State and parameter estimation plays an important role in many different engineering fields. Estimation of systems described by linear and nonlinear differential equations has been very well studied in the literature. Work in the past decade has been geared toward efficiently extending these algorithms to constrained systems. Of recent interest is the evaluation of state estimation techniques for differential-algebraic equation (DAE) systems. The algebraic equations in these studies are exact, an example being the mole fractions adding to unity. However, there are situations where algebraic equations can be of both certain and uncertain types. In this paper, we propose a modified extended Kalman filter (EKF) approach that can handle uncertainties in both differential and algebraic equations, and equality constraints. We also show the importance of this work in estimation of mole fraction, temperature, and pressure profiles in a water gas shift reactor. The impact of location and type of measurements on the estimation accuracy is also studied.