Distributing the Kalman Filter for Large-Scale Systems

By Usman A. Khan, José M. F. Moura. IEEE Transactions on Signal Processing, 2007

463 citations recorded by the source corpus.

This paper presents a distributed Kalman filter to estimate the state of a sparsely connected, large-scale, n -dimensional, dynamical system monitored by a network of N sensors. Local Kalman filters are implemented on nl-dimensional subsystems, nl Lt n, obtained by spatially decomposing the large-scale system. The distributed Kalman filter is optimal under an Lth order Gauss-Markov approximation to the centralized filter. We quantify the information loss due to this Lth-order approximation by the divergence, which decreases as L increases. The order of the approximation L leads to a bound on the dimension of the subsystems, hence, providing a criterion for subsystem selection. The (approximated) centralized Riccati and Lyapunov equations are computed iteratively with only local communication and low-order computation by a distributed iterate collapse inversion (DICI) algorithm. We fuse the observations that are common among the local Kalman filters using bipartite fusion graphs and consensus averaging algorithms. The proposed algorithm achieves full distribution of the Kalman filter. Nowhere in the network, storage, communication, or computation of n-dimensional vectors and matrices is required; only nl Lt n dimensional vectors and matrices are communicated or used in the local computations at the sensors. In other words, knowledge of the state is itself distributed.

Subfields: Artificial Intelligence, Computer Networks and Communications

View Paper: https://www.semanticscholar.org/paper/2baff04bced8a8ac164ab2d790743c4eb5314ac1

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Citations in the corpus

Adaptation, Learning, and Optimization over Networks (2014, background): “, [8, 32, 52, 83, 128, 138, 139, 143, 175, 176, 180, 225, 243, 266]) proposed useful extensions of the original consensus construction (7.”
State Estimation in Electric Power Grids: Meeting New Challenges Presented by the Requirements of the Future Grid (2012, background): “IEEE SIGNAL PROCESSING MAGAZINE [39] SEPTEMBER 2012 measurements to obtain an optimal state estimate.”
A Survey on Security Communication and Control for Smart Grids Under Malicious Cyber Attacks (2019, background): “Generally, distributed state estimation (DSE) [100]–[103] will supply an efficient way to reduce the computational complexity by applying a local processor to provide a local state estimation solution.”
Distributed model predictive control: A tutorial review and future research directions (2013, unknown): “In [108], a solution based on reduced-order and decoupled models for each subsystem was proposed, while subsystems with overlapping states were considered in the fully distributed schemes of [70], [142], [141] and in [151], where an all-to-all communication among subsystems was required.”
Distributed Sensor Localization in Random Environments Using Minimal Number of Anchor Nodes (2008, background): “These networks call for efficient distributed algorithms where each node communicates directly only with a few neighboring nodes (either sensors or anchors) and a low order computation is performed locally at the node and at each iteration of the algorithm, for example, see [1].”
Adaptive Networks (2014, methodology): “…time scale for performing multiple consensus iterations similar to (54b) over the states of the neighbors, and a second slower time scale for performing gradient vector updates or for updating the estimators by using the result of the consensus iterations (e.g., [81], [87], [89], and [106]–[109]).”
Diffusion Strategies for Distributed Kalman Filtering and Smoothing (2010, methodology): “Recent work [13] proposes an efficient algorithm for large-scale distributed Kalman filtering, where the transfer matrices are assumed to be sparse and localized, while [14] considers optimization of the consensus weights for a scalar state-space model.”
Control Principles of Complex Networks (2015, background): “…the minimum set of sensor nodes that assure the observability of nonlinear systems (Aguirre and Letellier, 2005; Khan and Doostmohammadian, 2011; Khan and Moura, 2008; Letellier and Aguirre, 2005; Letellier et al., 2006; Letellier and Aguirre, 2010; Siddhartha and van Schuppen, 2001) and its…”
A Theoretical Foundation of Network Localization and Navigation (2018, background): “However, joint spatial and temporal cooperation incurs associated costs such as additional communication and more complicated algorithms over the network: 1) the communication among nodes is required for inter-node measurements and information exchange; and 2) interdependency among the estimates of ”