Abstract: In this paper,a filtering theory is applied to the multiple closed-loop feedback system for tracking a single target in range,velocity,azimuth and elevation in an airborne radar.First of all,according to relative motion between.arget and antenna,the vector differential equation of the states used to control the four tracking loop is established.Then,the corresponding nonlinear filtering algorithm is derived.Finally,the results of computer simulation are given.The results of computer simulation show that in a wide range the time varying system using Kalman filter can keep better performance than the ordinary one without optimal filter.The system involving nonlinear filtering has a performance closed to the linear filtering one in steady-state response,but the former achieves performance improvement in transient response and in large error.Using Kalman filter,the tracking loops are coupled each other,and its performance is better than that of seperate loops.Finally,we show that a particular merit of this mathematical model,established in aim coordinate system,is less sensitive to target's manoeuvre.Therefore,the system performance is almost as good as an adoptive estimator,but which is sensitive to measurement noise.As the signal to noise ratio of radar varies in a wide range,we should take adaptive method in measuring noise.The technique used and results obtained are also available for ground radar,shipborne radar and other tracking systems,either active or passive.