Optimal Redundant Transmission for State Estimation with Packet Drops

In networked systems that suffer from data packet drops, transmitting multiple, redundant packets during each sampling interval can improve estimation performance, but at the expense of a higher communication rate. In recent work, this idea was developed to introduce the notion of a dynamic redundant transmission policy, with Markov decision theory used to find the optimal policy numerically. The purpose of this paper is to present an alternative approach to this problem. By relaxing the integer requirement on the number of packets transmitted, it becomes possible to explicitly find a real-time recursion for the optimal transmission function. The theoretical properties of this recursion are then analysed to propose a simple numerical procedure for finding the minimum over all real-valued transmission functions, by searching over a one-dimensional parameter space. This then yields an implementable, suboptimal policy when discretised to integer values. These results are supported by numerical studies in MATLAB.