A Distributed Implementation of Steady-State Kalman Filter

Yan, Jiaqi; Xu, Yang; Mo, Yilin; You, Keyou

doi:10.48550/arxiv.2101.10689

Cited by 1 publication

(11 citation statements)

References 15 publications

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“…Based on it, the proposed estimator is proved to be stable at each sensor side under the minimal requirements of network connectivity and collective system observability. This extends, in a non-trivial way, the results in our previous work [36] for the full transmission case.…”

Section: Introductionsupporting

confidence: 89%

“…This result is essential for us to design a framework of distributed estimation later in this paper. Moreover, this section extends in a non-trivial way, the results in [36] by performing model reduction, which results in the decomposition of Kalman filter with lower order. Consequently, the developed distributed estimator enjoys lower message complexity, as will be discussed in Section IV.…”

Section: A Lossless Decomposition Of Kalman Filtermentioning

confidence: 91%

“…where A u ∈ R n u ×n u and A s ∈ R n s ×n s ; any eigenvalue of A u lies on or outside the unit circle while all the eigenvalues of A s are strictly inside. We then introduce the following lemmas: 36]). Suppose that (X, p) is controllable, where X ∈ R n×n and p ∈ R n .…”

Section: A Lossless Decomposition Of Kalman Filtermentioning

confidence: 99%

“…Remark 1. The solution of (11), i.e., F i , can be obtained by following the construction proof of Lemma 3, which is provided in [36].…”

Section: Lemma 3 ( [36]mentioning

confidence: 99%

“…There, the local filters are to be used in a centralized manner, allowing a simpler structure with β = 0 n . The local filters of the form (14) was proposed in [36] for distributed estimation. Lemma 4 is included in the results there, but not explicitly.…”

Section: Lemma 3 ( [36]mentioning

confidence: 99%

See 4 more Smart Citations

A Framework for Distributed Estimation with Reduced Communication via Event-Based Strategies

Yan¹,

Mo²,

Ishii³

2022

Preprint

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In this paper, we consider the problem of distributed estimation in a sensor network, where multiple sensors are deployed to estimate the state of a linear time-invariant (LTI) Gaussian system. By losslessly decomposing the Kalman filter, a framework of event-based distributed estimation is developed, where each sensor node runs a local filter using solely its own measurement, alongside with an event-based synchronization algorithm to fuse the neighboring information. One novelty of the proposed framework is that it decouples the local filter from synchronization process. By doing so, we prove that a general class of triggering strategies can be applied in our framework, which yields stable distributed estimators under the minimal requirements of network connectivity and collective system observability. Moreover, the developed results can be generalized to achieve a distributed implementation of any Luenberger observer. By solving a semi-definite programming (SDP), we further present a low-rank estimator design to obtain the optimal gain of Luenberger observer such that the distributed estimation is realized under the constraint of message size. Therefore, as compared with existing works, the proposed algorithm enjoys lower data size for each transmission. Numerical examples are finally provided to demonstrate the proposed methods.

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Section: Introductionsupporting

confidence: 89%

Section: A Lossless Decomposition Of Kalman Filtermentioning

confidence: 91%

Section: A Lossless Decomposition Of Kalman Filtermentioning

confidence: 99%

“…Remark 1. The solution of (11), i.e., F i , can be obtained by following the construction proof of Lemma 3, which is provided in [36].…”

Section: Lemma 3 ( [36]mentioning

confidence: 99%

Section: Lemma 3 ( [36]mentioning

confidence: 99%