## 2 Observer-Based Estimation
### Kalman Filter
in [36] explains that the set of sigma points must be cautiously chosen and weighed to approximate the vehicle state appropriately. Therefore, a very careful and thoughtful tuning is needed for a successful implementation of a UKF, while an EKF is generally simpler. As mentioned before, several studies using UKF for VSA estimation have been carried out recently. In [36] [PERSON] et al. presents a sensitivity analysis to sampling time on both EKF and UKF has been performed. Sampling times have been varied from 1 ms to 40 ms, and no significant differences have been noted for sampling up to 5 ms. However, a big estimation error using EKF appears as the sampling time is increased towards 40 ms. As mentioned earlier, the deterioration of the VSA estimation is caused by the model linearization in EKF, which involves non-negligible linearisation errors and delays that are usually avoided by decreasing the sampling time. For instance, one of the most common issues coming from under-sampling is the well-known aliasing, which is an effect that causes a signal to become indistinguishable (or aliases of one another) when sampled or discretised. In the light of all of this, when using a UKF instead of an EKF, a longer sample time won't lead to a degradation of the observer estimation capabilities. On the other hand, a longer sample time means less computational effort required, and hence a better suitability to real-time applications or the possibility to use cheaper hardware without jeopardising the final estimation performance. Some remarkable VSA estimation via UKF application can be found in [38] by [PERSON] et al., where a simple four-wheel, three-DOF vehicle model was improved by using a linear, piece-wise tyre model that describes the Duggoff model using less parameters then the traditional Duggoff model. Results are promising; however, the authors validate this method via CarSim simulations only. In [36] by [PERSON] et al., the same vehicle model (except for the tyres, which are represented by means of the Magic Formula) was used with a separate calculation of tyre vertical forces to enhance the estimation without affecting the computational effort required. They also use a BMW sedan to perform some aggressive high-speed low-friction manoeuvres in order to verify the accuracy and robustness of the proposed method. The results showed good accuracy, even in extreme driving situations. In this case, a comparison between EKF and UKF has been reported, and results show that the EKF observer was outperformed by the UKF. Moreover, in [35] [PERSON] et al. shows a further improvement of UKF, where an UKF-based adaptive variable structural observer with dynamic correction has been presented. Basically, model uncertainty has been compensated with adaptive parameters, while a variable structure observer has been realised through using a sensor-based observer to compensate errors occurring in non-linear regions. An improved KF has also been proposed in [40] by [PERSON] et al. It has been achieved by merging the estimation outputs of two KF variants, namely the square-root cubature Kalman filter (SCKF) and the square-root cubature-based receding horizon Kalman filter (SCRHKF). The first one numerically approximates the multidimensional integrals by means of a third-degree spherical-radial cubature rule; it features good accuracy and high convergence speed, but accuracy may be reduced by model uncertainty and noise [41; 42; 49]. On the other hand, SCRHKF is robust against uncertainty and noise, but due to the use of a finite number of measurements, its convergence speed is slower than SCKF. Therefore, SCKF and SCRHKF have features that are complementary with each other. Hence, [PERSON] and [PERSON] [40] proposed a hybrid KF for VSA estimation that integrates the advantages of the two filters mentioned above while overcoming their issues. They verified the accuracy of this method by performing double lane change manoeuvres with a real-world vehicle at several speeds.