Asymptotic properties are re-investigated in this paper for the robust state estimator derived in [14]. A new formula is derived for the update of the pseudo-covariance matrix of estimation errors. Based on this formula, the restrictive orthogonality condition of [14] is successfully removed. Under the situation that plant nominal parameters are time-invariant, it is shown that, when some stabilizability and detectability conditions are satisfied, the robust estimator converges to a stable time invariant system. Moreover, when the system is exponentially stable, it has been proved that this estimate is asymptotically unbiased and its estimation errors are upper bounded.