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RLS Algorithms with Nonlinear Constraints and their Application to Reducing Estimates Fluctuations

The recursive least-squares (RLS) algorithm successfully is applied in a variety of applications. The main properties of the RLS are the high rate of convergence to the optimal solution and the robustness in relation to changing external conditions. However, it is known that the RLS estimates fluctuate strongly during the initialization period. The fluctuations depend on the signal-to-noise ratio (SNR) and the parameter vector dimension. In this paper, the new recursive algorithms taking in account the SNR are developed and studied. Our approach is based on the reduction of the problem to the estimation of the linear regression parameter with the restriction on the SNR in the form of the equality. The Gauss-Newton method is applied. The obtained theoretical results are illustrated by computer simulation.