Target Localization and Sensor Self-Calibration of Position and Synchronization by Range and Angle Measurements

The sensor position uncertainties and synchronization offsets can cause substantial performance degradation if the sensors are not properly calibrated. This paper investigates the localization of a constant velocity moving target and the self-calibration of sensors using a sequence of range and azimuth measurements observed at successive instants. A theoretical study by the Cramer-Rao Lower Bound (CRLB) reveals that the sensor positions can only be self-calibrated when there are at least two sensors and synchronization offsets can be handled by joint estimation. A low complexity sequential closed-form solution is proposed to estimate the target position and velocity first, and the coordinates of each sensor and synchronization offset afterward. While less intuitive, the analysis shows that the closed-form solutions for both the target and sensor parameters can reach the CRLB accuracy under small Gaussian noise. We also develop a semidefinite programming (SDP) solution by semidefinite relaxation (SDR) for joint localization and calibration from the Maximum Likelihood formulation, which exhibits higher noise tolerance than the closed-form solution. Simulations validate the analysis and the performance of the proposed methods.