Encoding-Decoding-Based Recursive Filtering for Fractional-Order Systems

Dear editor, This letter focuses on the encoding-decoding-based recursive filtering problem for a class of fractional-order systems. For the purpose of protecting security of the wireless communication network, a dynamic-quantization-based encoding-decoding mechanism is introduced to encrypt the transmitted measurement. Specifically, the measurement outputs are first encoded by the encoder into codewords which are then transmitted over the wireless communication network. After received by the decoder, the codewords are decoded and then sent to the filter. In light of the mathematical properties of truncated Gaussian distribution, the variance of the encoding-decoding-induced error between the decoded measurement and the real measurement is derived. An upper bound on the filtering error covariance is first obtained based on the variance of the encoding-decoding-induced error. Then, the minimal upper bound is derived by choosing proper filter gain. Finally, the efficiency and superiority of the proposed algorithm are verified through a simulation example.