This paper addresses the problem of joint data detection and channel estimation on continuous phase modulation (CPM) operating under a frequency-flat time-varying Rayleigh fading channel. The proposed framework comprises of two parts working in a joint manner: a symbol by symbol MAP CPM receiver and a channel tracking scheme. We first illustrate the robustness of MSK over modulation schemes without memory such as BPSK in joint data and channel estimation scheme. In order to adopt coherent demodulation, channel tracking is commonly used in time-varying channels. The underlying channel model in conjunction with data based estimate enables the Kalman filter to produce LMMSE estimates of the channel coefficients. Most literature do not consider the channel estimation error covariance in data detection. Here, A MAP data detection combined with Kalman tracking of channel coefficients is proposed in which we consider the channel error covariance for every step of MAP data detection. The simulation results show that the proposed scheme offers good performance in moderate or even high fading rate environments.