Measurement-level fusion method for distributed HFHSSWR under unknown parameters

Distributed shipborne high-frequency hybrid surface-sky wave radar (HFHSSWR) detects targets through the same sky-wave path and different shipborne surface-wave paths. This distributed configuration overcomes aperture constraints and low detection probabilities typical of single shipborne platforms. However, time-varying ionospheric height, time-varying measurement noise, and fixed array biases degrade target state estimation accuracy and tracking performance. These factors are highly correlated with each other as well as with multipath data association, which leads to an inference problem involving high-dimensional latent variables and renders exact solutions computationally intractable. We introduce a message-passing framework into distributed shipborne HFHSSWR to facilitate the joint inference of unknown time-varying parameters and multipath data association. This paper first establishes a measurement model for distributed shipborne HFHSSWR and provides a single-point initialization method. Inspired by the sky-wave mean-field–belief-propagation (MF–BP) network, we then construct MF–BP frameworks for two scenarios: (i) considering only the time-varying fluctuations of ionospheric height and measurement errors; and (ii) considering the time-varying fluctuations of ionospheric height and measurement errors as well as unknown fixed array biases. The proposed networks operate in a closed-loop iterative manner and can directly process measurements from multiple shipborne platforms and multiple propagation paths. Simulation results under different receiver deployment configurations and detection probability conditions show that the proposed method improves target state estimation accuracy and tracking performance compared with the reference algorithm.