In this paper, a novel tensor operator is introduced that directly solves the prediction step of the Bayes recursion for multi-dimensional discretized probability densities in Canonical Polyadic Decomposition form. The proposed operator combines computational efficiency with the possibility for non-linear and non-Gaussian scenarios. Based on the Continuous White Noise Velocity model, it enables a broad range of application in target tracking.

This paper focuses on state prediction for stochastic dynamic models with linear dynamics, emphasizing a recently proposed efficient and robust Lagrangian approach for solving the Chapman–Kolmogorov equation. In contrast to the standard Eulerian perspective, the Lagrangian method separates the solution into two sequential steps: advection and diffusion. Advection is handled by moving a carefully designed grid, while diffusion is addressed using the convolution theorem. This approach significantly reduces computational complexity while preserving the same accuracy. In this paper, we propose formulating diffusion as a continuous-time process, leading to a partial differential equation (PDE). Various methods for solving this PDE are presented and compared within a unified framework, along with evaluations of their properties and example implementations. We demonstrate that the continuous formulation can yield substantial reductions in computational complexity with only marginal loss in accuracy.

This paper presents the application of a novel target tracking technique employing tensor decompositions for discretizing the target state space. The time evolution of the conditional probability density is realized by a Fokker-Planck equation solver and the measurement update, as usual, by applying Bayes’ rule. The method is applicable to non-Gaussian and non-linear system equations and enables the treatment of complex non-Gaussian target state densities. In addition, the efficient tensor decomposition scheme, in principle, allows for high-dimensional target states. The new tracking filter is applied to the problem of tracking an agile air target using bearing measurements from distributed acoustic and electromagnetic array sensors based on real data. It is shown that the new filter is able to initiate and maintain the target track with localization errors comparable to those of a standard particle filter.