Lane determination and lane sequence determination are important components for many Connected and Automated Vehicle (CAV) applications. Lane determination has been solved using Hidden Markov Model (HMM) among other methods. The existing HMM literature for lane sequence determination uses empirical definitions with user-modified parameters to calculate HMM probabilities. The probability definitions in the literature can cause breaks in the HMM due to the inability to directly calculate probabilities of off-road positions, requiring post-processing of data. This paper develops a time-varying HMM using the physical properties of the roadway and vehicle, and the stochastic properties of the sensors. This approach yields emission and transition probability models conditioned on the sensor data without parameter tuning. It also accounts for the probability that the vehicle is not in any roadway lane (e.g., on the shoulder or making a U-turn), which eliminates the need for post-processing to deal with breaks in the HMM processing. This approach requires adapting the Viterbi algorithm and the HMM to be conditioned on the sensor data, which are then used to generate the most-likely sequence of lanes the vehicle has traveled. The proposed approach achieves an average accuracy of 95.9%. Compared to the existing literature, this provides an average increase of 2.25% by implementing the proposed transition probability and an average increase of 5.1% by implementing both the proposed transition and emission probabilities.