GMSK CFO estimation and timing recovery
For optimum coherent detection in an AWGN channel, GMSK with partial response signaling (intentional overlap of pulses to increase the amount of data within a given time and therefore bandwidth efficiency) can be done with maximum likelihood sequence detection, combined with Viterbi decoding which basically compares the correlation of all possible phase trajectories (the number of which is increased substantially due to the pulse overlap) and selects with soft decision detection the most likely set of data bits that would have created that trajectory. With full response signaling there are just two possible trajectories since only one data bit is involved, but with partial response signaling there are multiple data bits to create each trajectory due to the longer duration from each data bit that is longer than a symbol period. For example if each transition lasted 2 symbols, there would be four possible phase trajectories corresponding to the 00, 01, 10, and 11 data patterns. The trajectories are unique to the patterns and thus by choosing the most likely trajectory (after removing phase, frequency and time offsets) the data can be demodulated. As the overlap increases (duration of the phase transition over multiple symbols) the complexity of the optimum receiver significantly increases due to the number of phase trajectories and it can be seen that a trellis diagram results where the Viterbi algorithm can be used to efficiently determine the most likely path through the trellis. Further Laurent Decomposition can be used to decompose the signal into PAM modulations and reduce the possible combinations, simplifying the receiver. Other sub-optimum receiver implementations exist as well.
Here are related links for GMSK demodulation, including further details for carrier recovery, symbol synchronization and using Viterbi decoding and the Laurent Decomposition:
https://www.mathworks.com/help/comm/ref/comm.gmskdemodulator-system-object.html
https://core.ac.uk/download/pdf/195023475.pdf
https://www.atlantis-press.com/article/125913177.pdf
https://etd.lib.metu.edu.tr/upload/1057348/index.pdf