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Harmonic signal analysis with Kalman filters using periodic orbits of nonlinear ODEs

The paper suggests a new approach to the problem of harmonic signal estimation. The idea is to model the harmonic signal as a function of the state of a second order nonlinear ordinary differential equation (ODE). The function of the right hand side of the nonlinear ODE is parameterized with a polynomial model. A Kalman filter and an extended Kalman filter are then developed. The proposed methodology reduces the number of estimated unknowns in cases where the actual signal generation resembles that of the imposed model. This is expected to result in an improved accuracy of the estimated parameters, as compared to existing methods.