Analysis of GNSS and IMU Sensor Data Fusion Using the Unscented Kalman Filter Method on Medical Drones in Open Air

Accurate and efficient position estimation is an important element in flight missions for autonomous aerial vehicles such as Unmanned Aerial Vehicles (UAVs). UAVs rely on sensors that provide information regarding position, speed, and orientation. GPS and IMU are sensors that can provide navigation information, where each sensor has characteristics that can complement each other’s shortcomings. Research related to the integration of GPS and IMU sensors for positioning with increasingly higher accuracy has been widely applied, one of which is the Kalman Filter method. Kalman filter not only performs digital signal filtering but is also capable of smoothing and predicting recursion to obtain the most accurate estimation results. Along with the development of the modification of the Kalman Filter, the Unscented Kalman Filter (UKF) method is a solution in overcoming nonlinear systems with estimation results approaching the actual value, so that the positioning accuracy is higher and convergent. This study intends to analyze the fusion performance of GPS and IMU sensor data using the UKF method on Medical Drones in an open space in order to obtain a position with high accuracy. UKF simulations on Medical Drones were carried out using a mathematical model on a 6 DOF (Degree of Freedom) UAV. The sensor data fusion performance was tested by comparing the results of the UKF method with the EKF on the Geopointer software. The results showed that the UKF simulation gave a positional accuracy of 0.022 m to the measurement data. The UKF simulation results in a better positioning accuracy when compared to EKF processing on the Geopointer software which only achieves a position accuracy of 8.467 m. The low accuracy of the EKF processing results is due to the mismatch of the IMU parameters obtained with the actual Medical Drone parameters.


Introduction
Since the 1990s, unmanned aerial vehicles or commonly called Unmanned Aerial Vehicles (UAV) have become widespread in the civilian market mainly due to advances in the field of microelectronics.Estimating position accurately and efficiently is an important element in flight missions for autonomous or unmanned aerial vehicles (Khamseh 2019).In order to locate and navigate an unknown environment, UAVs rely on sensors that provide information regarding position, speed, and orientation.There are sensors to provide direct navigation information such as the Global Positioning System (GPS) by providing position data, or indirect sensors such as inertial sensors that provide speed and orientation data.
Each sensor has characteristics that can complement each other's shortcomings.GPS has high accuracy in positioning for long periods of time, but the GPS signal cannot work optimally in locations where the receiver is unable to receive satellite signals such as in tunnels, buildings, or very dense forests.Cahyadi and Rwabudandi (2019).IMU as a complement to GPS does not depend on interference from outside signals that can block or interfere with the signal because measurements are made based on signal acceleration.In addition, the high frequency of IMU data and short acquisition time can interpolate GPS positions (Chu et al 2013).However, the IMU is prone to noise due to vibrations in the vehicle body, the effects of gravity, and the offset of the sensor.This condition causes the IMU data to experience a decrease in positional accuracy over time (Meng, Wang, and Liu 2017).The integration of GPS and IMU sensors is able to complement the characteristics of each sensor, so that positioning with higher accuracy can be applied.The method that is most often used lately to perform navigation data fusion is the Kalman Filter.The Kalman Filter is a set of mathematical equations using an optimal prediction-correction estimator to minimize the covariance of the estimation errors (Welch and Bishop 1995).In another sense, Kalman Filter is an algorithm that uses a set of observational data to estimate unknown variables more accurately.Besides being able to estimate state or parameter values by minimizing noise, which is quite strong, Kalman Filter does not take a long time and is easier to synthesize than other filtering methods such as Particle Filters (PF) (Sircoulomb et al., 2006).Kalman filter not only performs digital signal filtering but is also capable of smoothing and predicting recursion to obtain the most accurate estimation results.However, the standard Kalman Filter can only be applied to linear systems, whereas in practice almost all systems are nonlinear systems (Li et al. 2015).Along with the development of the modification of the Kalman Filter, the Unscented Kalman Filter (UKF) method is a solution in overcoming nonlinear systems with estimation results that are close to the actual value, so that the positioning accuracy is higher and convergent.
This study intends to analyze the fusion performance of GPS and IMU sensor data using the UKF method on Medical Drones in an open space in order to obtain a position with high accuracy.Medical Drone is a vehicle developed by the Directorate of Innovation and Science Technology Area, Sepuluh Nopember Institute of Technology (ITS) Surabaya for handling COVID-19 in the archipelago.As an unmanned aerial vehicle with the aim of delivering medical materials for handling people affected by COVID-19 in remote island areas, Medical Drones require an accurate navigation system in positioning to be able to work effectively.UKF simulations on Medical Drones were carried out on 6 DOF (Degree of Freedom) UAVs.Sensor data fusion performance testing is done by comparing the results of the UKF method with the EKF using Geopointer software.The results of this study are expected to be taken into consideration in estimating the position of the UAV accurately.

Sensor Fusion
Sensor fusion is done by 2 methods, namely through UKF Simulation and Geopointer software EKF method.The UKF simulation is done by creating a program according to a mathematical model that has been discretized and the Kalman filter algorithm consisting of prediction and correction stages.The prediction stage (time update) is carried out to calculate the average value (mean) of n ensembles which is then generated to obtain the estimated value of the UAV position at the prediction stage.
The prediction stage also calculates the error covariance.Furthermore, the correction stage (measurement update) calculates the estimated value of the UAV position correction by using the estimated value at the prediction stage and using measurement data, kalman gain, and the measurement matrix.Then, the average value of the estimated correction is calculated.This value is used to compare the value of the estimated UAV position with UKF to the actual value.

Validation
Validation

Trajectory Visualization
The visualization stage is carried out to visualize between trajectory of the measurement data and the estimation data.Then, both measurement and estimation trajectory will be overlaid to see the difference.

UAV Movement Mathematical Model
The mathematical model describes the movement and behavior of the UAV in relation to model inputs and external influences.Six DOF (Degree of Freedom) UAV refers to the three axes x, y, and z to produce translational and rotational motion as illustrated in Figure 3 (Sukandi 2010).
The fusion of GPS and IMU sensor data using the UKF algorithm will iterate over the prediction stage and the correction stage as many as the number of data epochs.

The Discretization of Mathematical Models
The UAV (1) -( 6) and UAV dynamics ( 7) -( 12) kinematic equations are continuous-time dynamic system models.To be able to fuse GPS and IMU sensor data using the UKF algorithm, the equations of the continuous time dynamic system model must be converted into a discrete time dynamic system model.The discretization of this mathematical model uses a finite difference method forward in order to be able to predict one time step in the future.The discrete forms of the kinematic and dynamic model equations are written in table 2 below.

Table 2. UAV Mathematical Model Discretization Results
Where k = k-th time ∆t = time lapse from k to k+1 The discrete time dynamic system model that is formed is a system model without noise.The system model is nonlinear because each variable depends on other variables and the system is in a large state space, so the Unscented Kalman Filter method is needed to estimate it.There are external factors that affect the motion of the UAV, it is also necessary to develop an external force dynamic model.The discretization of the dynamic model of the external force is obtained using the third derivative of Gauss-Markov.The results of discretization of all state variables produce a state matrix with dimensions of 30x30.
This noiseless system model still cannot represent the actual field conditions, for that it is necessary to model random noise generated from a normal distribution with error covariance (  ) and (  ) 1 and mean 0. This noise then makes the deterministic model a stochastic model.

Simulation of Unscented Kalman Filter (UKF)
The UKF was carried out using a UAV mathematical model at 6 DOF.In the simulation using MATLAB, running the program was carried out 10 times with k iterations of measurement data, namely 10918.The UKF simulation was carried out with 2 simulations, namely Simulation I using 9 parameters of measurement data and Simulation II using 6 parameters of measurement data.This is done to prove the ability of the Kalman Filter to make estimates even with limited measurement data.The data structure used for each simulation is presented in table 3    The UKF simulation validation is done by calculating the average RMSE of 10 running programs, this is because the noise changes every time the program runs.The comparison of the RMSE values above showed that Simulation II produced a better estimation with a smaller RMSE value than the Simulation I for both the position and angular velocity variables.Simulation I only achieved positional accuracy of 0.070 meters while Simulation II was able to achieve positional accuracy of up to 0.022 meters.These results show something different from most Kalman Filter studies where simulations with more measurement data input produce better accuracy.This condition can be caused by a large error in the attitude data (ϕ, θ, ψ), so that when this data is included in the UKF calculation it will reduce the accuracy of the estimation results.The attitude data is processing data obtained from the IMU sensor and not data from direct measurements.
To be able to recognize this anomaly, the error characteristics in the attitude data need to be analyzed by experimenting with various UKF simulation parameters using different combinations of attitude data.The intended simulation is to use coordinate measurement data and angular velocity as in Simulation II and then add 1 or 2 variations to the combination of attitude data variables.There were 6 simulation experiments carried out with 3 simulations using 8 measurement data inputs and 3 other simulations using 7 measurement data inputs.The use of the variation of the measurement data variables is described as follows: • Simulation A: using θ and ψ measurement data • Simulation B: using ϕ and ψ measurement data • Simulation C: using ϕ and θ measurement data • Simulation D: using ϕ measurement data • Simulation E: using θ measurement data • Simulation F: using ψ measurement data The comparison of RMSE and maximum residuals from the six simulations is presented in the following Table 5: Based on Table 5 above, it is known that Simulations A and B produced a larger RMSE and residue than Simulation C. The difference between Simulations A and B and C is the presence of yaw attitude data (ψ).This shows that the yaw attitude data (ψ) is the data that has the largest error between the other two attitude data.In the simulation with 7 input measurement data, Simulation F is a simulation with the largest RMSE value and residue compared to D and E. Simulation F which only uses attitude yaw (ψ) data further shows that there is a large error in the attitude yaw (ψ) measurement data.This result has been proven by previous GPS-IMU integration research which showed that yaw (ψ) has a larger error than roll (ϕ) and pitch (θ).

Simulation of Extended Kalman Filter (EKF)
EKF estimation is done using Geopointer software, so in this case the UAV mathematical model is not needed.In EKF processing the required input data and the resulting output are shown in Table 6.The coordinates of the EKF processing results which are still in the form of a geodetic coordinate system are first projected to the 49S zone UTM coordinate system to facilitate coordinate plotting.The EKF estimation trajectory resulting from processing with Geopointer software is presented in Figure 4   Based on the graph in Figure 5, it can be seen that the EKF estimation results decrease in accuracy, especially in the z variable with increasing time.This is indicated by the red line which is outside the trend of the measurement data in the last few epochs.Meanwhile, in the variables x and y, the EKF estimation results appear to have a trend that is almost similar to the measurement data.To validate the EKF estimation results, the RMSE and maximum residual are calculated so that the following results are obtained: Based on the RMSE value, it was found that the EKF processing resulted in a positional accuracy of 8.467 meters with the largest RMSE and maximum residual occurred in the z variable, namely 7.203 meters and 250.639 meters.Meanwhile, the smallest RMSE and maximum residue occurred in the y variable, namely 2,728 meters and 23,648 meters.This is in accordance with the visualization of the EKF estimation in Figure 7 where the z variable has the largest deviation.The estimation results between UKF and EKF have significantly different trajectories.The UKF estimation results have a trend that is almost similar to the measurement data, this shows that UKF estimation has a higher accuracy than the EKF method.The UKF estimation accuracy provides an increase in measurement position of up to 88.6%.This accuracy is similar to GPS measurements using the RTK method.The difference in accuracy achieved between the UKF simulation and EKF estimation could be due to the lack of information about IMU parameters on the UAV Medical Drone vehicle which is required when processing using Geopointer software.On the other hand, the UKF simulation was carried out using a dynamic model with assumptions that were adjusted to the environmental conditions in the open air that affect the movement of the UAV Medical Drone so that a more accurate estimate was obtained.

Conclusion
In this paper, the fusion of GPS and IMU sensors using the UKF method in Simulation II with 6 measurement data is able to produce an i-Boat position accuracy of 0.022 m to the measurement data.The maximum residuals from the x, y, z positions generated from the UKF simulation are 0.107 m, 0.089 m, and 0.139 m, respectively, against stand-alone GPS measurement data.The UKF method produces a better positional accuracy than the EKF on the Geopointer software which only achieves a positional accuracy of 8,467 meters.

Figure 2 .
Figure 2. Six Degrees of Freedom (DOF) UAV The mathematical model for fusion of GPS and IMU sensor data on the UAV consists of two models, namely the kinematic model and the dynamic model.

Figure 5 .
Figure 5. Graph of Comparison of Measurement Variables and Estimation of EKF

4
Comparison of UKF and EKFPositioning on the UAV Medical Drone system is carried out by utilizing the Here3 GPS device, namely a navigation type GPS that uses the u-blox M8 receiver module.Based on the specifications, GPS Here3 is able to achieve an accuracy of 2.5 m in stand-alone measurements, while in RTK measurements, the accuracy of GPS Here 3 is able to reach 0.025 m.Comparison of UKF simulation and EKF estimation against measurement data that perform stand-alone GPS measurements is carried out to determine the level of accuracy of the estimation results that have been carried out.The results of the comparison of accuracy are shown in Figure6as follows.

Figure 6 .
Figure 6.Comparison of the accuracy of UKF simulation and EKF estimation is used to check if algorithm UKF can estimate properly.It was carried out to test the performance of the UKF method through the RMSE value.1250 (2023) 012019

Table 3 .
UKF Simulation Data Structure

Table 4 .
UKF Simulation Maximum RMSE Value and Residue

Table 6 .
Data Structure in EKF simulasi simulation