Beidou No.3 receiver positioning calculation method based on improved graph optimization

Abstract

The invention discloses a Beidou No.3 receiver positioning calculation method based on improved graph optimization, and the method employs the observation information received by a receiver, and selects the observation information with high contribution degree to the state estimation of the receiver in real time based on an observation information covariance / space geometric configuration optimization strategy, so as to carry out the optimal estimation of the state of the receiver. The method comprises the following steps: constructing system state nodes and observation nodes by using observation information such as high-contribution pseudo-range and Doppler selected by a receiver, and constructing a receiver position calculation global optimization graph model; a sliding window is utilized, observation information received by a receiver at a historical moment is reserved, a global optimization cost function is constructed by utilizing observation information from the historical moment to a current moment, and iterative optimization estimation is performed on a system state quantity by utilizing a least square method to obtain high-precision navigation data of the receiver. Compared with the prior art, the method has the advantages that the positioning precision is effectively improved, redundant stars are reduced, the calculation amount is reduced, and the positioning real-time performance and accuracy are improved.

Description

Technical Field

[0001] The invention belongs to the field of satellite navigation and positioning, and relates to a BeiDou-3 receiver positioning solution method based on improved graph optimization. Background Art

[0002] The BeiDou-3 satellite global navigation system provides global users with all-weather, all-day, high-precision positioning, navigation and timing services. It retains the original B1I and B3I signal frequencies of the BeiDou-2 system and adds B2a and B1C satellite signals. The BeiDou-3 satellite adds B1C and B2a frequencies, adopts new modulation methods and channel coding, and has further improved navigation performance compared to the original B1I and B3I frequencies. On this basis, it can achieve compatibility and interoperability with other GNSS systems, and provide a better user experience.

[0003] At present, the BeiDou-3 receiver mainly uses the least squares method and Kalman filter method for navigation and positioning solution. The least squares method uses the position information of multiple satellites solved by the navigation message and the corresponding observation information such as pseudorange and Doppler, and realizes the receiver navigation and positioning solution by constructing the receiver position and velocity solution objective function based on the least squares method. This receiver positioning solution method has the advantages of low system calculation complexity, high calculation efficiency, good real-time performance, and easy implementation, and has been widely used in actual engineering.

[0004] However, the receiver positioning solution method based on the least squares method has high requirements for the accuracy of the system initial value and model, which affects the position and velocity solution performance of the receiver. The Kalman filter method is another commonly used fusion estimation algorithm for receiver navigation positioning solution. It constructs the state recursion equation and observation equation of the system respectively through the receiver's own prediction information and the received pseudorange, Doppler and other observation information. The Kalman filter algorithm is used to perform optimal fusion estimation and online compensation on the receiver navigation state quantity to improve the receiver position solution accuracy. The Kalman filter estimation algorithm has the characteristics of good system real-time performance, simple model, and easy implementation, and has been widely used in actual engineering practice. However, this type of receiver position estimation algorithm first needs to perform modeling analysis in advance according to the number of observation information received by the receiver, and the system topology reconstruction performance is insufficient; secondly, the Kalman filter estimation algorithm generally uses the pseudorange, carrier, and Doppler observation information received by the receiver at the current moment to construct the system observation equation, and cannot use the observation information at the historical moment to further optimize the receiver navigation state estimation. The estimation accuracy of the system state quantity needs to be further improved. In order to improve the navigation and positioning performance of the receiver, the present invention discloses a BeiDou-3 receiver positioning solution method based on improved graph optimization. Summary of the invention

[0005] The object of the present invention is to provide a BeiDou-3 receiver positioning solution method based on improved graph optimization, so as to improve the navigation and positioning performance of the receiver.

[0006] The technical solution to achieve the purpose of the present invention is as follows: In order to improve the navigation and positioning performance of the receiver, the present invention discloses a BeiDou-3 receiver positioning solution method based on improved graph optimization. Utilizing the observation information received by the receiver, based on the observation information covariance / spatial geometric configuration optimization strategy, the observation information with high contribution to the receiver state estimation is selected in real time to optimally estimate the receiver state. On this basis, according to the factor graph optimization estimation theory, the high-contribution pseudorange, Doppler and other observation information selected by the receiver are used to construct system state nodes and observation nodes, and a global optimization graph model for receiver position solution is constructed. In order to further improve the accuracy of receiver position solution, the present invention adopts the concept of sliding windows. By retaining the observation information received by the receiver at historical moments, the global optimization cost function is constructed using the observation information from historical moments to the current moment, and the system state quantity is iteratively optimized and estimated using the least squares method to obtain high-precision navigation data for the receiver. The present invention includes the following steps:

[0007] Step 1: Establish the receiver positioning solution factor graph to optimize the model state nodes, including the receiver's position, speed, and clock error.

[0008] Step 2: Set the BDS-3 receiver positioning solution factor graph to optimize the model prior information, including the receiver’s position, speed, clock error and other prior information at the initial moment.

[0009] Step 3: According to the navigation performance of satellite pseudorange and Doppler observation information and the optimization strategy of spatial geometric configuration, select the satellite position, pseudorange and other observation information that have a high contribution to the receiver state optimization estimation accuracy, and determine the satellite subset involved in the positioning solution.

[0010] Step 4: According to the selected satellite subset observation information with high contribution to the system state, establish the receiver positioning solution pseudorange observation factor node and Doppler velocity observation factor node. Based on the selected system state quantity and high contribution pseudorange observation and Doppler velocity observation factor nodes, establish the receiver positioning solution factor graph optimization model.

[0011] Step 5: Based on the constructed receiver positioning solution factor graph optimization model, the high-contribution pseudorange and Doppler observation information from the historical moment to the current moment is used to construct the global optimization cost function for receiver position and velocity solution.

[0012] Step 6: Use nonlinear least squares iteration to perform global iterative optimization on the receiver system state increment to obtain the optimal navigation solution for the receiver position and velocity, and obtain the receiver navigation positioning information.

[0013] Compared with the prior art, the present invention has the following significant advantages:

[0014] 1) The factor graph in the present invention is based on a sliding window during the optimization process, which effectively considers all historical information and current information. All this information can be connected through the Doppler factor, which makes full use of the time correlation of the measurement data and effectively improves the positioning accuracy. It can also be used to resist outliers and greatly improve the robustness of the system.

[0015] 2) The present invention selects observation information with high contribution to receiver state estimation in real time based on the observation information covariance / spatial geometric configuration optimization strategy to perform optimal estimation of the receiver state, selects satellites with high contribution to receiver state estimation, reduces redundant satellites, reduces the amount of calculation, and improves the real-time and accuracy of positioning. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 A flowchart of a BeiDou-3 receiver positioning solution method based on improved graph optimization;

[0017] Figure 2 Receiver positioning solution factor graph optimization model diagram, where x r,t are the state variables of the receiver r at time t, x r, 0 is the initial state of the system; is the Doppler velocity observation factor node at time t; is the observed pseudorange factor node of satellite s and receiver r at time t. DETAILED DESCRIPTION

[0018] The terms used in the present invention are only for the purpose of illustrating the embodiments of the present invention and are not intended to limit the present invention. Figure 1-2 , some embodiments of the present invention are described in detail.

[0019] BeiDou-3 receiver positioning solution method based on improved graph optimization, the flow chart is as follows Figure 1 As shown. The following steps are included:

[0020] Step 1: Establish the state node of the BeiDou-3 receiver positioning solution factor graph optimization model. The system state node of the receiver positioning solution can be constructed as follows:

[0021] X=[x r,0 ,x r,1 ,…,x r,n ] (1)

[0022] Among them, X represents the system state quantity in the factor graph optimization model, r represents the BeiDou-3 receiver, and x r,0 ,x r,1 ,…,xr,n represents the state of the receiver r at time 0, 1, ···, n. The state of the receiver r at time t is x r,t It can be expressed as follows:

[0023] x r,t =(p r,t ,v r,t ,δ r,t ) T (2)

[0024] Among them, p r,t represents the three-dimensional position of the receiver r at time t, v r,t represents the three-dimensional velocity of the receiver r at time t, δ r,t Represents the equivalent pseudorange measurement error of the receiver r time deviation at time t. (·) T Represents the transpose of a state quantity.

[0025] Step 2: Set the prior information of the graph optimization model of the BeiDou-3 receiver positioning solution factor. The prior information of the graph optimization model can be expressed as:

[0026] x r,0 =(p r,0 ,v r,0 ,δ r,0 ) T (3)

[0027] Among them, x r,0 Represents the state information of the receiver r at time 0 (initial time), that is, the initial state. r,0 represents the three-dimensional position of the receiver r at time 0, v r,0 represents the three-dimensional velocity of the receiver r at time 0, δ r,0 Represents the equivalent pseudorange measurement error of the receiver r time deviation at time 0. (·) T Represents the transpose of a state quantity.

[0028] Step 3: Through the observation information covariance / spatial geometry optimization strategy, the observation information with high contribution to the receiver state estimation is selected in real time to perform global optimization estimation of the receiver state, and a subset of satellites with excellent geometry, small pseudorange and Doppler standard deviations are selected from the visible stars to participate in the construction of the factor graph optimization model observation information. The star selection strategy equation σ can be expressed as:

[0029] σ=ωσ GDOP +(1-ω)σ UERE (4)

[0030] Among them, σ UERE represents the standard deviation of pseudorange and Doppler errors, σ GDOPis the geometric precision factor. ω is the weighting coefficient. Pseudorange, Doppler error mean square error and GDOP value are weighted and added together. From different satellite subsets, select the satellite subset with excellent geometric configuration and high error accuracy, that is, find the minimum value of σ, and participate in the factor graph optimization operation.

[0031] σ UERE is the standard deviation of pseudorange and Doppler errors, which are mainly caused by the errors encountered during the transmission between the satellite and the receiver, including satellite orbit error, clock error, ionospheric error, tropospheric error, multipath error, etc. It can be expressed as:

[0032] σ UERE =σ ρ +σ DV (5)

[0033] Among them, σ ρ is the standard deviation of pseudorange error, σ DV is the standard deviation of the Doppler error. For pseudorange observations, it is specifically reflected in the deviation of the pseudorange from the true distance. The standard deviation of the pseudorange error σ ρ It is expressed as follows:

[0034]

[0035] in, is the pseudo-range measurement value of satellite s received by receiver r at time t, is the geometric distance from satellite s to receiver r at time t, and m represents the number of satellites in the selected satellite subset.

[0036] σ GDOP It is the geometric factor of precision, which characterizes the geometric distribution of the unit vector pointed by the user receiver to the visible satellite relative to the user receiver. It can reflect the impact of the spatial relationship between the satellite and the receiver on the positioning accuracy. The better the spatial geometric configuration, the smaller the GDOP.

[0037] The GDOP value is generally solved by the trace of the pseudorange measurement matrix. It is expressed as follows:

[0038]

[0039] Where H is the Jacobian matrix of pseudorange observations, and trace(·) represents the trace operation of the matrix in brackets.

[0040] ω is the weighting coefficient of pseudorange, Doppler error standard deviation and geometric precision factor. The value of ω will change in different physical environments. When the receiver is in a good field of view and open space, ω is 0.5. When the field of view is limited and the ionosphere and troposphere have a greater impact, ω is 0.25.

[0041] Step 4: According to the selected satellite subset with high contribution to the system state, establish the receiver positioning solution pseudorange observation factor node and Doppler velocity observation factor node, and establish the receiver positioning solution factor graph optimization model, such as Figure 2 shown.

[0042] Step 4.1: Establish receiver positioning solution pseudorange observation factor node.

[0043] During the BeiDou-3 receiver positioning solution process, the receiver r receives the pseudo-range measurement value of satellite s at time t. It can be expressed as:

[0044]

[0045] in, represents the geometric distance from satellite s to receiver r, c represents the speed of light, δ r,t represents the receiver clock deviation, represents the equivalent pseudorange measurement error of the satellite clock bias, represents the ionospheric delay error, is the tropospheric delay error, Represents the receiver measurement noise error.

[0046] Step 4.2: Establish the receiver positioning solution pseudorange factor observation model.

[0047] The observation model of the receiver pseudorange factor can be expressed as follows:

[0048]

[0049] in, represents the noise associated with the pseudorange measurement, the pseudorange observation function It is expressed as:

[0050]

[0051] represents the three-dimensional position of satellite s at time t, p r,t represents the three-dimensional position of the receiver r at time t, δ r,t represents the clock deviation of receiver r at time t. ||·|| represents the modulo operation, that is, calculating the distance between receiver r and satellite s.

[0052] In this way, the measurement error function of the pseudorange factor can be obtained:

[0053]

[0054] in, is the observed pseudorange factor node of satellite s and receiver r at time t, represents the covariance matrix. ||·|| 2 Represents the modular square operation.

[0055] Step 4.3: Establish the receiver positioning solution Doppler velocity observation factor node.

[0056] Calculate the speed of the BeiDou-3 receiver using the least squares method based on the Doppler value and set the speed The status is represented as follows:

[0057]

[0058] where v r,t represents the speed of the receiver r at time t, represents the clock bias of receiver r at time t. Given the Doppler measurement of satellite s and receiver r at time t, The measured rate of change vector at time t Set to:

[0059]

[0060] Where λ represents the carrier wavelength of the satellite signal. are the Doppler measurements of satellites 1, 2, ..., s, ..., m and receiver r at time t. The observation function used to connect Doppler measurements and states can be expressed as:

[0061]

[0062] The superscript m is the total number of satellites, and the variable Representation and Correlated noise. Variables in the matrix represents the expected rate of change, variable and They are respectively expressed as the clock bias drift of receiver r and satellite m at time t. The distance between the satellite s and the receiver r can also be used Then the variable It can also be expressed as follows:

[0063]

[0064] Among them, ω earth represents the angular velocity of the Earth's rotation, and c represents the speed of light. Represents the direct vector between the receiver and the satellite. represents the three-dimensional velocity of satellite s at time t, v r,t represents the three-dimensional velocity of the receiver r at time t. represents the y-axis velocity of satellite s at time t, represents the x-axis velocity of satellite s at time t, v r,t,x represents the x-axis velocity of the receiver r at time t, v r,t,y represents the y-axis velocity of the receiver r at time t, p r,t,x represents the x-axis position of the receiver r at time t, p r,t,y represents the y-axis position of the receiver r at time t, represents the x-axis position of satellite s at time t, represents the y-axis position of satellite s at time t.

[0065] Step 4.4: Establish the receiver positioning solution Doppler velocity factor observation model.

[0066] The observation model of the receiver Doppler velocity factor can be expressed as follows:

[0067]

[0068] in, Represents the velocity measurement calculated from the Doppler measurement. represents the noise associated with the velocity measurement. Velocity observation function It is expressed as:

[0069]

[0070] Δt represents the time interval of observation, p r,t,x represents the x-axis position of the receiver r at time t, p r,t,y represents the y-axis position of the receiver r at time t, p r,t,z represents the z-axis position of the receiver r at time t. In this way, the measurement error function of the receiver velocity can be obtained:

[0071]

[0072] in, is the Doppler velocity observation factor node at time t, represents the covariance matrix. ||·|| 2 Represents the modular square operation.

[0073] Step 5: Using the concept of sliding window, the global optimization cost function is constructed using the observation information from historical moments to the current moment, which is expressed as follows:

[0074]

[0075] X *is the maximum a posteriori probability estimate of the receiver state; L is the length of the global optimization sliding window of the receiver state. In practical applications, the receiver hardware performance and the receiver state optimization estimation performance are comprehensively considered. In the present invention, the calculation amount of the navigation receiver positioning solution system and the receiver state optimization estimation accuracy are comprehensively considered, and the length of the global optimization sliding window of the receiver state is set to 10.

[0076] Step 6: Use nonlinear least squares iteration to perform global iterative optimization on the system state increment to obtain the solution that minimizes the error function and obtain the optimal navigation solution for the receiver position and velocity. The nonlinear least squares calculation formula is:

[0077] ΔX=(A T A) -1 A T Δb (20)

[0078] Where ΔX is the state increment, A is the observation matrix, T represents the transpose of the matrix, (·) -1 represents matrix inversion, and Δb is the observed residual.

[0079] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and intent of the present invention.

Claims

1. A BeiDou-3 receiver positioning solution method based on improved graph optimization, characterized in that: The specific steps are: Step 1: Establish the receiver positioning solution factor graph optimization model state node; Step 2: Set the prior information of the BeiDou-3 receiver positioning solution factor graph optimization model; Step 3: According to the navigation performance of satellite pseudorange and Doppler observation information and the optimization strategy of spatial geometric configuration, the satellite position, pseudorange and other observation information with high contribution to the receiver state optimization estimation accuracy are selected in real time to determine the satellite subset participating in the positioning solution; Step 4: According to the selected satellite subset observation information with high contribution to the system state, establish the receiver positioning solution pseudorange observation factor node and Doppler velocity observation factor node; based on the selected system state quantity and high contribution pseudorange observation and Doppler velocity observation factor nodes, establish the receiver positioning solution factor graph optimization model; Step 5: Based on the constructed receiver positioning solution factor graph optimization model, the receiver position and velocity solution global optimization cost function is constructed using the high-contribution pseudorange and Doppler observation information from the historical moment to the current moment; Step 6: Use nonlinear least squares iteration to perform global iterative optimization on the receiver system state increment to obtain the optimal navigation solution for the receiver position and velocity, and obtain the receiver navigation positioning information.

2. The BeiDou-3 receiver positioning solution method based on improved graph optimization according to claim 1, characterized in that: In step 1, the system state node of the receiver positioning solution is constructed as: X=[x r,0 ,x r,1 ,…,x r,n ] In the formula, X represents the system state quantity in the factor graph optimization model, r represents the BeiDou-3 receiving, and x r,0 ,x r,1 ,…,x r,n represents the state quantity of the receiver r at time 0, 1, ···, n respectively; The state quantity of the receiver r at time t is expressed as follows: x r,t =(p r,t ,v r,t ,d r,t ) T In the formula, p r,t represents the three-dimensional position of the receiver r at time t, v r,t represents the three-dimensional velocity of the receiver r at time t, δ r,t represents the equivalent pseudorange measurement error of the time deviation of the receiver r at time t; (·) T Represents the transpose of a state quantity.

3. The BeiDou-3 receiver positioning solution method based on improved graph optimization according to claim 1, characterized in that: The prior information of the graph optimization model in step 2 is expressed as: x r,0 =(p r,0 ,v r,0 ,d r,0 ) T In the formula, x r,0 represents the state information of the receiver r at time 0, i.e. the initial state; p r,0 represents the three-dimensional position of the receiver r at time 0, v r,0 represents the three-dimensional velocity of the receiver r at time 0, δ r,0 represents the equivalent pseudorange measurement error of the receiver r time deviation at time 0; (·) T Represents the transpose of a state quantity.

4. The BeiDou-3 receiver positioning solution method based on improved graph optimization according to claim 1, characterized in that: The satellite selection strategy equation σ is: s = ως GDOP +(1-ω)σ UERE In the formula, σ UERE represents the standard deviation of pseudorange and Doppler errors, σ GDOP is the geometric dilution of precision; ω is the weighting coefficient; The pseudorange, Doppler error mean square error and GDOP value are weighted and added together to screen from different satellite subsets, and the satellite subset with excellent geometric configuration and high error accuracy is selected, that is, the minimum value of σ is found to participate in the factor graph optimization operation.

5. The BeiDou-3 receiver positioning solution method based on improved graph optimization according to claim 1, characterized in that: In step 4, during the BeiDou-3 receiver positioning solution process, the receiver r at time t receives the pseudorange measurement value of satellite s for: In the formula, represents the geometric distance from satellite s to receiver r, c represents the speed of light, δ r,t represents the receiver clock deviation, represents the equivalent pseudorange measurement error of the satellite clock bias, represents the ionospheric delay error, is the tropospheric delay error, Represents the receiver measurement noise error.

6. The BeiDou-3 receiver positioning solution method based on improved graph optimization according to claim 5 is characterized in that: In step 4, establish the receiver positioning and pseudorange factor observation model: The observation model of the receiver pseudorange factor is shown as follows: In the formula, represents the noise associated with the pseudorange measurements, is the pseudorange observation function, represents the three-dimensional position of satellite s at time t, p r,t represents the three-dimensional position of the receiver r at time t, δ r,t represents the clock deviation of receiver r at time t; Measurement error function of pseudorange factor: In the formula, is the observed pseudorange factor node of satellite s and receiver r at time t, represents the covariance matrix, ||·|| 2 Represents the modular square operation.

7. The BeiDou-3 receiver positioning solution method based on improved graph optimization according to claim 6 is characterized in that: The measured rate of change vector at time t for: In the formula, is the measured change rate at time t, For speed, is the observation function connecting the Doppler measurement and the state, the variable For Correlated noise.

8. The BeiDou-3 receiver positioning solution method based on improved graph optimization according to claim 6, characterized in that: The observation model of the receiver Doppler velocity factor is expressed as follows: In the formula, represents the velocity measurement calculated from the Doppler measurement; represents the noise associated with the velocity measurement; Speed ​​Observation Function It is expressed as: In the formula, Δt represents the time interval of observation, p r,t,x represents the x-axis position of the receiver r at time t, p r,t,y represents the y-axis position of the receiver r at time t, p r,t,z represents the z-axis position of the receiver r at time t; the measurement error function of the receiver velocity is obtained: in represents the covariance matrix, ||·|| 2 Represents the modular square operation.

9. The BeiDou-3 receiver positioning solution method based on improved graph optimization according to claim 8, characterized in that: In step 5, a sliding window is used to construct a global optimization cost function using observation information from historical moments to the current moment, which is expressed as follows: Where: X * is the maximum a posteriori probability estimate of the receiver state; L is the length of the global optimization sliding window of the receiver state, is the Doppler velocity observation factor node at time t; is the observed pseudorange factor node of satellite s and receiver r at time t, and X represents the system state quantity in the factor graph optimization model.

10. The BeiDou-3 receiver positioning solution method based on improved graph optimization according to claim 1, characterized in that: The nonlinear least squares calculation formula in step 6 is: ΔX=(A T A) -1 A T Δb, Where ΔX is the state increment, A is the observation matrix, T represents the transpose of the matrix, (·) -1 represents matrix inversion, and Δb is the observed residual.

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