Recursive estimation of bilinear ARX systems with input-error
There is considered the problem of parameter estimation of bilinear ARX systems with noise in the input signals, described by the equations: r r1 r2 r3 (m) Zi - X b0 m) Zi - m = X a0 m) Xi-m + X X c0 mk X - „V k +^(0, W = Xi + 42(0, m=1 m=0 m=0 k=1 where x t, - unobserved and the observed input variables; Z t - the observed output variable; 4 1(i) - noise in the equation; 4 2(i) - the noise in the input signal. We propose a recursive algorithm for estimation of parameters, which is a generalization of the method of least squares. It is proved that that under non-restrictive conditions on the signals and noises, the proposed algorithm gives a strongly consistent estimators. The simulation results confirmed the high efficiency of the algorithm.