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 <sup>r</sup>1 <sup>r</sup>2 <sup>r</sup>3 <sup>(m)</sup> Zi - X b0 <sup>m)</sup> Zi - m = X a0 <sup>m)</sup> Xi-m + X X c0 <sup>mk</sup> X - „V k +^(0, W = Xi + 42(0, m=1 m=0 m=0 k=1 where x <sub>t</sub>, - unobserved and the observed input variables; Z <sub>t</sub> - the observed output variable; 4 <sub>1</sub>(i) - noise in the equation; 4 <sub>2</sub>(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.