Quadratic Filtering Based with Random Access Protocols and Probabilistic Quantization

This paper focuses on the design of quadratic filters for a class of linear discrete-time systems subject to non-Gaussian noises. To tackle data collisions and bandwidth constraints in network-based communication, the random access protocol (RAP) is employed to schedule the access opportunities for sensors, and the so-called probabilistic quantizer is applied to digitize measurement signals. An augmented system is constructed using Kronecker power to capture the full dynamic nature of the plant and communication behaviors. A quadratic filter is subsequently developed according to such an augmented system. Then, an upper bound matrix of the corresponding error covariance matrix is derived. The desired filter gain is obtained by minimizing this upper bound. Simulation results demonstrate that the proposed quadratic filter, which accounts for random access and quantization errors, significantly enhances state estimation accuracy and system robustness compared to traditional Kalman filtering scheme.