Recursive algorithms are presented for the on-line state and parameter estimation of a linear time-invariant discrete time system of large size. A variant of the observable canonical model with a one-way coupling form of the state model is chosen for developing a solution to the problem. Exploiting the canonical structure of the model, the proposed solution turns out to be computationally simpler than the existing solution, moreover a decentralized state and parameter estimation scheme can be developed in two steps. In the first step, the parameter of the system matrices are estimated by a recursive least-square algorithm or by a normalized stochastic approximation algorithm in a decoupled manner. These parameters are then employed for state estimation in step 2 using a centralized conventional Kalman filter or a decentralized adaptive Kalman filter, which in turn reduces instrumentation and telemetry costs. The results are illustrated by considering two different systems.