Multi-sensor System Filtering and Fault Detection under Unbiased Constraint and Colored Measurement Noise

For a class of distributed sensor systems with no initial prior information and unknown statistical characteristics of measurement noise the state estimation and fault detection performance in the sense of least squares are studied. In the actual system, the mean and covariance of the initial state cannot be known in advance, and the initial state deviation will be generated and propagated in the iteration, thus affecting the effect of state estimation. In addition, the measurement noise in the actual process is generally colored noise, and its statistical characteristics are unknown. A filter considering gain attenuation and precision decrease of sensor is proposed. The unbiasedness of the filter is proved and its parameters are deduced. The upper and lower bounds of the fault-free residual are used as the threshold to detect faults. Finally, a numerical example is given to illustrate the effectiveness of the proposed algorithm.