Real-time Vehicle Roll Angle Estimation based on IoT low-cost devices and Neural Networks

Given the high number of vehicle-crash victims, it has been established as a priority to reduce this figure in the transportation sector. For this reason, many of the recent researches are focused on including control systems in existing vehicles, to improve their stability, comfort and handling. These systems need to know in every moment the behavior of the vehicle (state variables), among others, when the different maneuvers are performed, to actuate by means of the systems in the vehicle (brakes, steering, suspension) and, in this way, to achieve a good behavior. The main problem arises from the lack of ability to directly capture several required dynamic vehicle variables, such as roll angle, from low-cost sensors. Previous studies demonstrate that lowcost sensors can provide data in real-time with the required precision and reliability. Even more, other research works indicate that neural networks are efficient mechanisms to estimate roll angle. Nevertheless, it is necessary to assess that the fusion of data coming from low-cost devices and estimations provided by neural networks can fulfill the reliability and appropriateness requirements for using these technologies to improve overall safety in production vehicles. Because of the increasing of computing power, the reduction of consumption and electric devices size, along with the high variety of communication technologies and networking protocols using Internet have yield to Internet of Things (IoT) development. In order to address this issue, this study has two main goals: 1) Determine the appropriateness and performance of neural networks embedded in low-cost sensors kits to estimate roll angle required to evaluate rollover risk situations. 2) Compare the low-cost control unit devices (Intel Edison and Raspberry Pi 3 Model B), to provide the roll angle estimation with this artificial neural network-based approach. To fulfil these objectives an experimental environment has been set up composed of a van with two set of low-cost kits, one including a Raspberry Pi 3 Model B, low cost Inertial Measurement Unit (BNO055 37€) and GPS (Mtk3339 53€) and the other having an Intel Edison System on Chip linked to a SparkFun 9 Degrees of Freedom module. This experimental environment will be tested in different maneuvers for comparison purposes. Neural networks embedded in low-cost sensor kits provide roll angle estimations very approximated to real values. Even more, Intel Edison and Raspberry Pi 3 Model B have enough computing capabilities to successfully run roll angle estimation based on neural networks to determine rollover risks situation fulfilling real-time operation restrictions stated for this problem.

The high rate of vehicle-crash victims has a fatal economic and social impact in today's societies.That is why nowadays road vehicles incorporate safety systems in order to reduce accidents.In particular, road crashes where heavy vehicles are involved cause more severe damage because they are prone to rollover.For this reason, many researches are focused on developing RSC (Roll Stability Control) systems.
Concerning the design of RSC systems with an adequate performance, it is mandatory to know the dynamics of the vehicle.One of the most important parameters related to rollover dynamics is the roll angle.The problem is that this angle cannot be measured directly using low-cost sensors, so that it is necessary to estimate it through the integration and processing of data acquired from lowcost devices or from the sensors installed on current vehicles (sensor fusion) [1,2].In previous works, roll angle is estimated using different sensor types: inertial angle sensor and a gyroscope [1], angular rate and accelerometer sensors [2], lateral accelerometers and gyroscope [3][4][5], lateral and longitudinal accelerometers and yaw rate and roll rate sensors [4,[6][7][8], on-board vehicle sensors and low-cost GPS [9,10] and lateral tire force sensors [11].These observers are based on Kalman filter [5,6,[9][10][11], robust estimators [2,3,7,8] or artificial intelligence techniques [6,12].
The design of RSC systems is a complex task as they have to fulfill some requirements, mutual to other safety vehicle systems: 1.-To acquire information from sensors which a high sampling frequency.
2.-To process sensor information in hard real time.
3.-To include actuators with fast-response time.
4.-To use low-cost systems in order to minimize the implementation cost in commercial vehicles.
5.-To develop an architecture which integrates all previous elements, guaranteeing high reliability and fault-tolerance.
The increase of computing power, the reduction of consumption and electric devices size, along with the high variety of communication technologies and networking protocols using Internet have yield to Internet of Things (IoT) development, being applied nowadays not only in smart manufacturing, healthcare, smart cities, but also, in transportation and smart vehicles [13][14][15][16][17][18].Also, some research works have focused on hardware and software architectural problems related to this trend, and applied to the vehicular environment described before [19][20][21][22].
With the objective of design small and low-cost on-board systems for vehicle applications [19][20][21][22], it is necessary that they have enough accuracy and small processing time to increase the vehicle safety by the inclusion both estimators and controllers.These small computers will not only acquire the data but also must process this data to estimate the study variables.Raspberry Pi 3 Model B and Intel Edison are two popular small single-board computers, because they have flexibility, low price and high support from the internet community.There are studies that use these systems like a processing device [23], in [24] a fusion data for autonomous and transportation systems was performed through a Raspberry Pi.In [25] Raspberry Pi is used for detecting E.coli in real time.In [26] the dynamics of a human-powered vehicles was acquired through a Raspberry Pi.Finally, in [27] a study about inherent capabilities of the Raspberry Pi was carried out.
Like Raspberry Pi, there are many studies that use Intel Edison for the same purposes although it is not a single-board computer.In [28] integration with biomedical devices are used to acquired real-time vital parameters on neonates.In [29] a prototype to analyze geospatial data was created with Intel Edison.In [30] a system for smart home based on Intel Edison is proposed.
Previous studies demonstrate that the previous low-cost devices can provide data in real-time with the required precision and reliability [23].
On the other hand, Artificial Neural Networks (ANN), have been used to estimate vehicular characteristics in previous studies, like [31] where an ANN is used to estimate truck static weights by fusing weight-in-motion data, [32] where an ANN is used to estimate friction coefficient of wheel and rail in trains, [33] where an ANN is used to predict intersection crashes, or [34] where an ANN is used to estimate the traffic density and vehicle classification.
With the increase of computational power in small and embedded devices, ANNs have become computationally feasible to be used in such systems.This enhances the capabilities that IoT devices can provide [35][36][37].However, in most cases it is necessary to assess that the fusion of data coming from low-cost devices and estimations provided by ANNs can fulfil the reliability and appropriateness requirements for using these technologies to improve overall safety in production vehicles.
The novelty reflected in this work is the analysis of the vehicle roll angle estimation using ANN and low-cost devices under high dynamic conditions, by following specific best practices and considerations.An architecture based on IoT has been developed integrating low-cost Inertial Motion Unit (IMU) and small single-board computer, that acquire the data from the IMU sensor and estimate the roll angle using ANNs.The outcome to the estimations have been compared with the measurements acquired by a high-end professional device (VBOX from Racelogic), used as the ground truth.Two different low-cost systems have been considered on this research systems (Raspberry Pi with IMU BNO0055 and Intel Edison with IMU LSM9DSO).These devices are compared in terms of estimation accuracy, processing time and reliability.
This article is structured as follows.In Section 2, the methodology is presented, including the experimental testbed design, experiments' definitions, and the data gathering and analysis.The experimental results and the calculation of the RMS error and processing time are presented in Section 3. Finally, in Section 4, the discussion and conclusion of the results and the method are exposed.

Methodology
This section begins with the description of the experimental testbed design defined to achieve the research goals; then, the experiments to gather the data required are specified; and finally, the data gathered to analyze real time estimators' performance and reliability are presented, indicating the data analysis strategies adopted in order to identify relevant results and conclusions.

Experimental Testbed Design
This research work experimental testbed design can be analyzed from two perspectives: hardware and software.

Hardware perspective
The experimental testbed is based on a Internet of Things (IoT) architecture, embedded in a vehicle.The complete architecture is packaged in a product that can be integrated in any vehicle, in this particular case, for testing purposes, a Mercedes-Benz van was used.The motivation to use this vehicle was to compare the results obtained during this research with those described in [6].
To properly perform the comparative analysis, three kits of sensors were considered: • Reference, or ground truth kit.This kit is composed of a VBOX 3i GPS dual antenna data logger [38] connected to an IMU (Inertial Measurement Unit) from Racelogic.To accurately measure the roll angle, the two antennas form a 90-degree angle with respect to the traveling direction.For IoT kits' synchronization and data gathering, the VBOX controller is connected to a laptop embedded in the vehicle [6].The IMU and the low-cost sensor kits were located in the vehicle's center of mass, as is depicted in Figure 1.These three kits were also interconnected using a WiFi router which handles the communications among them, so the experiments can be synchronized, and the outcome of the tests can be gathered.According to [44], the accurate positioning of IMU and controller is essential for precision enhancement of low-cost kits.The Experiments Manager has the responsibility to provide a user interface to let the researcher start and stop the experiments and register the information coming from the experimental kits.It is developed in C++.The specific classes included in this component are: • The experimental kits network bus is in charge of subscribing and unsubscribing the different experimental kits.Even more, it provides the possibility to send requests to the experimental kits (0, shutdown experimental kit; 1, keep running the experiment; 2, start the experiment; and 3, end the experiment) and to receive the information items provided by VBOX, Raspberry Pi and Intel Edison kits.• Dataset Manager that is in charge of taking the data coming from the kits and storing them in a CSV file.The information stored includes gyroscope and accelerator data gathered with a sampling rate of 50 Hz.• Experiments User Interface that provide the functionality to start and finish the experiments.It connects to the experimental kits network bus to start and finish an experiment in a synchronized way for all the experimental kits connected.
The VBOX Component is in charge of gathering the information provided from the Racelogic IMU sensor and GPS dual antenna data.It is developed in C#.The specific classes included in this component are: • The VBOX kit connector oversees publishing the experimental kit, receiving the orders from the experimental kits orchestrator connected and send to it information obtained during the experiment.• The VBOX proprietary software is in charge of managing the information received during the experiment execution.
The software to manage the Intel Edison experimental kit is in charge of gathering the information provided by gyroscope and accelerometer included in its hardware architecture.This component is implemented in C++.The specific classes included in this component are: • The kit bus that is in charge of publishing the experimental kits in the network, receiving the requests form experimental kits network bus and send to the kit orchestrator the orders for starting and stopping the experiment.• The kit orchestrator is in charge of creating an empty data structure to store the results in RAM memory after receiving the "start experiment" signal from the kit bus, and sending the data structure having the data gathered during the experiment to the Experiments Manager for storage purposes, after receiving the "end experiment" signal.The information sent is routed through the kit bus and the experimental kits network bus to reach the Dataset Manager in the Experiments Manager.The Raspberry Pi kit has the same class structure as the Intel Edison kit. Sensors drivers were developed in C++ due to the recommendations provided in [23], and trying to keep the code as much similar as possible to maximize objectivity in the comparison of performance results against other devices with different hardware architectures (as the Intel Edison).
Raspberry Pi 3 and Intel Edison kits present wireless communication interfaces that ease the connectivity among components and allow to place them in virtually any point of the vehicle without worrying about setting up specific communication wires.Even more, the sensors used by these low-cost platforms are straightforwardly attached to the development boards by using the GPIO ports.By means of a wireless (IEEE 802.11g) access point, they can be connected to the experiments manager, which signals them their operation mode via a TCP socket connection.This software component uses ANNs to estimate the vehicle roll angle.The proposed model employs a Back-Propagation (BP) algorithm, which is one of the most widely-used methods for training a neural network.The specific neural network considered has been implemented as described in [6].The architecture of the BP neural network is shown in Figure 3.The ANN has a single hidden layer of 15 neurons, four inputs (the lateral acceleration, aym, the longitudinal acceleration, ax, the yaw rate, ψ ̇ and the roll rate φ̇) and one output (the vehicle roll angle, φ).The contribution provided by this research work to the Neural Network considered in [6] is its implementation in C++ using the FANN framework [45] to obtain an estimator component able to satisfy the real-time restrictions related to embed this estimator in a control unit installed in an operating vehicle.

Experiments Definition
The hypotheses to evaluate during this research work are the following: • H1: The roll angle estimated (φe) by the low-cost sensor kits is similar to the roll angle provided (φa) by expensive experimental kits (i.e., VBOX-based kits).• H2: The performance of the low-cost sensor kits (i.e., Raspberry Pi 3 Model B and Edison Kits) estimating the roll angle achieves the levels required for real-time processing embedded in operating vehicles.
To evaluate the previous hypothesis, five controlled experiments were executed several times (see Table 2).The experiments consider typical maneuvers such as J-turn and lane change maneuvers.These maneuvers are the most common used to test the vehicle's behavior.Furthermore, a long test simulating a general execution has been done.In the experiments carried out, the lateral acceleration and the roll rate are the variables that have suffered higher variation, and for this reason, these variables are considered in order to analyze the accuracy of different devices.The experimental tests have been carried out in Leganes (Madrid, Spain) using a Mercedes Sprinter, as can be seen in Figure 4 during a period were the setting had no traffic restrictions interfering with the appropriate execution of the considered experiments.

Data Gathering and Analysis
The data obtained for each of the previously-defined experiments (see Table 2) were stored by the controller of each kit in a CSV formatted file, identifying the experiment and its execution date and time.The variables considered were the lateral acceleration, aym, the longitudinal acceleration, ax, the yaw rate, ψ ̇ and the roll rate φ̇, the actual roll angle φa (only obtained in VBOX kit, that acts as the ground truth, together with the GPS coordinates) and the estimated roll angle, φe (only calculated by low-cost sensor kits).
The measures were gathered according to the sampling rate stated for the experiments, which was 50 Hz.Figure 5 and 6 present an example of the data gathered in each experiment.The accuracy of roll angle estimation using NN and data collected by low-cost sensor kits was calculated comparing these data against the roll angle obtained from GPS-dual antenna by the Racelogic VBOX (Ground Truth).In Section 3, the results obtained in the different tests will be presented.

Threats to Validity
To analyze the validity of the results obtained in this experimental work, several threats were considered prior to the experiments' execution: • Internal validity is the extent to which a causal conclusion based on the experiments defined is appropriate avoiding the introduction of systematic errors in the data used to determine the results and conclusions.• External validity is the extent to which the results of a study can be generalized to other situations.
(A) Internal validity: In this research, the only factor contributing to internal validity is related to the specific sensors used to configure each low-cost kit and the software components implemented to manage the required data: • The first threat was mitigated using two different kits for each type, in order to prevent possible errors produced by sensors that may provide incorrect values.Even more, all the kits considered were tested in a static environment, preconfiguring the corresponding calibrations to assure that specific sensors included were providing appropriate data.• Regarding the software components, the possible threats were mitigated implementing an exhaustive unit testing process.It ensures that each functionality is properly processing the received values and that synchronization among devices is correctly implemented.• The ANN based estimators were properly trained and compared with information coming from experiments carried out in previous research works [6,23].• To verify the validity of the results, each maneuver was repeated, at least, three times consecutively.

(B) External validity:
In the scope of this research, the factors that influence the external validity are related to the replication of this experiment.These replications must consider several relevant factors: sensors and controllers included in the experimental kits, their location in the vehicle and road conditions: • Regarding sensors and controllers, the possible threats were mitigated using sensors and controllers available on the market having regular features [46][47][48].On this regard, the conclusions obtained are valid for the low-cost sensors currently available on the market, and as the technology is always improving the prior conditions, the conclusions can be applied in forthcoming low-cost sensors.• Regarding vehicle conditions, the threats were related to the appropriate location of experimental kits in order to ensure equal conditions among them.This threat was mitigated creating a box to put the three sensor kits in a 3D printed enclosure (See Figure 1, box 4) that was located in the vehicle gravity center.These issues are important to replicate this experiment properly in other vehicles.In this research, as the experiments have been carried out with a real vehicle, it has been difficult to maintain the same exact driving conditions related to steering wheel angle and velocity.In spite of this problem, similar tests for typical maneuvers have been carried out.• Regarding road conditions and experiments execution, the threats were related to the representativeness of the scenarios considered.This threat was mitigated considering a road without relevant slope variations and including different experiments with different types of directions, constant and variable speed.

Results
As is indicated in Section 2, a Mercedes Sprinter was used for this work (see Figure 1).Three different kind of experiments were carried out: two different maneuvers, J-Turn and lane change, and a normal circulation test.For J-Turn and lane change maneuvers, five similar tests were performed in order to assess the validity of the results.

Test 1. J-turn
The first test is performed in a roundabout with a radius of 22 m (see Figure 7) at a constant speed (close to 40 Km/h).Figure 8 shows the roll angle estimated by the Raspberry Pi (blue) and Intel Edison (green).In order to verify the estimation accuracy, results have been compared with the roll angle measured with the VBOX GPS dual antenna (yellow), which is considered as the ground truth.Estimations are very similar in both devices, and that the usage of low-cost devices do not impact in the ANN estimator performance.To quantify this impact, the norm, the root mean square (RMS) and maximum errors have been calculated.The norm error as a function of time is calculated as follows [7]: Where θGT represents the ground truth data, θlc represents the low-cost sensor data and µGT is the mean value of the ground truth data obtained during the period T. deviation has been included for the RMS error (see Table 3).The results show that the error is very similar in both devices and it is higher than the estimated roll angle using VBOX IMU data.The difference between Raspberry Pi 3 Model B and Intel Edison for the norm and RMS error is about 3% and 0.05⁰, respectively.Concerning the maximum errors, the difference is about 0.3⁰.An important aspect to consider in this kind of system is the temporal performance and real time constraints.For the given case, the system needs to be able of processing the inputs and apply the ANN estimator in less than 20 ms, corresponding to the sampling rate of 50 Hz forced by the low-cost sensors.
Figures 9 and 10 show the relationship between the sensors' measured data processing time (normalization + ANN estimation + denormalization) for both Intel Edison and Raspberry Pi 3 Model B respectively, and the established threshold corresponding to the sampling rate (50 Hz).
In table 4, a comparison of time performance between Intel Edison and Raspberry Pi 3 Model B is presented.To quantify the performance of the devices, the mean and maximum processing times have been calculated.It has been also calculated the mean deviation to assess the stability of the devices.Results show that both devices estimate roll angle four orders of magnitude lower than the required sample rate threshold of 20 ms.Results show that the processing times for Raspberry Pi 3 Model B are higher than the Intel Edison ones.Concerning the mean and maximum times, the differences are about 0.5e -3 ms and 12 ms respectively.Regarding Mean Deviation, the difference is about 0.008 ms, so it is possible to conclude that results are homogeneous as far as performance and response times are concerned.

Test 2. Double Lane Change
The second test is carried out in a straight line when the vehicle does a slalom at constant speed (See Figure 11).Figure 12 shows the roll angle estimated by the Raspberry Pi (blue), Intel Edison (green) and the data provided by the Racelogic IMU (yellow).In order to verify the accuracy of the estimation, they have been compared with the roll angle measured with the GPS dual antenna of VBOX, which is considered as the ground truth.It can be seen that the estimation is very similar in both cases and that using low-cost devices do not impact in the ANN performance.
To quantify this impact, the norm, RMS and maximum errors have been calculated (see Table 5).To verify the validity of the results, three similar tests for the Lane Change maneuver have been carried out.To quantify the dispersion of data values, the standard deviation has been included for the RMS error.The results show that the errors are very similar in both devices and they are higher than the estimated roll angle using VBOX IMU data.The difference between Raspberry Pi 3 Model B and Intel Edison for the norm and RMS errors are about 0.6% and 0.03⁰, respectively.Concerning the maximum errors, the difference is about 0.2⁰.In Table 6, a time performance comparison between Intel Edison and Raspberry Pi 3 Model B is presented.To quantify this performance for both devices, the mean and maximum processing times have been calculated.It has been also calculated the mean deviation in order to assess the stability of the devices.Results show that both devices estimate roll angle four orders of magnitude lower than the required sample rate threshold of 20 ms.Results show that the processing times for Raspberry Pi 3 Model B are higher than the Intel Edison ones.Concerning to mean and maximum times the difference is about 0.7e -3 ms and 7.9 ms.Regarding mean deviation, the difference is about 3.8e -3 ms, so it is possible to conclude that results are homogeneous as far as performance and response times are concerned.

Test 3. General Circulation
This lasts test is carried out in the circuit shown in Figure 4.In this test not only J-Turn and Lane Change maneuvers are performed, but also the course of a real circuit under usual circulation conditions.The vehicle is driven at every moment with the most appropriate speed for the road and the situation, doing severe maneuvers at low and medium speed circulation (between 20 and 60 Km/h), and smooth movements.
Figure 15 shows the roll angle estimated by the Raspberry Pi (blue), Intel Edison (green) and the data provided by the Racelogic IMU (yellow) that is considered as ground truth.In this test the calculated error is higher than the other two tests.This kind of tests are prone to suffer noise, and as is indicated in [23], the low-cost sensors used are very sensitive to noise.Table 7 shows that the error is higher in Intel Edison than in Raspberry Pi, in this case Intel Edison present some atypical data.The difference of the norm and RMS error is about 96% and 0.9⁰ respectively.Concerning the maximum errors, the difference is about 3⁰.orders of magnitude lower than the required sample rate.Results show that the processing times for Raspberry Pi 3 Model B are higher than the Intel Edison ones.Concerning the mean and maximum times, the difference is about 0.7e -3 ms and 5.1 ms, respectively.Regarding Mean Deviation, the difference is about 0.1e-6 s, so it is possible to conclude that results are homogeneous as far as performance and response times is concerned.

Discussion
The following discussion is focused on the precision and the performance of the low-cost devices.

Precision
Results show the estimation of the roll angle obtained from low-cost devices is like the measurements directly obtained from Racelogic VBOX. Figure 15 shows that there exists noise in the estimated values.One reason is that the low-cost sensors are more prone to noise as is indicated in [23] and ANNs are very sensitive to noise.As future work, it is planned to integrate filters via software components to solve the noise related issue.Despite the noise influence, the average RMS error in Intel Edison and in Raspberry Pi is 0.8⁰.

Processing capability
The temporal performance and real time constraints are main aspects to consider in order to integrate estimators and controllers in embedded low-cost devices.The results show that the processing time to get the data, execute its normalization, perform the roll angle estimation via ANN and the denormalization of the outcome, is four orders of magnitude lower than the required sample rate threshold of 20 ms.The average mean processing time is 14.5e -3 ms for Raspberry Pi 3 Model B and 13e -3 ms for Intel Edison.This difference allows to integrate filters in order to reduce the noise in data collected from the sensors as it is indicated in 4.1 and to develop and embed more complex estimators and controllers.
To minimize the processing time and allow an objective performance comparison among the low-cost kits, some optimizations were considered before deploying and executing the software components.The most relevant optimizations include: • Development of same C++ source code for Intel Edison and Raspberry Pi 3 Model B. Usage of same compiler (gcc version 6.3.0) in both platforms, and the same linker and compiler flags, considering the maximum optimization level for speed (-O3 [49]).These additional optimizations perform, among others, predictive commoning optimization, this is, reusing computations (especially memory loads and stores) performed in previous iterations of loops, with result beneficial considering the processor caches in both Intel Edison and Raspberry Pi 3 Model B. • Usage of light and optimized Fast Artificial Neural Network Library (FANN [45]), version 2, compiled directly in the platforms using cmake, and the last source code revision from GitHub [50], that present among its multiple benefits the cache optimization for extra speed.• Multiple revisions of source code to keep it clean and simple.Algorithmic optimizations to keep a low-profile memory usage, and increased performance (i.e.avoiding copies of objects, like the ANN instance, by passing it by reference).

Conclusions
In accordance to the results obtained, it can be concluded that low-cost experimental kits including embedded ANN estimators provide roll angle estimations very close to actual values.Even more, Intel Edison and Raspberry Pi 3 Model B have enough computing capabilities to successfully run roll angle estimation based on ANNs to determine rollover risks situation fulfilling real-time operation restrictions stated for this problem.
The results can be used to design, implement and test an efficient, versatile and scalable lowcost hardware/software architectures able to be integrated in commercial vehicles.
Even more, the performance levels achieved indicate the possibility to embed, in the low-cost experimental kits, more complex estimators using a sensor fusion approach to obtain roll angle estimations closer to the actual values based on Kalman filters, combining neural networks and Kalman filters and considering deep learning techniques including other parameters obtained from other sources (i.e.road characteristics).In this line, more complex estimators for other variables (such side slip, etc.) could be integrated in low-cost experimental kits to improve the vehicle stability control in real time.

Figure 5 .
Figure 5. Example of CSV file contents for data registered by VBOX kit during the experiments' execution.

Figure 6 .
Figure 6.Example of CSV file contents for data registered by low cost sensor kits during the experiments' execution.

Figure 8 .
Figure 8. ANN estimated + ground truth roll angle for J-Turn maneuver

Figure 9 .Figure 10 .
Figure 9. Test 1. Processing time of each iteration for Raspberry Pi

Figure 12 .
Figure 12.ANN estimated + ground truth roll angle for double lane change

Figure 15 .
Figure 15.ANN estimated + ground truth roll angle for general circulation

Table 1 .
Technical specifications of hardware elements included in the study.

•
The Sensors Handler is responsible of registering data items from sensors attending to the preconfigured sampling rate (50 Hz for this research work).•The Roll Angle Estimator is a software component that implements an ANN to estimate the roll angle corresponding to the lateral acceleration, aym, the longitudinal acceleration, ax, the yaw rate, ψ ̇, and the roll rate φ̇ as input variables.A more detailed description of this estimator is provided in 2.1.3.• The NTP Client is in charge of registering the actual date-time in the hardware controller of the experimental kit to ensure that all the kits in the testbed have the same date-time.This enables and eases comparison of results during the data analysis stage in this research work.

Table 3
contains the errors measured.To verify the validity of the results, three similar tests for the J-turn maneuver have been carried out.To quantify the dispersion of data values, the standard

Table 3 .
Test 1.Errors of estimated roll angle on Raspberry Pi and Intel Edison compared with the measured roll from VBOX (ground truth).

Table 5 .
Test 2. Errors of estimated roll angle on Raspberry Pi and Intel Edison compared with the measured roll from VBOX (ground truth).

Table 6 .
Test 2. Processing time on Raspberry Pi and Intel Edison.

Table 7 .
Test 3.Errors of estimated roll angle on Raspberry Pi and Intel Edison compared with the measured roll from VBOX (ground truth).

Table 8 .
Test 3. Processing time on Raspberry Pi and Intel Edison.
Figure 16.Test 3. Processing time of each iteration for Raspberry Pi Figure 17.Test 3. Processing time of each iteration for Intel Edison