Optimal linear state estimation over a packet-dropping network using linear temporal coding

• Published in: Automatica (Oxford) Vol. 49; no. 4; pp. 1075 - 1082
• Main Authors: He, Lidong, Han, Dongfang, Wang, Xiaofan, Shi, Ling
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.04.2013; Elsevier
• Subjects: Algorithms; Applied sciences; Channels; Coding; Coding, codes; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Control theory. Systems; Correlated noise; Exact sciences and technology; Information, signal and communications theory; Innovation sequence approach; Kalman filter; Linear temporal coding; Modelling and identification; Networks; Noise; Noise measurement; Packet-dropping network; Packets (communication); Signal and communications theory; Software; Telecommunications and information theory; Temporal logic; Correlated noise; Packet-dropping network; Linear temporal coding; Innovation sequence approach; Kalman filter; Performance evaluation; Lossy channel; Network management; Optimal estimation; Mean square error; Linear coding; Innovation; Linear combination; Linear estimation; System identification; State estimation; Time code; Packet switching; Network flow; Measurement sensor; Transmission channel; Color noise; Recursive algorithm; Orthogonal projection; Discrete time; Signal to noise ratio; Recursive estimation
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2013.01.043

We consider the problem of linear minimum mean square error estimation for a discrete-time system over a packet-dropping network. In order to improve the estimation performance, different from the standard approach of sending the current measurement data, we choose sending a linear combination of the current measurement and the measurement collected at the previous time, a method called linear temporal coding. We assume the packet arrival sequence is unknown and the noise contained in the packet may come from sensor or communication channel. In an effort to cope with colored noise caused by measurement combination, after comparing with the classic state augmentation approach and measurement differencing approach, we derive a recursive estimation algorithm by means of orthogonal projection principle and innovation sequence approach. Our algorithm consists of two parts: smooth and estimate. For large measurement noise case, numerical example shows the benefit of using linear temporal coding strategy, compared with directly sending the current data. On the contrary, when communication noise plays the dominating role, for scalar system we prove there is no benefit to choose this scheme.