The Tensor Unscented Kalman Filter

Tensors can efficiently represent high-dimensional data, simplify the modeling and computation of complex systems and enhance the performance and flexibility of algorithms in tasks such as multi-sensor fusion and nonlinear system estimation. Meanwhile, the unscented Kalman filter (UKF) directly handles nonlinear systems through the unscented transformation, avoiding linearization errors. This ensures estimation accuracy and numerical stability, making it suitable for highly nonlinear scenarios. Based on the Bayesian filtering principle, this article derives the UKF for recursively estimate tensors based on the streaming tensor measurements. The proposed algorithm leverages the tensor Kronecker product for deriving the covariance of tensor distribution based on the sigma points, which allow for accurately propagating the first two moments of tensor posterior. Simulation results show that the proposed tensor UKF (TUKF) in this letter outperforms the state-of-art algorithm, thus verifies the effectiveness of TUKF.