Adaptive Period Estimation For Sparse Point Processes

In this paper, adaptive period estimation for time varying sparse point processes is addressed. Sparsity results from signal loss, which reduces the number of samples available for period estimation. We discuss bounds and minima of the mean square error of fundamental period estimation suitable in these situations. A ruleset is derived to determine the optimum memory length which achieves the minimum estimation error. The used low complex adaptive algorithm operates with variable memory length N to fit optimally for the recorded time varying process. The algorithm is of complexity $3\mathcal {O}(N)$, in addition to that the overall complexity is reduced to $3\mathcal {O}(1)$, if a recursive implementation is applied. This algorithm is the optimal implementation candidate to keep synchronicity in industrial wireless sensor networks operating in harsh and time varying environments.