For the problem of multisensor-multitarget tracking, the sensor bias has great influence on the accuracy of track fusion. Thus, the sensor bias should be estimated at first in the system of information fusion. However the performance of the traditional methods of bias estimation will degrade dramatically in the complex environment that exists the misassociations and observed outliers. Therefore, an algorithm of robust estimation based on the recursive approximate least absolute deviation(RALAD) is proposed, aiming to decrease the adverse impacts of the misassociations and observed outliers. A smooth approximate function in the square-root form is used to replace the least absolute cost function, and the recursive framework is derived based on the Newton method and its rank-one modification. It is verified by the condition number analysis that the proposed algorithm has better numerical stability than the Huber-based method. Performance comparisons between the proposed and existing algorithms are carried out through two simulation examples. The results show that the proposed algorithm is obviously superior to the existing algorithms, and it can improve the estimation accuracy significantly in the case of the misassociations and observed outliers.