Abstract: In the strong tracking filter with multiple suboptimal fading factors,the non-negative definiteness of the estimated state's mean square error matrix might be lost under the influence of the round-off error during calculations,thus resulting in the divergence of the filtered data.A modified strong tracking filter with multiple suboptimal fading factors is proposed based on the UD decomposition algorithm.By the UD decomposition of the one-step forecast mean square error matrix in which the fading matrix is introduced,the decomposition matrices are used in the process of updating the filter measurement information,then the stability of the algorithm's numerical value is intensified.Besides,a method of calculating the fading matrix is presented based on the least squares,not only the calculation efficiency of fading factors is improved but their dependence on the apriori knowledge is removed.Simulation results show the effectiveness of the algorithm.