Distributed Kalman filtering based on consensus strategies

Abstract

In this paper, we consider the problem of estimating the state of a dynamical system from distributed noisy measurements. Each agent constructs a local estimate based on its own measurements and estimates from its neighbors. Estimation is performed via a two stage strategy, the first being a Kalman-like measurement update which does not require communication, and the second being an estimate fusion using a consensus matrix. In particular we study the interaction between the consensus matrix, the number of messages exchanged per sampling time, and the Kalman gain. We prove that optimizing the consensus matrix for fastest convergence and using the centralized optimal gain is not necessarily the optimal strategy if the number of exchanged messages per sampling time is small. Moreover, we showed that although the joint optimization of the consensus matrix and the Kalman gain is in general a non-convex problem, it is possible to compute them under some important scenarios. We also provide some numerical examples to clarify some of the analytical results and compare them with alternative estimation strategies.

Particle filtering with applications in networked systems: a survey

“…In [107], the authors consider a two-stage distributed Kalman filter which consists of a measurement update step and a fusion step using consensus algorithm. The interaction between the filter gain, the consensus matrix and the number of communications is analyzed in depth.…”

Feature-based map merging with dynamic consensus on information increments

“…Distributed averaging methods automatically avoid problems of double counting information; however, they suffer from the delayed data problem, that takes place when the nodes execute the state prediction without having incorporated all the measurements taken at the current step, giving rise to disagreement in the robot estimates [19]. An interesting solution is given in [16] but its convergence is proved only in the absence of observation and system noises.…”

Distributed Kalman filtering

“…Other publications cited in Table 2.12 are [28], [30], [31,180], [33], [80], [10], [99], [102], [103], [104], [111], [112,113], [118], [209], [210], [222], [243], [322], [327], [328] and [320] repectively.…”

“…In [33], a network is modeled as a Bernoulli random topology and establish necessary and sufficient conditions for mean square sense and almost sure convergence of average consensus when network links fail. Other DKF methods and its applications can be seen in [26], [27], [28], [29], [30], [31], [32], [123], [153], [218], [219] and [220].…”