A method based on the extended Kalman filter is developed for the estimation of the core coolant mass flow rate in pressurized water reactors. The need for flow calibration can be avoided by a direct estimation of this parameter. A reduced-order neutronic and thermal-hydraulic model is developed for the Loss-of-Fluid Test (LOFT) reactor. The neutron detector and core-exit coolant temperature signals from the LOFT reactor are used as measurements in the parameter estimation algorithm. The estimation sensitivity to model uncertainties was evaluated using the ambiguity function analysis. This also provides a lower bound on the measurement sample size necessary to achieve a certain estimation accuracy. A sequential technique was developed to minimize the computational effort needed to discretize the continuous time equations, and thus achieve faster convergence to the true parameter value. The performance of the stochastic approximation method was first evaluated using simulated random data, and then applied to the estimation of coolant flow rate using the operational data from the LOFT reactor at 100 and 65% flow rate conditions.