A maximum likelihood estimator for situations when full information on turning movement counts is available is derived and used as a component for a maximum likelihood algorithm which only requires entering and exiting counts. Several algorithms based on minimizing the error between observed and predicted exiting counts are also developed. Some actual traffic data are collected and used to develop realistic simulations for evaluating the various estimators. Generally, the maximum likelihood algorithm produced biased but more efficient estimates, while prediction error minimization approaches produced unbiased but less efficient estimates. Constraining the recursive version of the ordinary least-squares estimator to satisfy natural constraints did not affect its long run convergence properties.