1. INTRODUCTION
A reliable and continuous navigation results can be obtained if a number of radio navigation systems are used when navigations through GNSS are not available or navigation performance is degraded due to intentional radio interference such as jamming or spoofing (White et al. 1998, Kaplan & Hegarty 2006). One of the research results on integration of the GNSS with other terrestrial radio navigation systems is the Alternative Positioning, Navigation and Timing (APNT) plan by the Federal Aviation Administration (Department of Transportation 2007, Department of Defense 2010). In the APNT plan, integrated system is proposed using Distance Measuring Equipment (DME) that can maintain navigation performance even when navigation through GPS are not available or navigation performance is degraded (Williams et al. 2008, Eldredge et al. 2010, Lo et al. 2010). The UK proposed an alternative navigation system which integrates the eLoran in order to reduce dependency on GPS in marine environments (Williams et al. 2008).
Before the integrated navigation systems are deployed, various functions in the system are checkd and navigation performance of the system is evaluated. M&S software can be used to reduce time and cost consumed in this process (Maria 1997, Lee 2007).
When performance of radio navigation systems is evaluated through M&S software, environments where radio navigation receivers are operated can be simulated using a software-based signal generator. In relation to this, research results on software-based signal generators can be found. To evaluate performance of GPS Software Defined Radio (SDR) receiver, the University of Calgary designed a software-based Intermediate Frequency (IF) GPS signal generator for L1 Coarse/Acquisition code (Dong et al. 2004). Chungnam National University also designed a software-based GPS spoofing signal generator to evaluate an anti-spoofing algorithm for GPS receivers (Lim et al. 2008). In addition, the Korea Electronics and Telecommunications Research Institute designed a GNSS signal generation simulator consisting of satellite orbit generation unit, navigation message generation unit, error generation unit, and IF signal generation unit to develop and verify the satellite navigation algorithm (Kim et al. 2009). Chungnam National University designed a GNSS multi-band IF signal generation software that can generate GPS L1/L2/L5 signals and Galileo E1/E5 signals, and verified its performance using a commercial software based GPS L1 receiver (Cho et al. 2012). In addition, Chungnam National University designed a GPS/Inertial Measurement Unit (IMU) data generator that generates GPS signals and IMU data in an M&S software that evaluates the performance of the ultra-tightly coupled GPS/INS (Ji et al. 2012).
Although research results on GPS signal generators or data generator software have been introduced, it is necessary to have a software-based navigation environment generation module that can generate measurements of various radio navigation systems including GNSS as well as terrestrial radio navigation systems to evaluate performance of the integrated navigation system. Research results on the previously mentioned GPS signal generators aim to evaluate the performance of GNSS SDR receivers or ultra-tightly coupled GPS/INS integrated navigation system.
This paper proposes a design method of navigation environment generation module of M&S software for performance evaluation of the integrated navigation system of GNSS and terrestrial radio navigation systems. A navigation environment generation module that generated measurements of GPS, KPS, and eLoran is designed. Performance is verified first through MATLAB. To show that the proposed navigation environment generation module can be used in the M&S software for performance evaluation of the integrated navigation system, an M&S software is implemented.
In Section 2, M&S software for performance evaluation of the integrated navigation system is briefly explained. In Section 3, the design method of the navigation environment generation module that generates measurements of the navigation algorithm is described. In Section 4, results of validity of the navigation environment generation module through MATLAB are presented and applicability of this to the M&S software is demonstrated. Finally, in Section 5, concluding remarks and further studies are presented.
2. M&S SOFTWARE OF INTEGRATED NAVIGATION SYSTEM
The M&S software of the integrated navigation system provides the navigation environments and performance evaluation results according to the design specifications of the integrated navigation system. It also shows an area where a given required navigation performance is satisfied and provides a function that derives a position of additional signal source to maximize the area if the area is not suitable for the operation of the navigation system. A navigation algorithm and measurements which are inputs of the algorithm are needed to evaluate performance. Furthermore, the integrated navigation system can be developed more effectively if various parameters can be set or evaluation results are displayed through the graphical user interface (GUI).
The integrated navigation system M&S software configuration is shown in Fig. 1. The integrated navigation system M&S software consists of navigation environment generation module navigation algorithm module, analysis module, and GUI module.
Fig. 1. Integrated navigation M&S software structure.
Users of M&S software or developers of the navigation system can set parameters required to generate measurements by the navigation environment generation module through the GUI module. The position of the navigation signal sources based on the coverage analysis results is reflected to generate measurements in the navigation environment generation module. The navigation algorithm module performs the navigation for measurements generated by the navigation environment generation module and results are provided to users or developers through the GUI.
3. NAVIGATION ENVIRONMENT GENERATION MODULE
A radio navigation system consists of navigation signal sources and receivers (Groves 2013). As shown in Fig. 2, a receiver receives signals transmitted from the navigation signal sources and generates measurements. In a navigation system using high frequency bands such as DME or VHF Omni-directional range (VOR), signals may not reach receivers as they are blocked by terrain or buildings between signal source and receiver (Groves 2013). As shown in Fig. 2, navigation environment generation means simulation of three-dimensional (3D) motion of a vehicle, characteristics of navigation signal sources, characteristics of radio propagation channels, and some parts of receivers. The errors included in the measurements can be divided into errors due to signal sources, errors occurred in the signal propagation process, and errors generated in the receiver (Kaplan & Hegarty 2006, Groves 2013). Position error, velocity error, and clock error of navigation signal sources affect measurements. Errors are generated to the characteristics of channels through which signals are transmitted. The errors generated in receivers occur when navigation signals are passed through the radio frequency front end and correlators (Kaplan & Hegarty 2006, Groves 2013). Measurements may not be obtained or large errors may occur in measurements due to jammer's attack (White et al. 1998).
Fig. 2. Navigation environment generation.
Considering the above characteristics, the navigation environment generation method applicable to the M&S software of the integrated navigation system is shown in Fig. 3. The navigation environment generation module consists of reference trajectory generation algorithm, signal visibility determination algorithm, true measurement generation algorithm, error generation algorithm, and jamming attack influence generation algorithm. As shown in Fig. 3, the reference trajectory is generated first from a scenario that represents the vehicle motion. Availability of signal sources is determined based on navigation warfare scenarios after determining the visibility of signal sources based on terrain information, position of navigation sources, and characteristics of navigation signals. True measurements are generated from the position of signal sources and reference trajectory. And the measurements which are inputs of the navigation algorithm are generated by adding errors occurred in signal sources, errors occurred in the navigation signal transmission process, errors occurred in the receiver, and errors occurred due to jamming attack to the true measurements.
Fig. 3. Navigation environment generation module.
3.1 Reference Trajectory Generation Algorithm
Structure of the reference trajectory generation algorithm is shown in Fig. 4. Motion of the vehicle is represented by a combination of constant acceleration, banking, rise/fall, and turning which are basic motion units. As shown in Fig. 4, angular velocity and acceleration of the vehicle are calculated from the basic motion units and related parameters. The attitude of the vehicle is calculated from the angular velocity, and vehicle's velocity is calculated from the attitude and acceleration. Finally, the position of the vehicle is calculated from the velocity.
Fig. 4. Reference trajectory generation algorithm.
3.1.1 Calculation of angular velocity and acceleration
In case of the constant acceleration motion, acceleration is generated as in Eq. (1) and the initial value of acceleration is zero. And angular velocity is zero.
\(a_k^{NED}\left[m\right]=a_{input},\ \left(m\neq1\right)\) (1)
where \(a_k^{NED}\left[m\right]\) denotes acceleration of the \(m\)-th sample in the \(k\)-th trajectory segment, and \(a_{input}\) is the acceleration of the vehicle.
In case of the banking motion, the roll rate is the input parameter \({\dot{\phi}}_{input}\), pitch rate and yaw rate are zero. And acceleration is zero.
In case of the rise/fall motion, the pitch rate of the vehicle is the input parameter \({\dot{\theta}}_{input}\). The roll rate and yaw rate are zero. The centripetal acceleration \(\left|a_\theta\right|\) is generated from the motion parameter as in Eq. (2)
\(\left| a_\theta \right| = {\parallel v_{init}\parallel^2 \over \parallel v_{init}\parallel/\dot{\theta}} =\parallel v_{init}\parallel \dot{\theta}\) (2)
where \(v_{init}\) denotes the initial speed of the vehicle and \({\dot{\theta}}\) denotes pitch rate.
In case of the turning motion, the yaw rate is the input parameter \({\dot{\psi}}_{input}\). The roll rate and pitch rate are zero. The centripetal acceleration is \(\left|a_c\right|\) generated from the motion parameter as in Eq. (3)
\(\left|a_c\right|=\left|g \tan{\phi_{init}}\right|\) (3)
where \(g\) denotes gravitational acceleration, and \(\phi_{input}\) the initial roll angle of the vehicle.
3.1.2 Attitude calculation
In case of the constant acceleration motion, attitude is the same as the initial value.
In case of the banking motion, a roll angle is given in Eq. (4). The pitch and yaw do not change.
\(\phi_k\left[m\right]=\phi_k[m-1]+\phi_{inc},m≠1\) (4)
where \(\phi_k\left[m\right]\) denotes the roll angle of the \(m\)-th sample in the \(k\)-th trajectory segment. \(\phi_{inc}\) denotes roll angle increment per sample in Eq. (5).
\(\phi_{inc}=\frac{\phi_{target}-\phi_{init}}{round\left(\left |\phi_{target}-\phi_{init}\right | /\dot{\phi}\Delta t \right ) }\) (5)
where \(\phi_{target}\) denotes the target roll angle. \(\dot\phi\) denotes the roll rate. \(\Delta t\) is the sampling time. round denotes the rounding operator to the first decimal place.
In case of the rise/fall motion, the pitch angle is represented in Eq. (6). The roll and yaw do not change.
\(\theta_k\left[m\right]=\theta_k[m-1]+\theta_{inc},m≠1\) (6)
where \(\theta_k\left[m\right]\) denotes the pitch angle of the \(m\)-th sample in the \(k\)-th trajectory segment. \(\theta_{inc}\) denotes the pitch angle increment per sample in Eq. (7).
\(\theta_{inc}=\frac{\theta_{target}-\theta_{init}}{round\left(\frac{\left|\theta_{target}-\theta_{init}\right|}{\dot{\theta}\Delta t}~~~\right)}\) (7)
where \(\theta_{target}\) denotes the target pitch angle.
In case of the turning motion, the yaw angle is given in Eq. (8). The roll and pitch do not change.
\(\psi_k\left[m\right]=\psi_k\left[m-1\right]+\psi_{inc},\ (m\neq1)\) (8)
where \(\psi_k\left[m\right]\) denotes the yaw angle of the \(m\)-th sample in the \(k\)-th trajectory segment. \(\psi_{inc}\) denotes the yaw angle increment per sample in Eq. (9).
\(\psi_{inc}=\frac{-\textrm{sign} \left(\psi_{init}\right)\psi_{amount}}{round\left(\frac{\psi_{amount}}{\dot{\psi}\Delta t}\right)}\) (9)
where \(\psi_{amount}\) denotes the turning angle and \( \textrm{sign}\) denotes sign function.
3.1.3 Calculation of velocity
In case of the constant acceleration motion, the velocity is given in Eq. (10).
\(v_k^{ENU}\left[m\right]=v_k^{ENU}\left[m-1\right]+a_{input}(m)\Delta t,\ \left(m\neq1\right)\) (10)
where \(v_k^{ENU}\left[m\right]\) is the velocity in the navigation coordinate system (East North Up coordinate system) of the \(m\)-th sample in the \(k\)-th trajectory segment.
In case of the banking motion, the velocity is constant as in Eq. (11).
\(v_k^{ENU}\left[m\right]=v_k^{ENU}\left[m-1\right],\ \left(m\neq1\right)\) (11)
In case of the rise/fall motion, the velocity is given in Eq. (12).
\(v_k^{ENU}[m]=\begin{bmatrix}\cos(-\gamma) & \cos(-\gamma)& 0 \\ -\sin(-\gamma) & \cos(-\gamma) & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix}\cos(\theta_{inc}) & 0 & -\sin(\theta_{inc})\\ 0&1&0 \\ \sin(\theta_{inc}) & 0 & \cos(\theta_{inc})\\\end{bmatrix} \)
\( \left[\begin{matrix}\cos{(}-\gamma)&\sin{(}-\gamma)&0\\-\sin{(}-\gamma)&\cos{(}-\gamma)&0\\0&0&1\\\end{matrix}\right]v_k^{ENU}[m-1] \) (12)
where \(\gamma\) is the direction angle in the northeast plane in Eq. (13).
\(\gamma={\tan}^{-1}{\left(\frac{\left(v_{init}\right)_N}{\left(v_{init}\right)_E}\right)}\) (13)
where \({\left(v_{init}\right)_N}\) is the velocity in the north direction at the start. \({\left(v_{init}\right)_E}\) denotes the velocity in the east direction at the start.
In case of the turning motion, the velocity is given in Eq. (14).
\(v_k^{ENU}\left[m\right]=\left[\begin{matrix}\cos{(}-\psi_{inc})&\cos{(}-\psi_{inc})&0\\-\sin{(}-\psi_{inc})&\cos{(}-\psi_{inc})&0\\0&0&-1\\\end{matrix}\right]v_k^{ENU}[m-1],(m≠1)\) (14)
3.1.4 Calculation of position
The position of the vehicle is obtained from velocities of constant acceleration motion, banking motion, rise/fall motion, and turnnig motion.
In case of the constant acceleration motion, the position is given in Eq. (15).
\(p_k^{ENU}\left[m\right]=p_k^{ENU}\left[m-1\right]+v_{init}(m)\Delta t+0.5a_{input}\left(m\Delta t\right)^2,\ \left(m\neq1\right)\) (15)
where \(p_k^{ENU}\left[m\right]\) is the position in the navigation coordinate system (East North Up coordinate system) of the \(m\)-th sample in the \(k\)-th trajectory segment.
In case of the banking motion, the position is given in Eq. (16).
\(p_k^{ENU}\left[m\right]=p_k^{ENU}\left[m-1\right]+v_k^{ENU}[m]Δt,m≠1\) (16)
In case of the rise/fall motion, the position is given in Eq. (17).
\(\left[\begin{matrix}(p_k)_E\left[m\right]\\(p_k)_N\left[m\right]\\(p_k)_U\left[m\right]\\\end{matrix}\right] = \left[[\begin{matrix}\gamma\cos\beta_{up/down}\cos\gamma+r\cos(\beta_{up/down}-\pi+\theta_k[m])\cosγ\\ γ\cos\beta_{up/down}\sin\gamma+r\cos(\beta_{up/down}-\pi+\theta_k[m])\sin\gamma\\ γ\sin\beta_{up/down}+r\sin(\beta_{up/down}-\pi+\theta_k[m])\\\end{matrix}\right] +\left[\begin{matrix}(p_{init})_E\\ (p_{init})_N\\ (p_{init})_U\\\end{matrix}\right] (m≠1)\) (17)
where \(\gamma\) is the direction angle of the vehicle in the northeast plane, and \(\gamma\) is the rising radius of the vehicle. \((p_{init})_E, (p_{init})_N\) and \((p_{init})_U\) are the components in the east, north, and up directions of the initial position, respectively. \((p_{k})_E, (p_{k})_N\) and \((p_{k})_U\) are the position components in the east, north, and up directions at the \(k\)-th trajectory segment. \(\beta_{up/down}\) is the angle between the vector from the vehicle to the center of the rotation and the northeast plane in Eq. (18).
\(\beta_{up/down}={\tan}^{-1}{\frac{(v_{init})_U}{\sqrt{\left(v_{init}\right)_E^2+\left(v_{init}\right)_N^2}}}+\frac{\pi}{2}\textrm{sign}(\theta_{tangent}-\theta_{init})\) (18)
In case of the turning motion, the position is given in Eq. (19).
\(\left[\begin{matrix}(p_k)_E\left[m\right]\\(p_k)_N\left[m\right]\\(p_k)_U\left[m\right]\\\end{matrix}\right]= \left[\begin{matrix} \gamma\cos\beta_{banking}+r\cos(\beta_{banking}-\pi+\psi_k[m])\\\gamma\sin\beta_{banking}+r\cos(\beta_{banking}-\pi+\psi_k[m])\\0\\\end {matrix}\right]+ \left[\begin{matrix} (p_{init})_E\\(p_{init})_N\\(p_{init})_U \\\end{matrix}\right](m≠1)\) (19)
where \(\beta_{banking}\) is the angle between the vector from the vehicle to the center of the rotation radius and the east axis in Eq. (20).
\(\beta_{banking}={\tan}^{-1}{\left(\frac{(v_{init})_N}{(v_{init})_E}\right)}-\frac{\pi}{2}\textrm{sign}(\phi_{init})\) (20)
3.2 True measurement Generation Algorithm
The structure of the true measurement generation algorithm is shown in Fig. 5. Visibility and availability of signal sources from the navigation signal source information and available signal source information are determined first. The position and velocity of the signal sources whose visibility and availability are guaranteed are obtained, and true measurements are calculated from the position and velocity of the signal sources and reference trajectory.
Fig. 5. True measurement generation algorithm.
Fig. 6. GPS true measurement generation algorithm.
Fig. 7. DME true measurement generation algorithm.
Fig. 8. eLoran true measurement generation algorithm.
Figs. 6-8 show the true measurement generation algorithm of GPS, DME, and eLoran, respectively. As shown in Fig. 6, ephemeris data are first extracted from the Receiver INdependent EXchange (RINEX) file in the true measurement generation algorithm of GPS. Visibility of satellite is determined through ephemeris data and reference trajectory. Availability of satellites is determined based on the available satellite information. After calculating the position and velocity of the satellite whose visibility and availability are guaranteed, the true range and the true range rate are generated from the position and velocity of the satellite, and reference trajectory. In the true measurement generation algorithm of DME in Fig. 7, visibility of the station is determined from the position of the DME station and reference trajectory. The true range is generated from the position of available DME station and reference trajectory. Since eLoran is rarely affected by geographic features in the signal propagation, the true range and the true range rate are generated directly from the position of available eLoran station and reference trajectory as shown in Fig. 8
3.3 Error Generation Algorithm
Errors due to the position and velocity uncertainty of signal sources, errors occurred in signal propagation process, errors occurred in the receiver, and white Gaussian noise are generated selectively to the characteristics of target system, operation environments of target system, and purpose. Since the integrated navigation algorithm in this paper performs navigation for measurements after correcting errors that are already known to the receiver, errors that are not compensated in the receiver are generated in the proposed navigation environment generation module and added to the true measurements. The error generation algorithm is given in Fig. 9 and Eq. (21).
Fig. 9. Measurement error generation algorithm.
\(e=e_{source}+e_{trasmit}+e_{receiver}+w\) (21)
where \(e_{source}\) is the position and velocity error of the signal source, is the error occurred in the signal propagation process. \(e_{receiver}\) is the error occurred in the receiver, and \(w\) is a white Gaussian noise.
3.3.1 Errors due to position and velocity uncertainty of signal source
In satellite navigation systems such as GPS and KPS, errors due to position and velocity uncertainty of signal source are given in Eq. (22).
\(e_{source}=\Delta D_{i,s}\) (22)
where \(\Delta D_{i,s}\) is difference between satellite position calculated from ephemeris information of satellite and actual satellite position.
In terrestrial radio navigation systems, errors due to position and velocity uncertainty of signal source is given in Eq. (23).
\(e_{source}=\Delta D_{i,g}\) (23)
where \(\Delta D_{i,g}\) the position error of the station is difference between station position in the receiver and actual station position.
3.3.2 Errors occurred in the signal propagation process
The error in the signal propagation process of a satellite navigation system is given in Eq. (24).
\(e_{trasmit}=c\left(\Delta T_i+\Delta I_i\right)\) (24)
where denotes the speed of light. \(\Delta T_i\) is the tropospheric delay error. \(\Delta I_i\) is the ionospheric delay error.
The error occurred in the signal propagation process of terrestrial radio navigation systems is given in Eq. (25).
\(e_{trasmit}=\Delta\rho_{PF}+\Delta\rho_{SF}+\Delta\rho_{ASF}\) (25)
where \(\Delta\rho_{PF}\) is the Primary Factor caused by difference between signal propagation speed in the atmosphere and that in free space. \(\Delta\rho_{SF}\) is the Secondary Factor which is the delay when the signal is propagated in the sea surface. \(\Delta\rho_{ASF}\) is the Additional Secondary Factor, which is the delay when the signal is propagated in the ground surface.
3.3.3 Errors occurred in the receiver
The error occurred in the receiver of the satellite navigation system is represented in Eq. (26).
\(e_{receiver}=c(b_{c,s}+\Delta v_s)\) (26)
where \(b_{c,s}\) is the clock bias error of the receiver and \(v_s\) is thermal noise.
The error occurred in the receiver of the terrestrial radio navigation system is represented in Eq. (27).
\(e_{receiver}=c(b_{c,g}+\Delta v_g)\) (27)
where \(b_{c,g}\) is the clock bias error of the receiver and \(v_g\) is the thermal noise.
3.4 Influence of Jamming Attack Generation Algorithm
The structure of influence of the jamming attack generation algorithm is shown in Fig. 10. The navigation warfare scenario includes jammer's position, power, frequency, and operation time length of jammer. The measurements are significantly affected as the jammer is closer to the vehicle and jammer's power is stronger. If the influence of jamming attack is large, the algorithm determines that signal sources are not available. As shown in the figure, availability of signal source is determined first from the reference trajectory and navigation warfare scenario, and then measurement errors occurred by jamming attack for available signal sources are generated.
Fig. 10. Measurement error generation algorithm.
4. VERIFICATION OF THE NAVIGATION ENVIRONMENT GENERATION MODULE
To demonstrate the applicability of the proposed design method of the navigation environment generation module to an M&S software, the functions were verified first through MATLAB, and the operations of the navigation environment generation module were verified in the M&S software for integrated navigation system. Navigations were performed for the true measurements in order to verify the navigation environment generation module. The specifications of GPS and eLoran were used in the implementation. Research results of KPS were utilized for the KPS since it is at a developing stage (Choi et al. 2012, Min et al. 2017).
4.1 Results of Verification Through MATLAB
After the position, velocity and attitude of the vehicle were calculated for the true measurement, they were compared to the reference trajectories.
4.1.1 Reference trajectory
Fig. 11 shows the reference trajectory. The vehicle is stationary for 900 sec, and in motion for 2,500 sec. The initial position of the vehicle is 35.34° of latitude, 126.19° of longitude, and 100 m of altitude. The vehicle rises up to 8 km of altitude. The vehicle moves with forming a pattern of ∞ and falls.
Fig. 11. Reference trajectory.
4.1.2 Results of measurement generation
Measurement generation results of GPS, KPS, and eLoran are shown in Figs. 12-14 when the vehicle is stationary for 900 sec. The figures show that the measurements change as GPS and KPS satellites move, while the measurements of eLoran are constant.
Measurement generation results of GPS, KPS, and eLoran are shown in Figs. 15-17 when the vehicle is in motion for 2,500 sec.
Fig. 12. GPS measurements.
Fig. 13. KPS measurements.
Fig. 14. eLoran measurments.
Fig. 15. GPS measurments.
Fig. 16. KPS measurements.
Fig. 17. eLoran measurements.
4.1.3 Navigation results
The navigation results of GPS, KPS, and eLoran were obtained using the least square method. The navigation results are shown in Figs. 18-20 when the vehicle is stationary for 900 sec. Navigation errors are shown in Figs. 21-23. Figures show that position errors in all navigation systems are smaller than 10-8 m in the north, east, and down directions, and the velocity errors are also smaller than 10-8 m/s. The Root Mean Square Error (RMSE) of the navigation results of GPS, KPS, and eLoran are presented in Table 1 when the vehicle is stationary for 900 sec. The table shows that the position errors in all navigation systems are smaller than 5×10-12 m in the north, east, and down directions, and the velocity errors are zero.
Fig. 18. GPS navigation result.
Fig. 19. KPS navigation result.
Fig. 20. eLoran navigation result.
Fig. 21. GPS position error and velocity error.
Fig. 22. KPS position error and velocity error.
Fig. 23. eloran position error and velocity error.
Table 1. Position and velocity error when the vehicle is stationary.
| Position error (RMSE) (m) | Velocity error (RMSE) (m/s) | |||||
| North | East | Down | North | East | Down | |
| GPS KPS eLoran |
0 0 0 |
0 0 0 |
\(3.69×10^{-12}\) \(3.69×10^{-12}\) 0 |
0 0 0 |
0 0 0 |
0 0 0 |
Navigation results of GPS, KPS, and eLoran are shown in Figs. 24-26 when the vehicle is in motion for 2,500 sec as in Fig. 11. Navigation errors are shown in Figs. 27-29. The figures show that differences between all navigation results and the reference trajectories in Fig. 11 are less than 6×10-4 m. It can be seen that the position errors in the navigation system are smaller than 10-8 m in the north, east, and down directions, and the velocity errors are also smaller than 10-8 m/s. Furthermore, the RMSE of the navigation results of GPS, KPS, and eLoran are given in Table 2 when the vehicle is in motion for 2,500 sec as in Fig. 11. The table shows that the position errors in all navigation systems are smaller than 10-4 m in the north, east, and down directions, and the velocity errors are smaller than 5×10-11 m/s. Errors are due to numerical errors, and the results show that the generated measurements are valid.
Fig. 24. GPS navigation result.
Fig. 25. KPS navigation result.
Fig. 26. eLoran navigation result.
Fig. 27. GPS position error and velocity error.
Fig. 28. KPS position error and velocity error.
Fig. 29. eloran position and velocity error.
Table 2. Position and velocity error when the vehicle is in motion.
| Position error (RMSE) (m) | Velocity error (RMSE) (m/s) | |||||
| North | East | Down | North | East | Down | |
| GPS KPS eLoran |
\(2.75×10^{-4}\) \(2.75×10^{-4}\) \(2.75×10^{-4}\) |
0 0 0 |
\(7.04×10^{-11}\) \(7.04×10^{-11}\) 0 |
\(1.66×10^{-11}\) \(2.48×10^{-11}\) \(2.48×10^{-11}\) |
\(4.56×10^{-11}\) \(2.48×10^{-11}\) \(2.48×10^{-11}\) |
0 0 0 |
4.2 Verification Through M&S Software
To demonstrate the applicability of the proposed design method, an M&S software was implemented on Visual C++.
Parameters required to generate the navigation environment can be set through the GUI of M&S software as in Fig. 30. The initial position, velocity, attitude, and basic motion unit of the vehicle for the generation of the reference trajectory as well as motion parameters in relation to the basic motion unit can be set as in the left window of Fig. 30. The database file of the navigation signal sources can be loaded as in the center window. The the navigation system error parameters are directly set as in the right window.
Fig. 30. Navigation environment generation parameter setting through GUI.
The same trajectory was generated in Fig. 11 by setting initial value, basic motion unit, and motion parameters through the GUI, and the true measurements were generated based on the same navigation signal source information as the case through MATLAB.
Result display of M&S software GUI is shown in Fig. 31. Measurements of navigation systems can be seen in the upper left window in Fig. 31, and the sky plot of GPS and KPS is in the center left window. The navigation results are shown in the lower left window, and reference trajectory, navigation results, and positions of stations of the terrestrial radio navigation system are shown in the right window.
Fig. 31. Navigation result on M&S software GUI.
5. CONCLUDING REMARKS AND FURTHER STUDIES
A method of designing a navigation environment generation module in M&S software of the integrated navigation system was proposed in this paper. The navigation generation module consists of reference trajectory generation algorithm, true measurement generation algorithm, and error generation algorithm. Visibility determination algorithm or jamming attack influence generation algorithm can be added to the type of navigation system, characteristics, purpose, and presence of jamming. In order to show effectiveness of the proposed navigation environment generation module design method, the functions in the module were verified first through MATLAB. And the Visual C++ based M&S software was implemented. True measurements of GPS, KPS, and eLoran were generated from the reference trajectory. Navigation results obtained from the true measurements were compared with the reference trajectories.
In the near future measurement generation algorithms of DME, VOR, Loran-c, and mobile/fixed pseudolite as well as the influence of jamming attack on measurements will be carried out.
ACKNOWLEDGMENTS
This work has been supported by the National GNSS Research Center Program of Defense Acquisition Program Administration and Agency for Defense Development.
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