State estimation over a lossy network using linear temporal coding

We consider state estimation for a discrete-time system over a lossy 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 consider the case when the packet arrival sequence is unknown. 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. Numerical example shows the benefit of using linear temporal coding strategy, compared with directly sending the current data.