On Canonical Polyadic Decomposition of Non-Linear Gaussian Likelihood Functions

Non-linear filtering arises in many sensor applications such as for instance robotics, military reconnaissance, advanced driver assistance systems and other safety and security data processing algorithms. Since a closed-form of the Bayesian estimation approach is intractable in general, approximative methods have to be applied. Kalman or particle based approaches have the drawback of either a Gaussian approximation or a curse of dimensionality which both leads to a reduction in the performance in challenging scenarios. An approach to overcome this situation is state estimation using decomposed tensors. In this paper, a novel method to compute a non-linear likelihood function in Canonical Polyadic Decomposition form is presented, which avoids the full expansion of the discretized state space for each measurement. An exemplary application in a radar scenario is presented.