Measurement Error Estimation and Its Applications in Bearing-Only Localization

To clarify the impact of the sensor-target geometry on bearing measurement error estimation, this study conducts an in-depth investigation into the optimal placement of homogeneous/heterogeneous sensors and the optimal bearing measurement error estimation based on bearing-only localization technology. Firstly, a weighted least squares (WLS) bearing measurement error estimation algorithm is proposed, and its influencing factors are analyzed. Secondly, the equivalence among the A-, D-, and E-optimality criteria in the sense of mean squared error (MSE) is obtained, as well as the optimal placement of homogeneous/heterogeneous sensors. Heterogeneous and homogeneous sensors share the same optimal placement form if the bearing measurement accuracy of the sensor is regarded as the weight of distance, i.e., each sensor is equidistant from the target and the separation angles between adjacent sensors are equal. Furthermore, key issues such as the optimal MSE, optimal (estimation, performance, and accuracy) indices, optimal bearing measurement error, and the relationship between MSE and bearing measurement error are discussed. It is pointed out that each bearing measurement error is zero in the statistical sense when the sensors are optimally placed, and the system can achieve the optimal localization accuracy by simultaneously satisfying both the relative sensor-target geometry condition and the measurement error condition. Finally, the specific application of bearing measurement error estimation in the error quadrilateral is presented, and main content and conclusions of this paper are verified by simulations.