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

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.

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