A Bernoulli Optimal Kalman Filter for a Multi-sensor System with Random Data Packet Dropouts and Delays
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A Bernoulli Optimal Kalman Filter for a Multi‑sensor System with Random Data Packet Dropouts and Delays Su‑Min Han1 · Fu‑Zhong Wang1 · Yong‑Sheng He1
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract A distributed filtering method is proposed to solve the packet dropouts and delays in a multi-sensor wireless sensor network. For an asynchronous multi-sensor system with sensors of different working frequencies, a distributed Bernoulli optimal Kalman filter (BOKF) is constructed to decrease the dropouts and delays with random multistep states. In the BOKF algorithm, a wireless Bernoulli transmission output model is established and applied to solve random multi-step delays between the sensor nodes and the local processors. Moreover, the paper presents the concept of data arrival probability p and corresponding simulations analyze the influence of the data arrival probability p to the filtering accuracy. The effectiveness of the methodology is verified by a system including two types of sensors, which can be represented by a linear time-varying system and a linear time invariant one. It is shown that the Bernoulli transmission output model and the BOKF have decent performance in the two types of system, the data arrival probability p is changing oppositely with the filtering accuracy. Keywords Multi-sensor · Kalman filter · Dropouts and delays · Wireless transmission
1 Introduction In the wireless communication, the network becomes unreliable because of data losses, delays, bandwidth limitation, energy consumption, etc., resulting in transmission errors and disturbances, even data errors [1]. Especially in the popular wireless sensor networks(WSNs), due to node saturation, network congestion and random delays, data packet losses, measurement noises, transmission errors, packets from a sensor node to a processor via the wireless network protocol are more likely to be lost or delayed [2, 3]. * Su‑Min Han [email protected] Fu‑Zhong Wang [email protected] Yong‑Sheng He [email protected] 1
School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo 454000, People’s Republic of China
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When a wireless transmission system contains a variety of sensors with different types and different frequencies, data packet losses and latency will lead to further data disorder, affecting the subsequent data processing, mining and decision. Therefore, the filtering of multi-sensor systems is important research topics. In recent years, literatures have been published frequently about data dropouts, delays and random measurement errors in the WSNs [2–7]. Generally, scholars have studied the relatively effective protocols and sensor structures, and data compression, reconstruction, compensation algorithms to reduce data losses and delays [2–7]. However, with the exception of the above research fields, Kalman filtering and Robust filtering are also the issues of the relevant research fields [8–10]. In this respect, two main aspects are
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