An optimal interpolation (OI) sequential algorithm is implemented for a three-dimensional primitive equation model to assimilate current measurements from acoustic Doppler profilers moored on the Oregon shelf as a part of the Coastal Ocean Advances in Shelf Transport (COAST) upwelling experiment (May--August 2001). A stationary estimate of the forecast error covariance required by the OI is computed based on the error covariance in the model solution not constrained by data assimilation. Lagged model error covariances are used to account for the effect of previously assimilated data. The forecast error covariance has a shorter alongshore spatial scale than the model error covariance unconstrained by the data, as an effect of propagating dynamical modes. Assimilation of currents from one or two of the moorings located on the path of the upwelling jet helps to improve the model data rms error and correlation at the mooring sites located at an alongshore distance of 90 km, south or north from the assimilation sites. The coastal jet is deflected offshore over Heceta Bank, and assimilation of data from an inner-shelf mooring in the jet separation zone does not help to improve prediction in the far field. Larger improvements are obtained for the first part of the study period (yeardays 146--190). In the second part (days 191--237) the geometry of our limited area model possibly limits prediction accuracy. In numerical experiments involving assimilation of data from only one mooring the actual and expected rms error improvements are compared, providing a consistency test for the forecast error covariance.