1. A method of generating projected vehicle information for use in traversing a vehicle transportation network, the method comprising: receiving, by at least one of a sensor or an electronic communication interface of a host vehicle, remote vehicle spatial state information for a remote vehicle; identifying vehicle transportation network information representing a portion of the vehicle transportation network based on the remote vehicle spatial state information; generating, by a processor in response to instructions stored on a non-transitory computer readable medium, at least one initial probability value based on a comparison of the remote vehicle spatial state information and the vehicle transportation network information at an initial time point, each initial probability value indicating a likelihood that the remote vehicle is following a single lane within the vehicle transportation network information; generating, for a plurality of time points including the initial time point forming a period of time, a deviation of the remote vehicle between adjacent values for the remote vehicle spatial state information relative to the vehicle transportation network information; generating, for each single lane and for each deviation, a new probability value that corresponds to the deviation; updating, for each single lane and for each deviation, the likelihood that the remote vehicle is following the single lane by modifying a previous probability value at a previous time point of the plurality of time points, starting with the initial probability value, using the new probability value of a current time point; generating, for the remote vehicle, a trajectory using the likelihood as updated; and traversing, by the host vehicle, the vehicle transportation network using the vehicle transportation network information and the trajectory for the remote vehicle.