Distributed Nonlinear Kalman Filter with Communication Protocol

Abstract

This paper proposes an optimal design of the general distributed nonlinear Kalman-based filtering algorithm to tackle the discrete-time estimation problem with noisy communication networks. The algorithm extends the Kalman filter by enabling it to predict the noisy communication data and fuse it with the received neighboring information to produce a posterior estimate value. In the prediction step, the unscented transformations of the estimate values and covariances originated in the Unscented Kalman Filter (UKF) are exploited. In the update step, a communication protocol is appended to the posterior estimator, which consequently leads to a modified posterior error covariance containing the covariance of the communication term with its communication gain. Both Kalman and communication gains are then optimised to collectively minimise the mean-squared estimation error. Afterwards, stochastic stability analysis is performed to guarantee its exponential boundedness. To exemplify the performance, this algorithm is applied to a group of robots in a sensor network assigned to estimate an unknown information distribution over an area in the optimal coverage control problem. Comparative numerical experiments finally verify the effectiveness of our design.

Original language	English
Pages (from-to)	270-288
Number of pages	19
Journal	Information Sciences
Volume	513
Early online date	2 Nov 2019
DOIs	https://doi.org/10.1016/j.ins.2019.10.053
Publication status	Published - Mar 2020

Keywords

Communication protocol
Distributed nonlinear Kalman filter
Nonlinear estimation
Optimal coverage control
Sensor network

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10.1016/j.ins.2019.10.053

main_INS_14969Accepted author manuscript, 790 KB

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title = "Distributed Nonlinear Kalman Filter with Communication Protocol",

abstract = "This paper proposes an optimal design of the general distributed nonlinear Kalman-based filtering algorithm to tackle the discrete-time estimation problem with noisy communication networks. The algorithm extends the Kalman filter by enabling it to predict the noisy communication data and fuse it with the received neighboring information to produce a posterior estimate value. In the prediction step, the unscented transformations of the estimate values and covariances originated in the Unscented Kalman Filter (UKF) are exploited. In the update step, a communication protocol is appended to the posterior estimator, which consequently leads to a modified posterior error covariance containing the covariance of the communication term with its communication gain. Both Kalman and communication gains are then optimised to collectively minimise the mean-squared estimation error. Afterwards, stochastic stability analysis is performed to guarantee its exponential boundedness. To exemplify the performance, this algorithm is applied to a group of robots in a sensor network assigned to estimate an unknown information distribution over an area in the optimal coverage control problem. Comparative numerical experiments finally verify the effectiveness of our design.",

keywords = "Communication protocol, Distributed nonlinear Kalman filter, Nonlinear estimation, Optimal coverage control, Sensor network",

author = "Hilton Tnunay and Zhenhong Li and Zhengtao Ding",

note = "Funding Information: This work is supported by Indonesia Endowment Fund for Education (LPDP), Ministry of Finance, Indonesia; and the Science and Technology Facilities Council under Grant ST/N006852/1. Publisher Copyright: {\textcopyright} 2019",

year = "2020",

month = mar,

doi = "10.1016/j.ins.2019.10.053",

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AU - Tnunay, Hilton

AU - Li, Zhenhong

AU - Ding, Zhengtao

N1 - Funding Information: This work is supported by Indonesia Endowment Fund for Education (LPDP), Ministry of Finance, Indonesia; and the Science and Technology Facilities Council under Grant ST/N006852/1. Publisher Copyright: © 2019

PY - 2020/3

Y1 - 2020/3

N2 - This paper proposes an optimal design of the general distributed nonlinear Kalman-based filtering algorithm to tackle the discrete-time estimation problem with noisy communication networks. The algorithm extends the Kalman filter by enabling it to predict the noisy communication data and fuse it with the received neighboring information to produce a posterior estimate value. In the prediction step, the unscented transformations of the estimate values and covariances originated in the Unscented Kalman Filter (UKF) are exploited. In the update step, a communication protocol is appended to the posterior estimator, which consequently leads to a modified posterior error covariance containing the covariance of the communication term with its communication gain. Both Kalman and communication gains are then optimised to collectively minimise the mean-squared estimation error. Afterwards, stochastic stability analysis is performed to guarantee its exponential boundedness. To exemplify the performance, this algorithm is applied to a group of robots in a sensor network assigned to estimate an unknown information distribution over an area in the optimal coverage control problem. Comparative numerical experiments finally verify the effectiveness of our design.

AB - This paper proposes an optimal design of the general distributed nonlinear Kalman-based filtering algorithm to tackle the discrete-time estimation problem with noisy communication networks. The algorithm extends the Kalman filter by enabling it to predict the noisy communication data and fuse it with the received neighboring information to produce a posterior estimate value. In the prediction step, the unscented transformations of the estimate values and covariances originated in the Unscented Kalman Filter (UKF) are exploited. In the update step, a communication protocol is appended to the posterior estimator, which consequently leads to a modified posterior error covariance containing the covariance of the communication term with its communication gain. Both Kalman and communication gains are then optimised to collectively minimise the mean-squared estimation error. Afterwards, stochastic stability analysis is performed to guarantee its exponential boundedness. To exemplify the performance, this algorithm is applied to a group of robots in a sensor network assigned to estimate an unknown information distribution over an area in the optimal coverage control problem. Comparative numerical experiments finally verify the effectiveness of our design.

KW - Communication protocol

KW - Distributed nonlinear Kalman filter

KW - Nonlinear estimation

KW - Optimal coverage control

KW - Sensor network

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DO - 10.1016/j.ins.2019.10.053

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VL - 513

SP - 270

EP - 288

JO - Information Sciences

JF - Information Sciences

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