The problem of error estimation and compensation in strapdown inertial navigation system (SINS) is investigated in this paper. The error dynamic model is derived and employed for this purpose. Information gathered from a micro-electro-mechanical inertial measurement unit (MEMS IMU) is fused with camera information in a loosely coupled integration scenario. Although this integration is computationally efficient, it suffers from fault propagation in the navigation algorithm. To overcome this problem, it is proposed in this paper to estimate and compensate for the propagated faults in a timely manner to provide a short start-up and computation time. This goal is achieved through the design of decentralized error estimation and compensation algorithms running in parallel with the inertial navigation system. To this end, firstly, the sparse error system is decomposed to cascaded subsystems using a combination of structural and behavioural decomposition methods. Then, cascaded Kalman filters (KFs) and decentralized state feedback regulators are designed for error estimation and compensation, respectively. The experimental results based on data from the 3D MEMS IMU and camera system are provided to demonstrate the efficiency of the proposed method.