Recursive multi‐sensor fusion estimation under the coding‐based relay network

Abstract This paper studies the recursive fusion estimation issue for a class of linear time‐varying multi‐sensor systems with amplify‐and‐forward (AF) relays. The AF relay is located between the sensor and the estimator to forward measurement signals for facilitating long‐distance transmission. A binary encoding scheme is used to regulate signal transmission via a digital network where the signal is encoded into a bit string and decoded at the endpoint of the receiver. Because of the uncertainty of the network and the existence of channel noises, a set of Bernoulli distributed random variables is introduced to characterize the random bit flip phenomenon. The purpose of the addressed problem is to design a fusion estimator to simultaneously reflect the impact of multiplicative noises, the AF relay, the binary encoding scheme, and the random bit flip on the filtering error covariance. First of all, an upper bound for the filtering error covariance of the local estimator can be acquired, and by minimizing such an upper bound, the parametric form of the gain matrix is obtained. Subsequently, the fusion estimation is given based on the covariance intersection fusion strategy. Finally, a simulation example is presented to verify the effectiveness of the proposed multi‐sensor fusion estimation.