## 2 Problem Scenario  
The overall control scheme is depicted in Figure 1, where two main parts can be distinguished:  
* Robot simulator, which contains some complex vehicle modeling aspects as a result of using the features of the specialized Simscape Multibody simulation tool, and includes a dynamic proportional-integral (PI) controller for controlling the velocities of the wheels. More details can be found in Section 4. * Control structure, which includes a path-tracking controller (in this case, the Pure Pursuit algorithm), PI controllers for angular orientation and linear and angular velocities, an inverse kinematics computation block, and a state estimator (in this case, the proposed NUDREKF). The control structure generates the path reference based on waypoints and then generates the consequent actions to control the actuators. The main novelty of the NUDREKF  
Figure 1: Control structure with NUDREKF estimator for the vehicle. concerning the DREKF [23] is the consideration of possible irregularities in the sampling period, such as loss of information from the sensors. The control structure uses two different periods: \(T\) as the estimation and control period, and the sensing period for vehicle orientation and angular velocity; \(NT\) as the vehicle position sensing period, where \(N\in\mathbb{N}^{+}\) is the multiplicity between both periods. The position output will be more slowly sampled (at period \(NT\)) due to real hardware constraints in the beacon system. The beacon system also suffers from information losses denoted by \(\gamma_{i}\). Let us, respectively, denote \((. )_{k}^{T}\) and \((. )_{k}^{NT}\) as a \(T\)-period and an \(NT\)-period signal or variable, where \(k\in\mathbb{N}\) are iterations at the corresponding period. In more detail, the control structure works as follows:  
* At the current instant \(kT\), from a set of waypoints and the current position estimation \((\widehat{X},\widehat{Y})_{k}^{T}\), the Pure Pursuit path-tracking algorithm [9] generates the reference linear velocities along the X-axis and Y-axis of the vehicle body, \((V_{x}^{ref},V_{y}^{ref})_{k}^{T}\). Other important parameters of the algorithm are the reference linear velocity \(V^{ref}\), the look ahead distance \(L^{ref}\), and the minimum distance \(e\) from the robot to the target point. More details about the Pure Pursuit algorithm will be given in Section 3.3. * The reference linear velocities \((V_{x}^{ref},V_{y}^{ref})_{k}^{T}\) are injected to linear velocity PI controllers to generate the velocity control actions \((V_{x}^{u},V_{y}^{u})_{k}^{T}\). These PI controllers are used to reduce the negative effect that may cause dead-zones and possible external disturbances over the reference linear velocities. The vehicle inverse kinematics block transforms the velocity control actions \((V_{x}^{u},V_{y}^{u},W_{y}^{u})_{k}^{T}\) into dynamic references \((\omega_{1}^{ref},\omega_{2}^{ref},\omega_{3}^{ref},\omega_{4}^{ref})_{k}^{T}\). * From these dynamic references \((\omega_{1}^{ref},\omega_{2}^{ref},\omega_{3}^{ref},\omega_{4}^{ref})_{k}^{T}\), the internal dynamic PI controller (included in the robot simulator) computes the control signal to be applied to the vehicle. These control actions will be applied under Zero-Order Hold (ZOH) conditions. * As a result, the robot outputs will be obtained. The vehicle is equipped with a virtual beacon. Four fixed beacons are additionally placed on the walls of the simulation environment, emulating a beacon-based indoor positioning system. The measurements \((d_{1},d_{2},d_{3},d_{4})_{k}^{NT}\) are the distances between the virtual mobile beacon and the four fixed beacons, which are located in a known place with respect to the world system of the simulator. * Any vehicle output measurement \((\omega_{1},\omega_{2},\omega_{3},\omega_{4},\psi)_{k}^{T}\), \((d_{1},d_{2},d_{3},d_{4})_{k}^{NT}\) may be disturbed by Gaussian noise, which will be created from a set of independent seeds in order to generate a reproducible pseudorandom noise.