# Autonomous Vehicles: Vehicle Parameter Estimation Using Variational Bayes and Kinematics
## 2 State of the Art
### Bayesian State Estimation Approaches  
To define the likelihood function required for Bayes filters, several implementations have been proposed in the literature. For example, the authors in [36] developed a Kalman filter framework that provided accurate estimates of vehicle position, velocity and altitude (5-10 centimeter root mean square (RMS)). The approach was evaluated using a dataset containing over 60 km of highway and dynamic urban scenes in which the global navigation satellite system (GNSS) reception ranged from good to weak/none. The developed multi-sensor fusion algorithm adaptively utilized diverse localization approaches based on inertial measurement unit (IMU), real time kinematic (RTK) and light detection and ranging (LIDAR) sensors. Figure 2: Proposed approach of this study for vehicle parameter estimation. The on-board sensory systems measure the wheel movement (\(\Delta\phi_{t}\) and \(\Delta\phi_{t}\)). Based on simulated global vehicle poses (gray arrows), we derive hidden vehicle parameters (\(\Theta=(r_{r},r_{l},B)\)). An Extended Kalman Filter Dead Reckoning (EKFDR) approach to tackle the ego-localization problem in areas of weak GPS reception was presented in [37]. The developed EKFDR corrects both deterministic (e.g., production-related) and stochastic (e.g., slip due to wet road) errors based on a novel Map Matching (MM) algorithm that reduces both the cross- and along track errors. This new MM approach is used in the correction step of the EKFDR to update the state propagation. Doing so they achieved a maximum error of 15.4 m and an average error of 5.2 m during a 43 km long test drive, thus outperforming low-cost GPS systems. EKF can also be used to localize multiple robots at the same time. A recursive _Interim Master_ Decentralized Cooperative Localization (D-CL) localization approach for a swarm or robots was presented in [38]. Here the state prediction is completely decoupled, thus no communication between the robots is needed during this step. Intra-network communication is only needed in the update step of the EKF if a relative measurement between two robots is made. The robot that produced the relative measurement is declared as the interim master and utilizes the data provided by the landmark robot to calculate the update variables for the other robots. Another novel approach for the bayesian state estimator Particle Filter (PF) was introduced in [39]. The authors of this work proposed a map-relative PF based localization for autonomous unmanned air vehicles (UAV) with a downward facing camera. Similarity calculation using the Pearson Correlation Coefficient, between map and aerial images that were converted to probability distributions using image similarity to likelihood conversion function, were used as input for the PF. Evaluation on a simulated dataset showed that the proposed method outperformed state of the art ORB-SLAM2 with an 2.6 times higher average precision. A further work [40] introduced a novel approach for PF based localization by combining road intensity (e.g., road markings) and vertical (e.g., trees, street poles or houses) information. The authors assumed that each feature in a previously built map might partially change. Accordingly, they used different measurement models by estimating weights for each particle using an entropy-based cost function. By doing so they adaptively changed the contribution of the intensity and vertical features thus creating a robust localization PF for environments that exhibited changes in its structure. The approach was validated by utilizing a 6 months old high definition map, of a 19 km long urban area, and a survey vehicle and it was compared against several reference localization algorithms and ground truth data. The results showed that the proposed algorithm could outperform other localization algorithms. A comparison of EKF and PF for simulated GPS and inertial navigation system data can be found in [41]. As the Bayes filter does not define model capabilities, limitations are encoded in the likelihood functions.