This paper presents a case study of real-time traffic state estimation. The adopted general approach to the design of universal traffic state estimators for freeway stretches is based on stochastic macroscopic traffic flow modeling and extended Kalman filtering, which are outlined in the paper. The reported investigations were conducted by use of eight-hour traffic measurement data collected from a freeway stretch of 4.1 km close to Munich, Germany. Some key issues are carefully investigated, including the tracking capability of the designed traffic state estimator, significance of the online model parameter estimation, sensitivity of the estimator to the initial values of the estimated model parameters as well as to the related noise standard deviation values, and the capability of the estimator to handle biased flow measurements. The achieved results are quite satisfactory.