High-Precision Positioning Simulation and Experimental Research of Special Operation Vehicles Based on Network RTK

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Introduction
In the 21st century, the felds such as artifcial intelligence, information technology, machinery and electronics, and precision manufacturing have been developed by leaps and bounds.Accordingly, unmanned and automatically operated special vehicles are also used in a wide range of applications, such as industry, agriculture, and fre protection.Since manual operation is not suitable in high-temperature, highly polluting, and high-risk environments, unmanned vehicles are used to replace workers to detect and collect information in harsh and dangerous environments.Furthermore, technologies used in unmanned automatic special vehicles are extensive, including automatic control technology, computer science, and machine vision, which is worthy of studying [1][2][3].
RTK (real-time kinematic) technology uses GPS carrier phase observations to correct the positioning system, thus carrying out real-time dynamic relative positioning.With the continuous advancement of RTK technology, it has been widely used in transportation, engineering mapping, geological disaster monitoring, and other felds and gradually replaced the traditional navigation and positioning methods [4][5][6].Modern society places greater demands on the navigation precision.However, a single navigation technology has difculty in adapting to the complex working environment.In practical engineering applications, various navigation methods are often combined to complement each other and achieve high-precision positioning [7,8].Tis study focused on the research on high-precision positioning technology of unmanned special operation vehicles by using SINS (strapdown inertial navigation system) and satellite navigation integrated positioning, and relevant tests were carried out.

GNSS Diferential Observation Equation.
In GNSS data processing, the functional relation between the original observation of the receiver and various factors afecting signal propagation is the GNSS observation equation.In GNSS positioning, satellites constantly broadcast navigation signals, and the receiver calculates the received pseudorange, carrier phase, and Doppler information to achieve navigation and positioning [9].Te pseudorange and carrier phase observations are two primitive observations which have the following observation equations: φ s r � ρ s r + c dt r − dt s  + T s r − I s r + λN s r + c s r + εφ s r . ( In equations ( 1) and ( 2), the superscript s denotes the observation satellite, the subscript r denotes the receiver, p and φ denote pseudorange and carrier phase observation, respectively, ρ indicates the actual distance between the satellite and the receiver when the signal is transmitted, c denotes the speed of light in vacuum, dt r and dt s d denote the receiver clock error and satellite clock error, respectively, indicating tropospheric error during the propagation of the signal through the atmosphere, I denotes the ionospheric error in the process of signal propagation in the atmosphere, λ denotes the carrier phase wavelength, N denotes the integer ambiguity in weeks, and εp and εφ denote other errors in pseudorange and carrier phase, respectively (including noise errors).

Double-Diference Observation Model.
Te principle of double-diference positioning is shown in Figure 1.Doublediference is a method of carrying out the intersatellite diference for another reference satellite [10,11].
Te base station receiver r and the mobile station receiver q perform diference calculation on the same satellite s.Te pseudorange and carrier phase observation equations of the base station r are equations ( 1) and (2), respectively.Te pseudorange and carrier phase observation equations for mobile station q are as follows: Te diference between equations ( 1) and ( 3) and the diference between equations ( 2) and ( 4) can eliminate the satellite clock diference dt q , thus obtaining a single diference model as follows: In equations ( 5) and ( 6), Δ denotes the single diference.With short baselines, the diference between ionospheric and tropospheric delay errors for base stations and mobile stations is small, so the diference between the troposphere and the ionosphere in equations ( 5) and ( 6) is regarded as equal to 0, which can be obtained as follows: ∆φ s rq � ∆ρ s rq + cdt rq + λ∆N s rq + ∆c s rq + ∆εφ s rq .(8) Assuming that the reference satellite is y, the single diference equation of the base station r and the mobile station q are as follows: ∆φ y rq � ∆ρ y rq + cdt rq + λ∆N y rq + ∆c y rq + ∆εφ y rq .(10) By diferentiating equations ( 7) and ( 9) and equations ( 8) and (10), the receiver clock diference term is eliminated to obtain the following double-diference observation equation: ( In the above equations, ∇∆ denotes the double-diference symbol.Te double-diference integer ambiguity retains the integer characteristic and can be efectively separated. Assuming that there are N available satellites, the number of observation equations for carrier phase and pseudorange is 2(N − 1), where the unknowns include three direction coordinates of baseline double-diference pseud range and N − 1 double-diference ambiguity.To solve the foat solution of ambiguity, 2(N − 1) ≥ 3 + (N − 1) is needed and the solution is N � 4. Terefore, the simultaneous observation of four visual satellites is the minimum requirement for a single system to realize diferential positioning [12,13].
When four satellites a, b, c, and d are used for calculation, a 6-dimensional equation group can be established by adding pseudorange double-diference observations.Taking the satellite a with large altitude angle as the main satellite, the following results can be obtained: where l m n   is the unit vector from the satellite to the receiver, δX δY δZ   is the correction number of the receiver's approximate coordinate, and ∇∆R is the doublediference pseudorange observation, and equation ( 12) is written in the following matrix form: In equation (13), H is the design matrix composed of the unit vector from the receiver to the satellite, X is the baseline vector and ambiguity solution to be solved, and the foat solution of ambiguity can be solved by the least square method as follows: In equation (14) In equation (16), Q denotes the covariance matrix of vector X, Q  m denotes the covariance matrix of baseline vector, Q  n represents the covariance matrix of ambiguity vector, and Q  m n and Q  n m denote the cross-covariance matrix of baseline vector and ambiguity vector, respectively.

Integer Ambiguity Estimation.
Integer ambiguity is crucial to achieve high-precision RTK positioning [14].At present, there are numerous ambiguity resolution methods, among which the LAMBDA algorithm has a perfect theoretical system, so the LAMBDA algorithm based on the least square estimation algorithm and the residual square of ambiguity is adopted.
Te foat solution  X is decomposed into the form of baseline vector and integer ambiguity vector, and the following is obtained: In equation (18), y is the double-diference observation of pseudorange and carrier phase,  m is the baseline vector, M is the coefcient matrix of the baseline vector, N is the integer ambiguity coefcient matrix,  n is double-diference integer ambiguity, and ε is unmodeled error amount.Terefore, the ambiguity solution is transformed into the least square.
In equation ( 18), Q y is the covariance matrix of y.
If ambiguity is independent of each other, the covariance matrix of the ambiguity is a diagonal matrix, and the optimal solution can be obtained by the nearest rounding.In general, due to the strong correlation between the ambiguity, the ambiguity covariance matrix is not a diagonal matrix, resulting in a low success rate through the rounding method.
Te integer ambiguity foat solution  X and the covariance matrix Q are obtained through equations ( 15) and ( 16), and then, the integer solution ń of the ambiguity is estimated by using the ambiguity vector foat solution  n and the covariance matrix Q  n to minimize the sum of residual squares of ambiguity, as follows:

Basic Principle of Strapdown Inertial Navigation.
Attitude update includes sensing the attitude information of the carrier and converting the measured real-time information to the navigation coordinate system to realize the position and speed update [15,16].Te solution process is as follows: Te initial information of navigation calculation is obtained through initial alignment.Ten, the real-time speed, position information, and attitude information of the unmanned vehicle are obtained by calculating the acceleration.SINS is shown in Figure 2.

State Equation of Integrated Navigation.
When combined navigation uses Kalman fltering for information processing, it is frst necessary to establish a state equation that refects the system state vector dynamic properties.[17,18].Generally speaking, the inertial navigation misalignment angle Φ, speed error δv n , position error δp, random constant drift of gyroscope ε b , and the random constant bias value of the accelerometer ∇ b are selected in the state equation and are taken as state vectors, and the state equation of the integrated n avigation system is as follows: Te state vector of the system state equation is as follows: Te system state transition matrix is as follows: Equation ( 22) is a 15-dimensional system transition matrix.In practical application, the zero drift of gyroscope, accelerometer, and magnetometer varies little with time, so the erasable term in the transition matrix is set as 0. Te system noise vector is as follows: In equation ( 23), w b g denotes the angular velocity measurement noise of the gyroscope and w b a denotes the specifc force measurement noise of the accelerometer..In integrated navigation, the position information and speed information obtained by the MEMS strapdown inertial navigation system are subtracted from the longitude, latitude, and speed information received by the GNSS receiver, and the obtained measurement equation of the speed and position of the unmanned vehicle is as follows:

Integrated Navigation Measurement Equation
where v n INS , v n GNSS ,  p INS , and  p GNSS are the inertial navigation speed, satellite navigation speed, inertial navigation position, and satellite navigation position, respectively.
In equation ( 25), v v denotes the speed measurement noise of the satellite receiver and v p denotes the position measurement noise of the satellite receiver.

Discretization of Continuous-Time Stochastic Systems.
Te continuous-time stochastic system given by equation (20) should be discretized.Equations ( 27)-( 29) can be approximated by equivalent discretization of equations ( 20) and (24). 4 Computational Intelligence and Neuroscience In the above equations, F(t) is approximately constant and F(t k−1 )T s is a small quantity, that is, 2 , ignoring the higher-order term of Taylor series expansion.
F(t k , t k−1 ) denotes the mean value of the system matrix in time period

Integrated Navigation Time Synchronization.
In SINS/ GNSS integrated navigation, the signal delay of inertial devices is relatively short, while the satellite signal has a relatively long delay from acquisition to positioning solution to transmission to navigation computer, and there is a time asynchrony error between the two.
In SINS/GNSS integrated navigation, the time asynchrony between the receiver and the inertial navigation system is shown in Figure 3. Te time lag of inertial navigation and satellite navigation is generally diferent, and the time asynchrony error is the relative lag of the two systems.Terefore, in the comparison of integrated navigation information, it is necessary to compensate for the time asynchrony error.
Te relationship between inertial navigation speed and satellite speed is as follows: In equation ( 29), a n is the average linear acceleration of the unmanned vehicle in the asynchronous time, which can be approximately obtained by diferential calculation of the speed of the inertial navigation system in two adjacent times, and the adjacent time is expressed as follows: T . ( In general, it is considered that the value of time asynchrony is relatively fxed. From equation (29), it can be calculated that the velocity asynchrony error between the satellite and the inertial navigation is as follows: Similarly, the position asynchrony error of the two is as follows: Te actual system is nonlinear, often using EKF (extended Kalman flter).EKF is the Taylor level frst, omitting its high-oriented item is approximately linear system, and then Kalman fltering.

Simulation Analysis.
To verify the feasibility of Kalman flter of integrated navigation, the navigation algorithm is compiled by MATLAB for simulation analysis.Te simulated motion trajectory parameters of the unmanned vehicle are generated according to the set motion state, and error parameters conforming to the actual application are added on this basis.Finally, the simulated IMU and GNSS data were input into the integrated navigation solution program, thus obtaining the navigation information such as the attitude (heading angle, pitch angle, and roll angle), speed, longitude, and latitude of the unmanned vehicle.

Simulation Device Parameters.
Te principle of the simulation is shown in Figure 4. Device errors of inertial sensors are added to simulate the pure inertial navigation and SINS/GNSS integrated navigation on the generated data.
Te simulation IMU generates the acceleration and angular velocity of the unmanned vehicle, while the threedimensional velocity of the unmanned vehicle is generated by GNSS.Te data update frequency of MEMS is 100 Hz, and the simulation device parameters are shown in Table 1.
Te navigation adopts the "east, north, and up" coordinate system, and the initial attitude is 0 °, 0 °, and 0 °.Te initial position is longitude 121.07014 °E, latitude 41.08478 °N, and 50 m high.Te initial speed is 0 m/s, the initial velocity error is 0.1 m/s, the initial attitude angle error is 0.03 °, 0.01 °, and −0.42 °, the initial position error is 0 m, and the data output frequency of satellite navigation is 10 Hz.

Simulation Results
. Due to the gyroscope drift and random walk of MEMS, its error is very large, and it cannot be used alone for a long time.Terefore, GNSS information is used for integrated navigation, and Kalman flter is used for data fusion to increase the precision and stability of integrated systems.Te simulation experiment is designed with a duration of 500 s.Te navigation experiment was carried out on the position, attitude angle, and speed under the pure inertial navigation and integrated navigation.

Computational Intelligence and Neuroscience
Te position and attitude errors of pure inertial navigation are shown in Figures 5 and 6.After 60 s, the position error begins to diverge.After 500 s, the position error can reach −169.1 m, −263.1 m, and −84.67 m.Te initial zero bias error of MEMS inertial measurement unit is large, which makes the navigation error result divergent with fast speed.After 500 s of navigation and positioning, the errors of pitch angle, roll angle, and heading angle reach 32.92 °, 10.87 °, and 32.65 °, which cannot meet the navigation accuracy.Terefore, pure inertial navigation cannot be used for positioning alone.
As shown in Figure 7, the position error of integrated navigation fuctuates greatly in the frst 50 s, and the longitude and latitude errors fuctuate around 0 in the following 450 s.Te position error converges quickly, which shows that the system error of navigation of inertial unit is well suppressed after adding GNSS information.Te reason for the fast convergence speed of the longitude and latitude error curves is that while adjusting the parameters of the Kalman flter P, Q, and R matrices, the coefcient of the P matrix is appropriately increased to improve the convergence speed of error curves.
Te attitude error of the combined navigation is shown in Figure 8.After using the Kalman flter, the navigation information is corrected by the fltering information, and the attitude error of the combined navigation remains largely fuctuating around 0.
Velocity errors for pure inertial and combined navigation "east, north, and up" directions are shown in Figure 9.If inertial navigation is adopted alone, the velocity errors in the east and north directions fuctuate greatly.When SINS/ GNSS integrated navigation is adopted after Kalman fltering, the fuctuation amplitude of velocity errors is signifcantly reduced and it basically fuctuates around 0.

Introduction to the Test Platform of Unmanned Vehicles.
Te external structure of the unmanned special operation vehicle mainly includes 3 Hikvision surveillance cameras, one 5 GHz 433 Mbps outdoor point-to-point network bridge, and two GNSS antennas, as shown in Figure 10.Te unmanned special operation vehicle is mainly used for realtime monitoring of the image, sound, air quality, and target temperature, around the observation area.Te RTK highprecision BDS/GPS dual-mode positioning and navigation system is used to calibrate the geographic position information and obtain position information of the unmanned vehicle in real time.2.

Static Test and Result Analysis.
Te number of satellites visible during static testing of unmanned vehicles and base stations is shown in Figure 12.Due to the main reason that the unmanned vehicle is equipped with two GPS antennas, the unmanned vehicle has more visible satellites than the base station in most of the time.In the same time period, if the unmanned vehicle is in a more ideal environment, the number of visible satellites will be more.However, there are more satellites in the base station between 223 and 279 seconds.Especially at the 274th second, the number of visible satellites of the unmanned vehicle is only 11, which may be due to the interference of satellite signals caused by the multipath efect.In the epoch of the static test, the base station has an average of 23.5 (23-24) visible satellites, and the unmanned vehicle has 28, which can meet the basic positioning requirements (the number of visible satellites ≥ 4).
Teoretically, the smaller the HDOP (horizontal dilution of precision), the higher the positioning precision, and its size fuctuates with the number of satellites.Te HDOP values of the unmanned vehicle and the base station are shown in Figure 13.HDOP of the unmanned vehicle is smaller than that of the base station.Te specifc values are  3  and 4.
Te pitch angle is stable at −0.0013 °and the standard deviation is 0.0021 °; the roll angle is stable at 0.0002 °and the standard deviation is 0.0074 °; and the heading angle is stable at 181.305 °and the standard deviation is 0.235 °.Te standard deviation of pitch angle and roll angle is relatively small, while the course angle has a relatively large standard deviation.Te mean and standard deviation of the easting speed and the mean and standard deviation of the northing  Computational Intelligence and Neuroscience speed are small with little fuctuation, which can meet the needs of high-precision positioning.

Dynamic Test and Result Analysis.
To verify the dynamic stability of the unmanned vehicle, its trajectory on the same rubber track was calibrated to make it move two laps on the set track.Te analyzed trajectory is shown in Figures 16 and  17.
Te remote controller was used to control the unmanned vehicle to move two laps on the rubber track, and the trajectory obtained on the upper computer is shown in Figures 16(a As can be seen through the upper computer display of the two movements of the unmanned vehicle and the MATLAB motion trajectory diagram, the satellite receiving state is good during the movement and the trajectory graph formed is clear.Terefore, the frst statistical data were selected to analyze the changes of the number of satellites received by the unmanned vehicle, the base station, and the HDOP value.Based on the data collected for the frst time, the error between the second data and the frst data was observed to analyze the positioning of the unmanned vehicle.
Te number of visible satellites of the unmanned vehicle and the base station in the dynamic test is shown in Figure 18 and Table 5. Te number of visible satellites of the base station is basically stable at 24 and 25 satellites, while the number of visible satellites of the unmanned vehicle varies greatly, up to 30 and at least 16.
Te HDOP of the unmanned vehicle and the base station in the dynamic test is shown in Figure 19.Te HDOP value of the base station is 0.7 or 0.8, while the HDOP value of the unmanned vehicle varies greatly, with a maximum of 1.4 and a minimum of 0.5.Te mean value and standard deviation are shown in Table 6.
For attitude errors, there are certain errors in about 120 seconds to 180 seconds, 300 seconds to 350 seconds, and      Te position error of the dynamic integrated navigation of the unmanned vehicle is shown in Figure 22.Te error in most time periods is 0, the maximum error in latitude is about 2.1 m, and the maximum error in longitude is about 2.8 m.Te main reason for the error is that the unmanned vehicle was disturbed by the surrounding environment during its movement, which afected its positioning precision and stability.Te main reasons for the fuctuation of curves in the fgure are insufcient   Te test results showed that if the pure inertial navigation system was used alone for a long time, its error would continue to accumulate with time, which would lead to the failure to complete the high-precision positioning Computational Intelligence and Neuroscience requirements.Terefore, integrated navigation should be used.
Each module of the unmanned vehicle worked well together, the performance was stable, and the positioning module was powerful, which could be applied to the actual situation.
When the unmanned vehicle was in an ideal environment, the satellite signal was better and the number of visible satellites received was relatively large.Using the integrated navigation, the attitude, position, and velocity information of the unmanned vehicle was ideal.When the unmanned vehicle was in a sheltered or complex environment, the error would increase, but it could still maintain a high positioning precision.

Conclusions
Tis study focused on high-precision positioning technology for unmanned autonomous operational special purpose vehicles, leading to the following conclusion.
Te combination of innovative attitude sensor and GNSS dual antenna measurement algorithm can greatly enhance the monitoring accuracy of the motion state of unmanned vehicles.Using BDS/GPS for positioning research, the spatial geometry of the satellite is ideal, the number of visual satellites received is relatively large, and the positioning efect is better than that of a single system positioning.
Te Kalman flter of integrated navigation and positioning was designed, which can efectively overcome the data divergence of inertial navigation and environmental constraints of satellite navigation and enhance the accuracy and stability of the positioning system.Simulations and experiments have verifed that the combined navigation and positioning system can meet the needs of practical applications.
Tis study used MAT-LAB to recalculate the saved data of the base station and unmanned vehicle and fnally obtained navigation data results.Te data update frequency of the GPS system was 10 Hz and that of MEMS was 125 Hz, the observation epoch was 1800 seconds, and the initial position of the unmanned vehicle was latitude 41.08478564 °N, longitude 121.0701494 °E, and 55.364 m high.

Figure 9 :
Figure 9: Pure inertial navigation and integrated navigation velocity errors.(a) North velocity error.(b) East velocity error.(c) "Up" velocity error.
) and17(a).Te obtained test data are sorted out, and then, the data are processed by MATLAB to convert the obtained motion data into graphic display.Te twodimensional representation of the motion of the unmanned vehicle is shown in Figures16(b) and 17(b).

Figure 12 :Figure 13 :
Figure 12: Te number of static visible satellites for unmanned vehicles and base stations.

Figure 16 :
Figure 16: Te frst trajectory of the unmanned vehicle.(a) Upper computer display of the frst trajectory of the unmanned vehicle.(b) MATLAB display of the frst trajectory of the unmanned vehicle.

Figure 17 :Figure 18 :
Figure 17: Te second trajectory of the unmanned vehicle.(a) Upper computer display of the second trajectory of the unmanned vehicle.(b) MATLAB display of the second trajectory of the unmanned vehicle.

Table 5 :
Visual satellite information statistics.Number of visible satellites of the unmanned vehicle Number of visible satellites of the base station Mean compensation of the inertial device and poor stability of the inertial device under dynamic conditions.Te static and dynamic tests of the dual antenna GPS/ MEMS integrated navigation system were carried out.

Table 2 :
Static integrated navigation location information statistics.

Table 3 :
Information statistics of static integrated navigation.

Table 4 :
Attitude information statistics of static integrated navigation.