Abstract: Aiming at the problem that existing incremental least mean square algorithms, which relied solely on the local data at each node to perform local estimation, suffered from low estimation accuracy under limited information exchange, we proposed an incremental recursive least squares algorithm based on cyclic network estimation. The algorithm performed  exponentially weighted summation of local loss functions node by node in the cyclic network, and recursively solved  the local estimate at each node by using only the local estimate of parameter and intermediate process matrix estimate from the immediately preceding node. It featured low demand for information exchange and high estimation accuracy. Through theoretical analysis of the mean and mean-square error of proposed estimation method,  the simulation experimental results are highly consistent  with the theoretical analysis. In different application scenarios, the  estimation accuracy of proposed algorithm is superior to the current comparative  incremental least mean square algorithms, providing an efficient and practical solution for parameter estimation in distributed cyclic networks.

Key words: adaptive algorithm, incremental form, recursive least squares