Bayesian Filtering for High-Dimensional State-Space Models With State Partition and Error Compensation

In the era of exponential growth of data availability, the architecture of systems has a trend toward high dimensionality, and directly exploiting holistic information for state inference is not always computationally affordable. This paper proposes a novel Bayesian filtering algorithm that considers algorithmic computational cost and estimation accuracy for high-dimensional linear systems. The high-dimensional state vector is divided into several blocks to save computation resources by avoiding the calculation of error covariance with immense dimensions. After that, two sequential states are estimated simultaneously by introducing an auxiliary variable in the new probability space, mitigating the performance degradation caused by state segmentation. Moreover, the computational cost and error covariance of the proposed algorithm are analyzed analytically to show its distinct features compared with several existing methods. Simulation results illustrate that the proposed Bayesian filtering can maintain a higher estimation accuracy with reasonable computational cost when applied to high-dimensional linear systems.