A computer implemented method for determining a yaw angle estimate or vehicle heading direction is presented. A data server may receive a plurality of telematics data originating from a client computing device and determine a first primary movement window from the telematics data. The data server may also determine a potential range of yaw angles from the plurality of telematics data from the first primary movement window and generate an equality that evaluates the potential range of yaw angles. The data server may further maximize the count of acceleration events of the telematics data from the first primary movement window to further generate one or more refined yaw angle estimates. The data server stores the one or more yaw angle estimates on a memory.