Data-Dependent Hidden Markov Model with Off-Road State Determination and Real-Time Viterbi Algorithm for Lane Determination in Autonomous Vehicles

TL;DR

The paper addresses lane-determination for autonomous vehicles by formulating a time-varying, data-dependent Hidden Markov Model that explicitly includes an off-road state to handle intersections and other non-lane scenarios. It couples emission and transition probabilities to real-time sensor data, enabling a real-time Viterbi decoding that avoids post-processing and reinitialization gaps. Key contributions include the data-dependent emission and transition models, a real-time Viterbi algorithm with informed initialization, and a lane model that accommodates non-parallel lanes. Experimental results with GNSS/RTK ground truth demonstrate a mean accuracy of about $95.9\%$, outperforming prior approaches without parameter tuning. This approach enhances robustness and applicability in real-world CAV systems by providing reliable lane sequence estimation in the presence of off-road events.

Abstract

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.

Figures (5)

• Figure 1: Viterbi lane determination algorithm for a 2 lane road represented as thin black lines. The blue portions show: (a) initialization, (b) time propagation and measurement update, and (c) termination.
• Figure 2: Lane reference frame: road segment m of lane $L_i$ has a reference frame with origin at ${}^g \mathbf{p} _{(v,m)}^i$ and axis $\mathbf{f}$ and $\mathbf{s}$. The symbol $\hat{ \mathbf{p} }_k$ is the estimated vehicle position at time $t_k$. The intersection frame $e$-axis points in the east direction.
• Figure 3: Illustration of the integral calculations in eqn. \ref{['eqn:FinalEm']} or \ref{['eqn:EmDenom']} for each lane for position estimate $\hat{ \mathbf{p} }_k$. Note that the distribution in the figure was offset to the left from the point $\hat{ \mathbf{p} }_k$ to clearly show each colored area along with the formulas.
• Figure 4: Probability distribution of the estimated vehicle position at times $t_k$ and $t_{k+1}$.
• Figure 5: Calculation of the joint probability of being in lane $L_4$ at time $t_k$ and lane $L_2$ at time $t_{k+1}$, as required for the numerator in Eqn. (\ref{['eqn:transP']}). The ellipse show the contours of constant probability defined by $\hat{ \mathbf{z} }$ and $^\ell_i \mathbf{C} _ \mathbf{z}$.