A METHOD FOR ESTIMATING THE PARAMETERS OF A STABLE DIFFERENCE EQUATION DRIVEN BY SINUSOIDS AND OBSERVED IN THE PRESENCE OF NONWHITE NOISE [report]

Jr Gardner, Leland A.
1966 unpublished
A computationally feasible and strongly consistent method is considered for estimating the coefficients of 0 t 1 t-1 p t-p t The steady-state solution is observed in the presence of nonwhite noise, and the system is driven by a certain selected superposition of sinusoids, u . When the noise is white, the estimates are shown to possess an asymptotic normal distribution with covariance matrix which depends on the coefficients only via the values of P i V ikuj.2 k=n evaluated at the input
more » ... es. Accepted for the Air Force I ranklin C. Hudson Chief, Lincoln Laboratory Office in O = RAR -1 (RD -)A(RD -)' , and the proper normalization for I. and r. is l/'vdT. . J J JJ We now compute L, R and D as functions of the eigenvalues. We have (G' -A.I) * = E(A.)' _1 F(\.y I. J J J J J By definition -f makes the left side the 0 vector, and hence F(A )'X. -0. These J J J equations are g] (A.) Furthermore, a J c -J 2 ,2 a. +b. J . 1 b. d. a J
doi:10.21236/ad0629934 fatcat:vvusadariraa5ktkyptzn4s3na