CRLB for multi-sensor rotational bias estimation for passive sensors without target state estimation

Bias estimation is a significant problem in target tracking applications and passive sensors present additional challenges in this field. Biases in passive sensors are commonly represented as unknown rotations of the sensor coordinate frame and it is necessary to correct for such errors. Many methods have used simultaneous target state and bias estimation to register the sensors, however it may be advantageous to decouple state and bias estimation to simplify the estimation problem. This way bias estimation can be done for any arbitrary target motion. If measurements are converted into Cartesian coordinates and differenced then it is possible to isolate the effects of the biases. This bias pseudo-measurement approach has been used in bias estimation for many types of biases and sensors and this paper applies this method to 3D passive sensors with rotational biases. The Cram´er-Rao Lower Bound for the bias estimates is evaluated and it is shown to be attained, i.e., the bias estimates are statistically efficient.