Multi-state Markovian-random walk adaptive filter for time-varying block sparse system identification

This paper presents a higher order multi-state Markov model for block sparsity model of a system impulse response. To capture the time-varying behavior of the system, a random walk model for temporal evolution is incorporated; resulting in a two-dimensional multi-state Markov-Random walk model across spatial and temporal domains. Additionally, a block batch data structure is utilized for the adaptive filter design. The proposed adaptive filter is aimed to find the Maximum A Posteriori (MAP) estimator of the batch time-varying impulse response. The associated optimization problem is demonstrated to be convex and efficiently solvable through the Steepest- Descent (SD) approach. Furthermore, the final recursion of the proposed adaptive filter is derived and a mean convergence analysis of the algorithm is provided. Simulation results show the effectiveness of the proposed algorithm under severe time-varying conditions of the system impulse response, where alternative algorithms may exhibit divergence or poor convergence. Synthetic experiments and real-world experiments using acoustic channel estimation further validate the superiority of the proposed algorithm.