position of a target with multiple AoA lines, which share a unique intersection–the target location–in the absence of noise. If observation uncertainty is included, a global intersection may not exist and advanced estimators are required. Least squares (LS) is a straightforward choice if the noise distribution is unknown [6]. If noise statistics are known, maximum likelihood (ML) is an option and is popular [10, 13]. Its good performance is guaranteed at the cost of computational load. The Stansfield estimator is a kind of weighted LS for independent Gaussian noise [19]; it is a compromise between estimation performance and computation. Reference [10] shows that the root mean square errors (RMSEs) of a Stansfield estimator are not necessarily larger than those of ML in bearings-only localization. Other approaches include total least squares [7], and so forth. The aforementioned works focus on line-of-sight (LOS) propagation, where a direct path exists between the target and sensors; nevertheless, practical problems may not necessarily have a LOS. When the wavefront (acoustic, light, or electromagnetic) of target radiation meets an interface between two media, reflection will happen [14]. The reflection is helpful for the extraction of target information in some circumstances, especially where LOS propagation is unavailable. An interesting application is over-the-horizon radar (OTHR) [9, 17] (see Fig. 1). If multiple geometrically complementary radar sensors are available, a fusion center can infer the position of the target with proper data association.1 Instead of LOS AoAs, this paper studies the localization with non-line-of-sight (NLOS) reflection measurements, where the radiation from a target reaches a sensor after a single specular reflection.