The design of distributed filtering based on lattice rule

•A distributed Kalman filter algorithm based on rank-1 lattice rule is proposed under the background of multi-micro targets, which uses fewer sampling points than other filters.•By constructing Lyapunov functional and using stochastic stability lemma, the stability of distributed filter is analyzed.•The effectiveness of the algorithm is verified by simulation, and the complexity of calculation is reduced while the accuracy is maintained. For the problem of multiple micro-target tracking and positioning, the high-dynamic and communication coupling are two cases in actual motion. The dynamic evolution and measurement among them are depicted by a nonlinear system. This paper proposes a new distributed lattice Kalman filter (DLKF) to cope with the two cases simultaneously. The prediction is based on the Cranley-Patterson shift and Korobov lattice rule to generate the low-difference sample points. The update stage is based on the weighted average consistency to fusion its innovation and the information of its neighbor. The stability of this distributed filter is proved by constructing the upper and lower bound of the Lyapunov functional. The finite steps consensus iteration strategies for the update fusion are also investigated. To evaluate the efficiency of the DLKF, it is compared with unscented Kalman filtering and its distributed form. The simulation results show that DLKF uses significantly fewer sampling points than other quasi-Monte Carlo (QMC) filters while maintaining the estimation accuracy. The computational complexity is significantly lower, which is the key factor for application to multiple micro-targets.