Parameter Estimation Method for Factorial Linear Dynamical Systems

Linear dynamical systems (LDS) are widely used for modeling time-series signals. However, with the increasing number of signal sources, observations often exhibit significant overlap, which poses challenges for conventional LDS-based analysis. Factorial LDS (FLDS) has been introduced to address this issue by factorizing the system's hidden state into multiple underlying random processes. Existing parameter estimation approaches rely on sampling-based algorithms, leading to high computational complexity. In this letter, we derive a factorized approximate expectation maximization (EM) algorithm for FLDS, providing an efficient alternative to the exact EM method. Meanwhile, a Fisher information based analysis is provided to give an intuitive explanation of the estimation results. Simulation results validate the effectiveness of the proposed algorithm and further show that the estimation accuracy can improve as the observation channel number increases.