A Gaussian Filter for High-Dimensional State-Space Models with State Partition and Multivariate Laplace Distribution

To address the computational burden induced by high-dimensional system structures, this article investigates linear Gaussian filtering (GF) with high-dimensional state-space and Multivariate Laplacian (ML) distribution. To mitigate the computational intractability arising from excessive dimensionality, a novel partitioned Gaussian filtering algorithm is proposed, which decomposes high-dimensional state vectors into substate blocks for tractable inference. This paper applies variational Bayesian (VB) inference and hierarchical Gaussian models to derive a filtering algorithm based on state partitioning and ML distributions in high-dimensional state spaces, aiming to reduce computational complexity. Simulation demonstrates that the proposed algorithm exhibits rapid convergence, steady-state stability, and effectiveness.