Consensus Kalman Filter for Weighted Directed Graphs

[Jan 2019 – May 2020]

Distributed state estimation algorithms have received considerable attention lately, owing to advancements in computing, communication and battery technologies. In this project, we sought to design a novel consensus-based distributed estimation algorithm that places emphases on robustness and optimality. The algorithm is developed by extending the Kalman-Consensus Filter (KCF) algorithm to incorporate weighted consensus. Our proposed algorithm has the following characteristics, one or several of which are missing from existing algorithms: i) it does not require tuning of design parameters; ii) its derivation does not involve ad-hoc steps or approximations; iii) it does not rely on consensus sub-iterations; and iv) by using weighted consensus at each sensor, the algorithm filters out any redundant, malicious and noisy information received from neighboring sensors.

To validate the proposed algorithm and compare it against those preceding it, we considered the problem of target-tracking using a network of cameras. In the figure below, the shaded (yellow) area represents the field of view of the corresponding camera; when the target moves out of the field of view, the camera is unable to record measurements of the target. Distributed estimation algorithms which use unweighted consensus (such as KCF) perform poorly in such a scenario, whereas the proposed algorithm is seen to estimate the target sufficiently well: (See image)

Our algorithm was also observed to achieve the lowest mean squared estimation error at each sensor, when compared to comparable algorithms in literature.


Principal Investigators

Related Publications

  • S. Khan, “Optimal Information-Weighted Kalman Consensus Filter,” Purdue University Graduate School, 2020, DOI: 10.25394/PGS.12218078.v1

  • S. Khan, R. Deshmukh, and I. Hwang, “Optimal Kalman Consensus Filter for Weighted Directed Graphs,” in 2019 IEEE 58th Conference on Decision and Control (CDC), pp. 7832–7837, IEEE, 2019, DOI: 10.1109/CDC40024.2019.9030070