An interval-varying auxiliary model based recursive least squares(AM-RLS) algorithm is derived for linear-in-parameter systems with missing data by means of the auxiliary model identification idea.In order to improve the computation efficiency, an interval-varying decomposition AM-RLS algorithm is proposed for estimating the system parameters.The introduction of the forgetting factors can improve the parameter estimation accuracy and accelerate the convergence rates of the interval-varying decomposition based AM-RLS algorithm.The simulation results show that the proposed algorithms can effectively estimate the parameters of the system.