Remote State Estimation for Nonlinear Systems Under Compression-Decompression Mechanism: A Modified Unscented Kalman Filtering Approach

In engineering practice, some large-scale systems have high-dimensional measurements that exhibit redundancy and are suitable to be compressed. Measurement compression-decompression is an effective approach to saving communication resources in networked control systems, and compressive sensing (CS) is a popular high-performance compression-decompression method for such measurements. In this paper, we investigate the remote state estimation for nonlinear systems under a compression-decompression mechanism on the measurement output. With the application of CS, a state estimator is designed based on the unscented Kalman filter. Despite the prominent advantages of CS, the presence of measurement noise and quantization errors in practice is inevitable, which could lead to a degradation in the performance of CS and an enlargement of state estimation errors. To address this challenge, we analyze the combined influence of measurement noise and quantization errors on the performance of data compression-decompression and state estimation. The design of estimator gains is approached by minimizing an upper bound of the estimation error covariance. Furthermore, a sufficient condition is derived to ensure the mean-square exponential boundedness of the estimation error. Finally, the effectiveness of the proposed method is verified through simulation experiments conducted on power grid systems, which are characterized by highly redundant measurements that are suitable for compression-decompression.