The paper presents an algorithm for on-line estimation of the intra- and inter-cell interference in the enhanced uplink (EUL) of the wideband code division multiple access (WCDMA) cellular system. The proposed Kalman filter estimator builds on measurements of the total wideband power of the WCDMA uplink, in combination with measurements of the powers of the dedicated physical control channels (DPCCH) that are available e.g. for power control purposes. In particular the paper presents a novel complexity reduction technique that reduces the computational complexity with a factor equal to the order of the Kalman filter. This order equals the number of uplink (UL) users. Simulation results show that the performance loss associated with the complexity reduction is insignificant.