This report examined several methods for estimating Origin- Destination (OD) matrices for freeways using loop detector data. Least squares based methods were compared in terms of both off- line and on- line estimation. Simulated data and observed data were used for evaluating the static and recursive estimators. For off- line estimation, four fully constrained least squares methods were compared. The results showed that the variations of a constrained least squares approach produced more efficient estimates. For on- line estimation, two recursive least squares algorithms were examined. The first method extends Kalman Filtering to satisfy the natural constraints of the OD split parameters. The second was developed from sequential quadratic programming. These algorithms showed different capabilities to capture an abrupt change in the split parameters. Practical recommendations of the choice of different algorithms are given.