In this note, the basic limit behaviors of the solution to Riccati equation in the extended Kalman filter as a parameter estimator for a sinusoidal signal are analytically investigated by using lira sup and lim inf in...In this note, the basic limit behaviors of the solution to Riccati equation in the extended Kalman filter as a parameter estimator for a sinusoidal signal are analytically investigated by using lira sup and lim inf in advanced calculus. We show that if the covariance matrix has a limit, then it must be a zero matrix.展开更多
The problem of increasing computation in pace with the growth of dimension is discussed for arbitrary dimensional frequency estimation of complex sinusoid signals. The conception of matrix core, the form of which do...The problem of increasing computation in pace with the growth of dimension is discussed for arbitrary dimensional frequency estimation of complex sinusoid signals. The conception of matrix core, the form of which doesnt change with dimension, is put forward. The deduced estimation formula shows that a N dimensional frequency estimation could be obtained by N one dimensional calculations. Obviously, while dimension increases, this method could reduce much computation.展开更多
In this paper,a sinusoidal signal frequency estimation algorithm is proposed by weighted least square method.Based on the idea of Provencher,three biggest Fourier coefficients in the maximum periodogram are considered...In this paper,a sinusoidal signal frequency estimation algorithm is proposed by weighted least square method.Based on the idea of Provencher,three biggest Fourier coefficients in the maximum periodogram are considered,the Fourier coefficients can be written as three equations about the amplitude,phase,and frequency,and the frequency is estimated by solving equations.Because of the error of measurement,weighted least square method is used to solve the frequency equation and get the signal frequency.It is shown that the proposed estimator can approach the Cramer-Rao Bound(CRB)with a low Signal-to-Noise Ratio(SNR)threshold and has a higher accuracy.展开更多
基金This work was supported by the National Natural Science Foundation of China （No. 61374084）.
文摘In this note, the basic limit behaviors of the solution to Riccati equation in the extended Kalman filter as a parameter estimator for a sinusoidal signal are analytically investigated by using lira sup and lim inf in advanced calculus. We show that if the covariance matrix has a limit, then it must be a zero matrix.
文摘The problem of increasing computation in pace with the growth of dimension is discussed for arbitrary dimensional frequency estimation of complex sinusoid signals. The conception of matrix core, the form of which doesnt change with dimension, is put forward. The deduced estimation formula shows that a N dimensional frequency estimation could be obtained by N one dimensional calculations. Obviously, while dimension increases, this method could reduce much computation.
文摘In this paper,a sinusoidal signal frequency estimation algorithm is proposed by weighted least square method.Based on the idea of Provencher,three biggest Fourier coefficients in the maximum periodogram are considered,the Fourier coefficients can be written as three equations about the amplitude,phase,and frequency,and the frequency is estimated by solving equations.Because of the error of measurement,weighted least square method is used to solve the frequency equation and get the signal frequency.It is shown that the proposed estimator can approach the Cramer-Rao Bound(CRB)with a low Signal-to-Noise Ratio(SNR)threshold and has a higher accuracy.
