Localized Distributed Kalman Filters for Large-Scale Systems∗

This paper presents a scalable method to design large-scale Kalman-like filters for a class of linear systems. In particular, we consider systems for which both the propagation of dynamics through the plant and the exchange of information between estimators/sensors is subject to delays. Under suitable assumptions on these delays, our proposed Kalman-like filter has the following desirable properties: (1) each local estimator only needs to collect the information within a localized region to estimate its local state, and (2) each local estimator can be designed by solving a local optimization problem using local plant model information. The decomposition of the global problem into local subproblems thus allows for the method to scale to arbitrarily large heterogeneous systems - this is clearly an extremely favorable property for large-scale estimation problems. The effectiveness of our algorithm is demonstrated on a randomized heterogeneous example with 51200 states, in which the traditional Kalman filter cannot be computed within a reasonable amount of time.