<p>For dual-rate controlled autoregressive (CAR) models with missing input data, traditional estimation algorithms usually perform poor results. This paper develops a multi-direction gradient iterative algorithm for dual-rate CAR models. By using the polynomial transformation technique, a CAR model is transformed into a controlled autoregressive moving average (CARMA) model whose collected data are all measurable. In addition, to increase the convergence rates, a multi-direction gradient iterative (DR-MD-GI) based Krylov subspace algorithm is proposed, its basic idea is to construct several orthogonal search directions in each iteration, thereby significantly accelerating the convergence rates and demonstrating significant enhancements in efficiency and reliability. Compared with the traditional methods, the proposed DR-MD-GI method has the following advantages: (1) make full use of all the collected data, thus can improve the estimation efficiency; (2) estimate unmeasurable inputs and noise using auxiliary models, thus can enhance the accuracy; (3) adaptively construct several directions in each iteration, thus can increase the convergence rates. The effectiveness of the proposed algorithm has been rigorously verified through two comprehensive simulation examples.</p>