An adaptive three-stage information filter of simultaneous state and unknown disturbance estimation in linear time-varying systems

An adaptive three-stage information filter is proposed to estimate unknown disturbances in discrete linear time-varying systems. By modeling unknown dynamic faults and observation abnormalities as parameter changes, the proposed filter is designed as three detachable filters, including the main information filter and two compensation filters. A rule for detecting the unknown dynamic and observation disturbances is presented based on a generalized likelihood ratio test. Under the classical uniform complete observability–controllability conditions and a persistent excitation condition, the exponential stability of the adaptive three-stage information filter is rigorously analyzed. The numerical examples are presented to illustrate the performance of the proposed algorithm. The results show that the proposed filter is a better trade-off between algorithm simplicity and efficiency; after the dynamic and observation disturbances change, the disturbance compensation converges after a transient.