The transceiver isolation of jammers on small platforms such as UAV is the key to affect the simultaneous operation of transceiver. As for the dynamic sparse systems, the conventional Kalman filter (KF) algorithm does not consider the sparsity of the coupling paths of interference signals, and the identification accuracy of paths attenuation coefficients are not enough, so that the isolation performance is poor. Aimed at the problems that starting from the correction step of KF algorithm and regarding this as equivalent to a convex problem, on the basis of this, the sparse constraints on estimated parameters are added, the correction steps of the algorithm are deduced again, and a KF algorithm with sparse constraint (SC) is proposed, by so doing, this makes full use of the prior information of the system to be identified and improves the sparse tendency of estimated parameters. The theoretical analysis and the simulation results show that the new algorithm can effectively apply to the system identification in the dynamic sparse environment, and improve the identification accuracy of KF algorithm for the dynamic sparse system. Moreover, the isolation degree of transceiver of jammer can be improved by 3~5 dB, improving the isolation performance of jammer.