The problem to track time-varying parameters in cellular radio systems is studied, and the focus is on estimation based only on the signals that are readily available. Previous work have demonstrated very good performance, but were relying on analog measurement that are not available. Most of the information is lost due to quantization and sampling at a rate that might be as low as 2 Hz (GSM case). For that matter a maximum likelihood estimator have been designed and exemplified in the case of GSM. Simulations indicate good performance both when most parameters are varying slowly, and when subject to fast variations as in realistic cases. Since most computations take place in the base stations, the estimator is ready for implementation in a second generation wireless system. No update of the software in the mobile stations is needed.