The robust Kalman filtering problem is investigated for uncertain stochastic systems with time-invariant state delay d0, bounded random observation delays and missing measurements. The described model is generalised to the case that d0≠d1, where d1 denotes the upper bound of random observation delays. The random delays and missing measurements are described by multiple Bernoulli random processes and their probabilities are assumed to be known. For robust performance, stochastic parameter perturbations are considered. Unlike the system augmentation approach, the robust Kalman filtering is derived in the linear minimum variance sense by using the innovation analysis approach, and the dimension of the designed filter is the same as the original systems. Moreover, the performance of the designed filter is dependent on the probabilities of delays and missing measurements at each step. An illustrative example is presented to demonstrate the effectiveness of the proposed design method.