The Cramer-Rao Lower Bound for 3-D state estimation from rectified stereo cameras

It is well known that any 3-D state estimate computed from stereo camera measurements is corrupted by heteroscedastic noise due to the nature of the perspective projection. It is also well understood that the image measurements used to estimate the 3-D state are inherently noisy. Despite the wealth of research in this area, the accurate statistical characterisation of the uncertainty for any 3D state estimation from stereo algorithm is less well understood. This paper presents the Cramer-Rao Lower Bound (CRLB) for 3-dimensional state estimation from a rectified stereo pair of cameras. The paper also presents a method for efficient stereo estimation via Bayesian triangulation that achieves the CRLB. These results provide a basis for 3D statistical estimation for camera-based sensor measurements.