The aim of the paper is to propose an estimation algorithm, called Interlaced Extended Kalman Filter (IEKF), for a class of discrete-time nonlinear systems. The vector state of the system is assumed to be partitionable into \(m\) parts (subsystems), whose dynamic equations are supposed to be affine for each of the corresponding part (subsystem). At each step of the algorithm, the EKF works independently from the others in the sense that it operates on its own part of the state vector, considering the other parts as known time-varying parameters. The IEKF algorithm divides the complete nonlinear estimation problem into \(m\) quasi-decoupled linear time-varying subproblems, thus yielding a reduction of the computational burden. The proposed estimation algorithm is well-suited for parameter and state estimation in linear systems whose matrices depend linearly on unknown parameters, and it may be used as a suboptimal reduced-order filter for parallel connected linear systems. The IEKF has been numerically tested and compared to the EKF and to some of its modified versions on several systems; in particular, simulations on the model of a geosynchronous satellite are reported. The numerical simulations of the IEKF procedure provide a good trade-off between the reduction of the computational load and the estimation accuracy.