Two-Stage Cubature Kalman Filtering Based on T-Transform and Its Application

According to the actual application system model which has bias, this paper analyzes the shortage of the conventional augmented algorithm, the two-stage cubature Kalman filtering algorithm, which is presented on the basis of a two-stage nonlinear transformation. The core ideas of the algorithm are to obtain the block diagonalization of the covariance matrix using the matrix transformation and avoid calculating the covariance of the state and bias to reduce the amount of calculation and ensure a smooth filtering process. Then, the equivalence of the two-stage cubature Kalman filtering algorithm and the cubature Kalman filtering algorithm is proved by updating equivalent transformation. Through the experiment of trajectory tracking of a wheeled robot, it is verified that the two-stage cubature Kalman filtering algorithm can obtain good tracking accuracy and stability with the presence of unknown random bias. Simultaneously, the equivalence of the two-stage cubature Kalman filtering algorithm and cubature Kalman filtering algorithm is verified again using the contrast experiment.

Transmission rate conditions for distributed filtering in sensor networks against eavesdropper

This paper studies the distributed secure estimation problem of sensor networks (SNs) in the presence of eavesdroppers. In an SN, sensors communicate with each other through digital communication channels, and the eavesdropper overhears the messages transmitted by the sensors over fading wiretap channels. The increasing transmission rate plays a positive role in the detectability of the network while playing a negative role in the secrecy. Two types of SNs under two cooperative filtering algorithms are considered. For networks with collectively observable nodes and the Kalman filtering algorithm, by studying the topological entropy of sensing measurements, a sufficient condition of distributed detectability and secrecy, under which there exists a code–decode strategy such that the sensors’ estimation errors are bounded while the eavesdropper’s error grows unbounded, is given. For collectively observable SNs under the consensus Kalman filtering algorithm, by studying the topological entropy of the sensors’ covariance matrices, a necessary condition of distributed detectability and secrecy is provided. A simulation example is given to illustrate the results.