Abstract
Robust state estimation is addressed in a noisy environment and within a distributed and networked architecture. Both bounded disturbances and random noises are considered. A Distributed Zonotopic and Gaussian Kalman Filter (DZG-KF) is proposed where each network node implements a local state estimator using symbolic Zonotopes and Gaussian noise Mergers (s-ZGM), a class of Set-membership and Probabilistic Mergers (SPM). Each network node communicates its own state information only to its neighbours. The proposed system includes a dedicated service called Unique Symbols Provider (USP) giving unique identifiers. It also includes Matrices with Labelled Columns (MLC) featuring column-wise sparsity, and symbolic zonotopes (s-zonotopes). This significantly enhances the propagation of uncertainties and preserves global dependencies that would otherwise be lost (or impeded) by the peer-to-peer communication through the network. A number of other network-related constraints can be managed within this framework. Numerical simulations show significant improvements compared to a non-symbolic approach.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1 Concretely, following the solution based on (Equation32(32) (32) )–(Equation33(33) (33) ) developed in the paragraph 8.1, the knowledge of and only requires the knowledge of time-varying matrix pairs and , respectively.
2 The size of an s-ZGM is precisely formalised in the Definition 8.1.
3 Either globally or locally.
4 For all the CPS agents.
5 is the relative complement of J in I.
6 MAC: Medium Access Control.
7 That is, under in (Equation36(36) (36) )–(Equation40(40) (40) ).
8 As formalised in definition 8.1.
9 Relative wrt steady position.