A Cramer-Rao Lower Bound for the Estimation of Bias with a Single Bearing-Only Sensor

This paper presents a metric for finding optimal sensor and target geometries that provide accurate estimates of bias during target tracking with a single sensor taking measurements of bearing. Since the bias cannot be measured directly, it is shown how to manipulate the equations of a Kalman filter to produce a pseudo measurement of bias and its associated measurement error covariance. These measurement error covariances are used to form a Cramer-Rao lower bound (CRLB) on the bias estimation variance as a function of sensor and target geometries. It is shown that highly accurate estimates of bias can be produced using a single sensor, even if the kinematic state estimate of the target is poor.