In this paper an estimation algorithm for a class of discrete-time nonlinear systems is proposed. The system structure we deal with is partitionable into m subsystems, each affine w.r the corresponding part of the state vector. The algorithm consists of a bank of m interlaced Kalman filters, and each of them estimates a part of the state, considering the remaining parts as known time-varying parameters whose values are evaluated by the other filters at the previous step. The procedure neglects the subsystem coupling terms in the covariance matrix of the state estimation error and counteracts the errors so introduced by suitably "increasing" the noise covariance matrices. Comparisons through numerical simulations with the extended Kalman filter and its modified versions proposed in the literature illustrate the good tradeoff provided by the algorithm between the reduction of the computational load and the estimation accuracy.