  Multiband fusion enhances WiFi sensing by jointly utilizing signals from
multiple non-contiguous frequency bands. However, in the multi-band WiFi
sensing signal model, there are many local optimums in the associated
likelihood function due to the existence of high frequency component and phase
distortion factors, posing challenges for high-accuracy parameter estimation.
To address this, we propose a two-stage scheme equipped with different signal
models derived from the original model, where the first-stage coarse estimation
is performed using a weighted root MUSIC algorithm to narrow down the search
range for the subsequent stage, and the second-stage refined estimation
utilizes a Bayesian approach to avoid convergence to bad suboptimal solutions.
Specifically, we apply the block stochastic successive convex approximation
(SSCA) approach to derive a novel stochastic particle-based variational
Bayesian inference (SPVBI) algorithm in the refined stage. Unlike conventional
particle-based VBI (PVBI) that optimizes only particle probability and incurs
exponential per-iteration complexity with particle count, our more flexible
SPVBI algorithm optimizes both the position and probability of each particle.
Additionally, it utilizes block SSCA to significantly improve sampling
efficiency by averaging over iterations, making it suitable for
high-dimensional problems. Extensive simulations demonstrate the superiority of
our proposed algorithm over various baseline methods.
