Abstract: The asymptotic normality of the nonlinear estimator, RB(β,γ), having two easily tuned parmeters, is proved concisely but rigorously by the Martingale Theory. The regularity conditions imposed to obtain the main result are fairly weak in enginecring applications. The asymptotic normality of the estimator along with its robustness, which was discussed in an authors, earlier paper, substantiates that the estimator is significantly better than the least-squares estimator and the ridge estimator in both estimate accuracy and convergene speed.