Key result
The proposed multi-state Markovian-random walk adaptive filter effectively estimated time-varying block sparse system impulse responses, outperforming alternative algorithms in acoustic channel experiments.
The proposed multi-state Markovian-random walk adaptive filter effectively estimates time-varying block sparse system impulse responses, outperforming alternative algorithms in severe time-varying conditions.
Proposed model may improve sparse adaptive filtering; leaves open validation in cardiovascular signal applications.
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.
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Zayyani et al. (2024) studied this question. Multi-state Markovian-random walk adaptive filter vs. Alternative algorithms was evaluated on System impulse response estimation under severe time-varying conditions. The proposed multi-state Markovian-random walk adaptive filter effectively estimated time-varying block sparse system impulse responses, outperforming alternative algorithms in acoustic channel experiments.
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