Geometrical fusion method for multi-sensor robotic systems

A general statistical fusion method motivated by the geometry of uncertainties is proposed for robotic systems with multiple sensors. The treatment of nonlinearity is generalized so as to include both the structural nonlinearity and the computational nonlinearity. First, assuming Gaussian noise additive to the sensory data, the uncertainty ellipsoid associated with the covariance matrix of the error of the sensory information is defined. Second, the optimal fusion is defined as the one, among all the possible linear combinations of sensory information, that minimizes the geometrical volume of the ellipsoid. The resultant fusion equation coincides with those obtained by Bayesian inference, Kalman filter theory, and the weighted least-squares estimation. Finally, the method is extended to include the fusion of partial information