In dual‐rate rational systems, some output data are missing (unmeasurable) to make the traditional recursive least squares (RLS) parameter estimation algorithms invalid. In order to overcome this difficulty, this study develops a bias compensation RLS algorithm for estimating the missing outputs and then the model parameters. The algorithm based on auxiliary model and particle filter has four steps: (i) to establish an auxiliary model to estimate unmeasurable outputs, (ii) to compensate bias induced by correlated noise, (iii) to add a filter to improve estimation accuracy of the unmeasurable outputs and (iv) to obtain an unbiased parameter estimation. Three examples are selected for simulation demonstrations to give further guarantees on the usefulness of the proposed algorithms. The comparative studies show that the bias compensation RLS is more effective for such systems with dual‐rate input and output data.