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  Aiming at the target tracking problem in fire control system,the satisfactory discrete-time bias-allowable estimator is investigated in this paper.For fire control system,the smoothness of forecasting target future positions is an important factor that affects shooting precision.Using lower order system model to estimate target state is a common method of smoothly forecasting the future position,which could produce system bias when the target is suddenly maneuvering.An important index in constraining system error called steady error coefficient is introduced into the performance index set with error variance upper bound and area pole indices.Assuming the maneuvering intensity of target is finite,an iterative algorithm in terms of linear matrix inequalities(LMIs) is proposed to solve the satisfactory bias-allowable estimation problem.The proposed bias-allowable estimator can ensure the accuracy and smoothness of the estimation output by using a lower order system model.Finally an example is presented to demonstrate the obtained results.……