Verification of drone formation relative positioning technology based on Beidou

High precision drone formation flight requires real-time knowledge of the three-dimensional position and velocity information of the carrier. The Beidou navigation system, due to its all-weather and high-precision characteristics, can provide good relative position results for drones. However, when drones move at high speeds and in complex environments, The Beidou navigation receiver may experience various errors, leading to poor positioning results or even inability to locate. This paper provides targeted technical design for the reliability of Beidou relative positioning in complex environments during drone flight, monitors navigation data in real time to improve the fixed reliability of overall ambiguity, and uses BeiDou signal simulator to simulate and generate observation data for analysis and processing. The test results show that this method improves the continuity and reliability of the fixed ambiguity of Beidou, and can meet the requirements of real-time formation flight of drone.


1.
Introduction Drone flight has the characteristics of fast speed and large attitude changes.During formation flight, it is necessary to determine the relative positions of each drone in real time to maintain the mission formation.As a global satellite positioning system, Beidou has the characteristics of real-time, allweather, and high-precision, which can provide high-precision and highly reliable relative positioning results for drone formations.In terms of GNSS relative positioning, foreign countries mainly use GPS navigation systems [2][3][4][5][6].Due to the lower number and configuration of navigation satellites compared to the BeiDou navigation system, high-precision positioning in China mainly uses the BeiDou navigation system.This article focuses on the real-time BeiDou relative positioning, and optimizes it from the aspects of data quality control and fixed reliability of integer ambiguity, and verifies it using BeiDou simulation dual frequency observation.

2.
Analysis of data failure issues The Beidou navigation receiver may encounter various faults during high-speed motion, and it needs to be monitored.Data fault monitoring mainly includes three aspects: signal related monitoring, data quality monitoring related to measurement data, and monitoring related to positioning and calculation.
 The monitoring of navigation signal quality related to the environment mainly includes the monitoring of ionospheric scintillation, ionospheric storms, abnormal signal distortion, severe multipath, low satellite signal power, and other faults.For relative positioning calculation, such faults are manifested as anomalies in pseudo range and carrier phase.
 The quality monitoring of navigation data related to Beidou navigation equipment mainly includes the monitoring of faults such as pseudo range gross errors, ephemeris anomalies, carrier cycle slip, etc.  The quality monitoring of positioning solution mainly includes the monitoring of faults such as pseudo range residual, carrier residual, and ambiguity accuracy determination.Integrity monitoring mainly uses redundant information to detect faults.The main method is the RAIM algorithm, which does not rely on external information and has a simple hardware structure.It is a recommended algorithm in navigation [7].Due to its algorithm limitations, it is difficult to meet high performance requirements and can only monitor measurement domain data, making it difficult to monitor the carrier phase observation, integer ambiguity, and residual mainly used in relative positioning.Therefore, other solutions need to be explored.
During high-speed flight of drones, changes in speed and attitude can easily cause frequent satellite loss of lock and recapture, making it difficult to search for carrier phase integer ambiguity.Therefore, targeted design is needed for this special operating condition.The most widely used and effective method for fixing carrier phase integer ambiguity is the LAMBDA search method.However, in highspeed flight environments of drones, the success rate of this method cannot reach 100% [8].If the ambiguity is fixed incorrectly, it will lead to the highest meter level deviation.Therefore, it is necessary to monitor the accuracy of ambiguity in real-time during drone formation flight.

Pseudorange Carrier Joint Calculation Technology
To accelerate the convergence of integer ambiguity, combined with the advantages of pseudorange and carrier phase, a pseudorange carrier joint solution method is adopted for relative positioning calculation.By combining the current epoch coefficient matrix and utilizing the previous epoch ambiguity and weight matrix, the decimal solution of the integer ambiguity can be calculated.
For n Beidou solution satellites, the carrier phase double difference observation equation contains 3 unknown relative position parameters and n-1 unknown integer ambiguity parameters.The number of unknown parameters exceeds the number of equations.To solve the carrier phase double difference observation equation mentioned above, it is necessary to comprehensively utilize both pseudo range and carrier wave observations.The following is the joint solution process of pseudo range carrier phase.By combining the double difference pseudorange equation and the double difference carrier phase equation, the following equation system can be obtained: Let M represent the tracking drone, and S represent the target drone.The above equation system can be expressed in the following matrix form: By adding a coefficient matrix and using the least squares method, it can be obtained that: Make   =    ，  =   ，  =   ，  =   ，  =    (  +  )，   =     ，the above equation can be abbreviated as: The relative position and integer ambiguity floating-point solution results can be obtained using the least squares method: ˆ=   −1 (  −    ˆ)

Method of fixing ambiguity
By utilizing the characteristics of wide lane combination wavelengths through dual frequency combination, the search speed for ambiguity can be accelerated; Utilizing the feature of eliminating ionospheric errors through ionospheric combination, improve the success rate of fixed integer ambiguity and the accuracy of position calculation [10].
Here are the specific steps for fixing the ambiguity of dual frequency: Step 1: Use the double difference observation values of the tracking spacecraft and the target spacecraft to calculate the floating-point solution ∇Δ 5 and its covariance matrix Q N 6 N 6 of the ambiguity of the wide lane combination using the least squares method, with: ∇Δ 1 and ∇Δ 3 are the integer ambiguity floating-point solutions of B1 and B3 double difference carrier observations.
Step 2: Substitute the floating-point solution ∇Δ 5 of ambiguity and the covariance matrix into the LAMBDA search module for fixed solution search until the integer solution ∇Δ ̂5 of wide lane ambiguity confirmed by ambiguity is obtained.
Step 3: For the short baseline situation, using the relationship between the wide lane combination and the B1 and B3 observation values, the double difference ambiguity ∇Δ 3 in the double difference observation equation can be replaced by ∇Δ 5 and ∇Δ 1 to obtain: ∇Δ 3 = ∇Δ 1 − ∇Δ 5 (9) By utilizing the relationship between the wide lane combination L5 and the ionospheric free combination L4, as well as the observed values of B1 and B3, the ambiguity parameters in the ionospheric free combination can be replaced with the wide lane combination ambiguity parameters and B1 ambiguity parameters.The Ionospheric-Free observation range is: Among them, ∇Δ L3 is the observation value of the ionospheric composite double difference carrier,  1 and  3 are the frequencies of B1 and B3 carriers, ∇ΔL 1 and ∇Δ 3 are the observation values of B1 and B3 double difference carriers, c is the speed of light, and ∇Δε ϕ is the carrier phase composite double difference.
Step 4: Bring the fixed solution of the integer ambiguity of the wide lane into the B3 observation equation or the combination observation equation without ionosphere, and the ambiguity parameter of the equation is only the integer ambiguity ∇Δ 1 of B1.By using the least squares method, the integer ambiguity floating-point solution of B1 and the corresponding covariance matrix can be obtained.
Step 5, use the LAMBDA search algorithm to search for the integer solution ∇Δ ̂1 .After confirming the ambiguity, complete the fixation of the B1 integer ambiguity [11].

4.
Simulation and calculation

Simulation data generation method
In order to verify the performance of the method introduced in the article in terms of fixed accuracy of full cycle ambiguity and positioning accuracy, a Beidou signal simulator was used to simulate the flight trajectory of drone formation for simulation verification.

Verification of relative positioning accuracy 1) Position results
Using the fixed integer ambiguity and high-precision relative positioning solution method introduced in the article, calculate and statistically analyze the relative position of the simulated drone.The input test data conditions are shown in Table 1, the relative positioning curve is shown in Figure 1, and the relative positioning results and error statistics are shown in Table 2 1.96cm Through data analysis, it can be seen that for this test data, the overall ambiguity is fixed correctly, and the statistical result of relative positioning measurement error is 1.96cm.

2) Baseline measurement convergence time
The convergence time of ambiguity is an important parameter for relative positioning, so the method introduced in the article is used to statistically analyze the convergence time of whole week ambiguity.Perform single epoch calculation on the original data and obtain relative positioning results.If the ambiguity fixation is not completed within 20 seconds, it is considered a fixation failure.If the fixation is successful, it is fixed again until the observation data is insufficient.From the statistical results in Table 3, it can be seen that the fixed success rate of ambiguity in this test is 100%.

Conclusion
During high-speed flight of drones, changes in speed and attitude can easily cause frequent satellite loss of lock and re capture, making it difficult to search for carrier phase integer ambiguity.This article focuses on the high-precision and high reliability of BeiDou relative positioning, optimizing data quality control and fixed reliability of integer ambiguity.It is validated using BeiDou simulation dual frequency observation.Simulation data testing results show that the adopted technical measures have the ability to detect data anomalies, ensuring the continuity and reliability of fixed ambiguity in BeiDou relative positioning, and meeting the requirements of drone formation flight.

Table 2 .
Positioning accuracy statistics

Table 3 .
Initialization time and success rate statistics