Recursive least squares and multi-innovation stochastic gradient parameter estimation methods for signal modeling. (English) Zbl 1370.94286
Summary: The sine signals are widely used in signal processing, communication technology, system performance analysis and system identification. Many periodic signals can be transformed into the sum of different harmonic sine signals by using the Fourier expansion. This paper studies the parameter estimation problem for the sine combination signals and periodic signals. In order to perform the online parameter estimation, the stochastic gradient algorithm is derived according to the gradient optimization principle. On this basis, the multi-innovation stochastic gradient parameter estimation method is presented by expanding the scalar innovation into the innovation vector for the aim of improving the estimation accuracy. Moreover, in order to enhance the stabilization of the parameter estimation method, the recursive least squares algorithm is derived by means of the trigonometric function expansion. Finally, some simulation examples are provided to show and compare the performance of the proposed approaches.
MSC:
| 94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |
| 93E24 | Least squares and related methods for stochastic control systems |
Keywords:
signal modeling; recursive algorithm; Fourier series; parameter estimation; least squares; sine signalSoftware:
SCALCGReferences:
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