Maximum-likelihood localization of a camera network from heterogeneous relative measurements

This paper proposes an algorithm for estimating the absolute pose (position and orientation) of n cameras using relative measurements between pairs of cameras. Our work is inspired by the recent work [1] where the same problem was considered and a distributed algorithm was proposed. In contrast to [1], which fused relative measurements of orientation and bearing between camera pairs, and produced a least squares estimate, we make two novel contributions. First, our algorithm is capable of fusing any type of relative measurement between cameras: relative orientation, relative position, relative bearing, or relative distance, or any combination thereof. Second, the algorithm determines a maximum likelihood estimate of the camera poses when the measurement noises distributions are Gaussian-like in their corresponding Riemannian manifolds. A gradient descent method on the product manifold (SO(3) × R³)ⁿ is used to compute the estimates. Unlike past probabilistic techniques, our assumed distribution for measurement noise on orientation and bearings are defined on the natural manifolds rather then any parameterization. Though the proposed algorithm is centralized in its computation, we discuss how the computations can be distributed among the cameras. Performance of the proposed algorithm is examined through simulations. Comparison with the algorithm in [1] with non-uniform sensor accuracy reveals which algorithm is most appropriate for a given scenario.