Tensor Network Kalman Filter for LTI Systems

An extension of the Tensor Network (TN) Kalman filter [2], [3] for large scale LTI systems is presented in this paper. The TN Kalman filter can handle exponentially large state vectors without constructing them explicitly. In order to have efficient algebraic operations, a low TN rank is required. We exploit the possibility to approximate the covariance matrix as a TN with a low TN rank. This reduces the computational complexity for general SISO and MIMO LTI systems with TN rank greater than one significantly while obtaining an accurate estimation. Improvements of this method in terms of computational complexity compared to the conventional Kalman filter are demonstrated in numerical simulations for large scale systems.