A new method for bias estimation on multiple frequencies with a Kalman filter is proposed. It consists of four steps: First, a least-squares estimation of ranges, ionospheric delays, ambiguities, receiver phase biases and satellite phase biases is performed. The code biases are absorbed in the ranges and ionospheric delays, and a subset of ambiguities is mapped to the phase biases to remove linear dependencies between the unknown parameters. In a second step, the accuracy of the bias estimates is efficiently improved by a Kalman filter. The real-valued a posteriori ambiguity estimates are decorrelated by an integer ambiguity transformation to reduce the time of ambiguity resolution. Once the float ambiguities have sufficiently converged, they are fixed sequentially in a third step. Finally, a second Kalman filter is used to separate the receiver and satellite code biases and the tropospheric delays from the ranges.