All-in-one: Certifiable Optimal Distributed Kalman Filter under Unknown Correlations
The optimal fusion of estimates in a Distributed Kalman Filter (DKF) requires tracking of the complete network error covariance, problematic in terms of memory and communication. A scalable alternative is to fuse estimates under unknown correlations, doing the update by solving an optimisation problem. Unfortunately, this problem is NP-hard, forcing relaxations that lose optimality guarantees. Motivated by this, we present the first Certifiable Optimal DKF (CO-DKF). Using only information from one-hop neighbours, CO-DKF solves the optimal fusion of estimates under unknown correlations by a particular tight Semidefinite Programming (SDP) relaxation which allows to certify, locally and in real time, if the relaxed solution is the actual optimum. In that case, we prove optimality in the Mean Square Error (MSE) sense. Additionally, we demonstrate the global asymptotic stability of the estimator. CO-DKF outperforms other state-of-the-art DKF algorithms, specially in sparse, highly noisy setups.
Code (0)
등록된 구현이 없습니다.
Tasks
AllSimilar Papers 제목 키워드 기반
ECO-DKF: Event-Triggered and Certifiable Optimal Distributed Kalman Filter under Unknown Correlations
This paper presents ECO-DKF, the first Event-Triggered and Certifiable Optimal Distributed Kalman Filter. Our algorithm addresses two major issues inherent to Distributed Kalman Filters: (i) fully distributed and scalabl…
A Distributed Implementation of Steady-State Kalman Filter
This paper studies the distributed state estimation in sensor network, where $m$ sensors are deployed to infer the $n$-dimensional state of a linear time-invariant (LTI) Gaussian system. By a lossless decomposition of op…
State EstimationOn Infinite-horizon System Level Synthesis Problems
System level synthesis is a promising approach that formulates structured optimal controller synthesis problems as convex problems. This work solves the distributed linear-quadratic regulator problem under communication …
Consensus optimization approach for distributed Kalman filtering: performance recovery of centralized filtering with proofs
This paper investigates the distributed Kalman filtering (DKF) from distributed optimization viewpoint. Motivated by the fact that Kalman filtering is a maximum a posteriori estimation (MAP) problem, which is a quadratic…
Distributed OptimizationDistributed Kalman Filters for Relative Formation Control of Mobile Agents
Formation control (FC) of multi-agent plays a critical role in a wide variety of fields. In the absence of absolute positioning, agents in FC systems rely on relative position measurements with respect to their neighbors…
Position