A method for integrity monitoring of high, medium and low orbit combined precision single-point positioning

Abstract

This invention provides a method for integrity monitoring using a combined high, medium, and low orbit precise single-point positioning system. The method includes: S10, determining the initial variance of ionospheric delay for each satellite based on the ionospheric puncture point of each satellite signal; S20, constructing the initial variance matrix of ionospheric delay; S30, obtaining the ionospheric delay variance matrix; S40, obtaining the weighted sum of squares of the post-hoc residuals; S50, determining whether the weighted sum of squares of the post-hoc residuals is less than a convergence threshold; if so, proceeding to S60; otherwise, increasing the weight factor by a preset step size and proceeding to S30; S60, using the current weight factor as the optimal weight factor; S70, obtaining the optimized weight ratio coefficient for each satellite; S80, constructing the optimized weight ratio coefficient matrix; S90, obtaining the state vector estimate and obtaining the observation vector prediction; S100, constructing a test statistic based on the innovation; S110, determining whether the test statistic is less than the test threshold; if so, determining that there is no integrity fault; otherwise, determining that an integrity fault exists.

Description

Technical Field

[0001] This invention relates to the fields of radio navigation, signal and information processing technology, and in particular to a method for integrity monitoring of high, medium and low orbit combined precision single-point positioning. Background Technology

[0002] The Global Navigation Satellite System (GNSS) provides precise spatiotemporal information, creating immense economic and social benefits for human life. However, the basic navigation and positioning services offered by GNSS systems typically have an accuracy of only 5-10 meters, failing to meet the urgent needs of industries and general users for high-precision navigation and positioning. Precise Point Positioning (PPP) technology employs a non-differential observation model, achieving high-precision absolute positioning globally by comprehensively considering various error sources. Therefore, it possesses significant advantages such as stand-alone operation, lower cost, and global coverage, providing a new technical support and solution for high-precision positioning for a wide range of GNSS users.

[0003] Current GNSS precise point positioning applications suffer from long convergence times due to the high altitude of satellite orbits, slow changes in constellation geometry, and strong correlations between observation equations between adjacent epochs. These times typically take tens of minutes to converge to centimeter-level positioning accuracy. However, with the development of low-Earth orbit (LEO) internet constellations and the planning of the next-generation BeiDou navigation system, LEO satellites operate at faster speeds and have longer trajectories within the same timeframe. One minute of LEO satellite operation is roughly equivalent to 20 minutes of geometric configuration changes for current medium-Earth orbit (MEO) satellites. The correlation between observation equations between adjacent epochs is significantly reduced, allowing for faster estimation and separation of various errors during positioning parameter estimation, thus substantially improving the convergence time of PPP positioning.

[0004] However, due to the relatively low manufacturing cost of low-Earth orbit (LEO) internet satellites, orbital altitudes below 1000km are subject to more complex perturbations and ionospheric delays. This results in LEO satellites having larger orbital errors and satellite clock errors compared to navigation satellites. Therefore, the effectiveness of integrity monitoring needs to be given special attention when performing joint positioning calculations using navigation satellites and LEO satellites. However, there is currently no effective integrity monitoring method. Summary of the Invention

[0005] This invention provides a method for integrity monitoring using a combined high, medium, and low orbit precision single-point positioning system, which can solve the above-mentioned technical problems.

[0006] This invention provides a method for integrity monitoring using a combined high, medium, and low orbit precision single-point positioning system, the method comprising:

[0007] S10. Determine the ionospheric penetration point of each satellite signal based on the position information of the receiver and each satellite; determine the initial variance of the ionospheric delay of each satellite based on the ionospheric penetration point of each satellite signal.

[0008] S20. Construct the initial variance matrix of ionospheric delay based on the initial variance of ionospheric delay for each satellite;

[0009] S30. Obtain the ionospheric delay variance matrix based on the initial variance matrix of the ionospheric delay and the weighting factors;

[0010] S40. Establish the basic observation equations for undifferentiated carrier phase and pseudorange. Use the ionospheric delay variance matrix as the first weight matrix to perform weighted least squares calculations on the basic observation equations for undifferentiated carrier phase and pseudorange to obtain the weighted sum of squares of the post-hoc residuals.

[0011] S50. Determine whether the weighted sum of squares of the post-test residuals is less than the convergence threshold. If yes, proceed to S60. Otherwise, increase the weight factor by the preset step size and proceed to S30.

[0012] S60. Use the current weight factor as the optimal weight factor;

[0013] S70. Based on the optimal weight factor and the initial variance of the ionospheric delay of each satellite, the optimal weight ratio coefficient of each satellite is obtained. Based on the optimal weight ratio coefficient of each satellite, the progressively relaxed constraints are added to obtain the optimized weight ratio coefficient of each satellite.

[0014] S80. Construct an optimized weight ratio matrix based on the optimized weight ratio coefficients of each satellite, and use the optimized weight ratio matrix as the second weight matrix;

[0015] S90. The receiver's position information and clock error are used as state vectors, and state equations are established based on the state vectors. The carrier phase and pseudorange are used as observation vectors, and observation equations are established based on the observation vectors. Kalman filter equations are established based on the state equations and observation equations. Robust adaptive Kalman filtering is performed on the Kalman filter equations based on the second weight matrix to obtain state vector estimates. Observation vector predictions are obtained based on the state vector estimates.

[0016] S100. Take the difference between the measured value of the observed vector and the predicted value of the observed vector as the information, and construct a test statistic based on the information.

[0017] S110. Determine whether the test statistic is less than the test threshold. If yes, determine that there is no integrity fault; otherwise, determine that there is an integrity fault.

[0018] Preferably, the initial variance of the ionospheric delay for each satellite is determined by the following formula:

[0019]

[0020] In the formula, Let be the initial variance of the ionospheric delay for the i-th satellite, where i = 1, 2, ..., m, and m is the total number of satellites. Let be the initial variance of the ionospheric delay. Let ele be the prior variance that varies with time and space, ele be the satellite's elevation angle, B be the geographic latitude corresponding to the ionospheric puncture point, and t be the local time at the puncture point.

[0021] Preferably, the ionospheric delay variance matrix is ​​obtained by the following formula:

[0022]

[0023] in,

[0024] In the formula, R I Let K be the ionospheric delay variance matrix, and K be the weighting factor. The initial variance matrix of the ionospheric delay. Let be the initial variances of the ionospheric delay for the 1st, 2nd, ..., mth satellites, respectively.

[0025] Preferably, the optimized weighting coefficients for each satellite are obtained using the following formula:

[0026]

[0027] In the formula, K i Let K be the optimized weight ratio coefficient for the i-th satellite, and K′ be the optimal weight factor. Let be the optimal weighting coefficient for the i-th satellite, α be the variance rate of change, and Δt be the time interval between the current observation time and the initial observation time.

[0028] Preferably, the optimized weighting coefficient matrix is ​​constructed using the following formula:

[0029]

[0030] In the formula, R K The optimized weighting coefficient matrix, K1, K2, ..., K m These are the optimized weighting coefficients for the 1st, 2nd, ..., mth satellites, respectively.

[0031] Preferably, the new information is obtained through the following formula:

[0032]

[0033] In the formula, r k For new information, Y k For the observed vector measurement value, The predicted value for the observation vector.

[0034] Preferably, the test statistic is constructed using the following formula:

[0035]

[0036] In the formula, T k To test the statistic, D k Let be the covariance matrix of the new information.

[0037] Preferably, the preset step size is set to 1.

[0038] By applying the technical solution of this invention, the ionospheric delay variance matrix is ​​adjusted using weighting factors, and post-hoc adjustment calculations are performed in conjunction with the initial ionospheric delay variance. A stepwise relaxation algorithm is then employed to reduce the impact of low-Earth orbit (LEO) satellite ionospheric delay on the converged PPP positioning accuracy. Furthermore, by using fused robust adaptive Kalman filter estimation to constrain the relevant errors introduced by LEO satellites, and by performing integrity monitoring based on innovation, the effectiveness and accuracy of integrity monitoring can be improved, thereby enhancing the practicality and usability of LEO-enhanced precise point positioning technology. This method can be used to support LEO navigation enhancement in satellite navigation terminals and integrated navigation systems, and has certain military and civilian application prospects. Attached Figure Description

[0039] The accompanying drawings, which form part of this specification, are provided to further illustrate embodiments of the invention and, together with the textual description, explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any creative effort.

[0040] Figure 1 A flowchart of a method for integrity monitoring of high, medium, and low orbit combined precision single-point positioning according to an embodiment of the present invention is shown;

[0041] Figure 2 A schematic diagram of an integrity monitoring method for high, medium, and low orbit combined precision single-point positioning according to an embodiment of the present invention is shown. Detailed Implementation

[0042] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0043] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0044] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0045] like Figure 1 and Figure 2 As shown, this invention provides a method for integrity monitoring using a combined high, medium, and low orbit precision single-point positioning system, the method comprising:

[0046] S10. Determine the ionospheric penetration point of each satellite signal based on the position information of the receiver and each satellite; determine the initial variance of the ionospheric delay of each satellite based on the ionospheric penetration point of each satellite signal.

[0047] S20. Construct the initial variance matrix of ionospheric delay based on the initial variance of ionospheric delay for each satellite;

[0048] S30. Obtain the ionospheric delay variance matrix based on the initial variance matrix of the ionospheric delay and the weighting factors;

[0049] S40. Establish the basic observation equations for undifferentiated carrier phase and pseudorange. Use the ionospheric delay variance matrix as the first weight matrix to perform weighted least squares calculation on the basic observation equations for undifferentiated carrier phase and pseudorange to obtain the weighted sum of squares of the post-hoc residuals. Among them, the basic observation equations for undifferentiated carrier phase and pseudorange are established by combining BeiDou satellite observation information and low-orbit satellite observation information.

[0050] S50. Determine whether the weighted sum of squares of the post-test residuals is less than the convergence threshold. If yes, proceed to S60. Otherwise, increase the weight factor by the preset step size and proceed to S30.

[0051] S60. Use the current weight factor as the optimal weight factor;

[0052] S70. Based on the optimal weight factor and the initial variance of the ionospheric delay of each satellite, the optimal weight ratio coefficient of each satellite is obtained. Based on the optimal weight ratio coefficient of each satellite, the progressively relaxed constraints are added to obtain the optimized weight ratio coefficient of each satellite.

[0053] S80. Construct an optimized weight ratio matrix based on the optimized weight ratio coefficients of each satellite, and use the optimized weight ratio matrix as the second weight matrix;

[0054] S90. The receiver's position information and clock error are used as state vectors, and state equations are established based on the state vectors. The carrier phase and pseudorange are used as observation vectors, and observation equations are established based on the observation vectors. Kalman filter equations are established based on the state equations and observation equations. Robust adaptive Kalman filtering is performed on the Kalman filter equations based on the second weight matrix to obtain state vector estimates. Observation vector predictions are obtained based on the state vector estimates.

[0055] Wherein, the state vector Observation vector

[0056] In the formula, δx, δy, and δz represent the positions of the receiver in the x, y, and z directions, respectively; δt represents the clock error of the receiver; θ represents the carrier phase; and ρ represents the pseudorange. The robust adaptive Kalman filtering process adopts existing filtering methods.

[0057] S100. Take the difference between the measured value of the observed vector and the predicted value of the observed vector as the information, and construct a test statistic based on the information.

[0058] S110. Determine whether the test statistic is less than the test threshold. If yes, determine that there is no integrity fault; otherwise, determine that there is an integrity fault.

[0059] This invention adjusts the ionospheric delay variance matrix using weighting factors and performs post-hoc adjustment calculations based on the initial ionospheric delay variance. A stepwise relaxation algorithm is employed to reduce the impact of LEO satellite ionospheric delay on the converged PPP positioning accuracy. By using fused robust adaptive Kalman filter estimation to constrain the correlation errors introduced by LEO satellites and performing integrity monitoring based on innovation, the effectiveness and accuracy of integrity monitoring are improved, thereby enhancing the practicality and usability of LEO-enhanced precise point positioning technology. This method can be used in satellite navigation terminals and integrated navigation systems supporting LEO navigation enhancement, and has promising military and civilian applications.

[0060] like Figure 2 As shown, low-Earth orbit (LEO) navigation enhancement can improve the accuracy and convergence time of precise point positioning through information enhancement and signal enhancement. Information enhancement refers to using LEO satellite communication to improve the communication rate and bandwidth of precise positioning service products, while signal enhancement refers to using the rapid changes in the geometry of LEO satellites to resolve the correlation between observation equations.

[0061] According to one embodiment of the present invention, the initial variance of ionospheric delay for each satellite is determined by the following formula:

[0062]

[0063] In the formula, Let be the initial variance of the ionospheric delay for the i-th satellite, where i = 1, 2, ..., m, and m is the total number of satellites. Let be the initial variance of the ionospheric delay. Let ele be the prior variance that varies with time and space, ele be the satellite's elevation angle, B be the geographic latitude corresponding to the ionospheric puncture point, and t be the local time at the puncture point.

[0064] Among them, variables and It can be set to 0.09m based on experience. 2 .

[0065] According to one embodiment of the present invention, the ionospheric delay variance matrix is ​​obtained by the following formula:

[0066]

[0067] in,

[0068] In the formula, R I Let K be the ionospheric delay variance matrix, and K be the weighting factor. The initial variance matrix of the ionospheric delay. Let be the initial variances of the ionospheric delay for the 1st, 2nd, ..., mth satellites, respectively.

[0069] In the initial search, K is set to 1.

[0070] According to one embodiment of the present invention, the optimized weighting coefficient for each satellite is obtained by the following formula:

[0071]

[0072] In the formula, K i Let K be the optimized weight ratio coefficient for the i-th satellite, and K′ be the optimal weight factor. Let be the optimal weighting coefficient for the i-th satellite, α be the variance rate of change, and Δt be the time interval between the current observation time and the initial observation time.

[0073] Where α takes the value 0.04m 2 / min; Δt is in minutes.

[0074] According to one embodiment of the present invention, the optimized weighting coefficient matrix is ​​constructed by the following formula:

[0075]

[0076] In the formula, R K The optimized weighting coefficient matrix, K1, K2, ..., K m These are the optimized weighting coefficients for the 1st, 2nd, ..., mth satellites, respectively.

[0077] According to one embodiment of the present invention, the information is obtained by the following formula:

[0078]

[0079] In the formula, r k For new information, Y k For the observed vector measurement value, The predicted value for the observation vector.

[0080] According to one embodiment of the present invention, the test statistic is constructed by the following formula:

[0081]

[0082] In the formula, T k To test the statistic, D k Let be the covariance matrix of the new information.

[0083] According to one embodiment of the present invention, the preset step size is set to 1.

[0084] In summary, this invention provides an integrity monitoring method for joint high, medium, and low Earth orbit (LEO) precise point positioning. It uses weighting factors to adjust the ionospheric delay variance matrix and performs post-hoc adjustment calculations based on the initial ionospheric delay variance. A stepwise relaxation algorithm is employed to reduce the impact of LEO satellite ionospheric delay on the converged PPP positioning accuracy. By using fused robust adaptive Kalman filter estimation to constrain the correlation errors introduced by LEO satellites and performing integrity monitoring based on innovation, the effectiveness and accuracy of integrity monitoring are improved, thereby enhancing the practicality and usability of LEO-enhanced precise point positioning technology. This method can be used in satellite navigation terminals and integrated navigation systems supporting LEO navigation enhancement, and has certain military and civilian application prospects.

[0085] For ease of description, spatial relative terms such as "above," "on top of," "on the upper surface of," "above," etc., are used herein to describe the spatial positional relationship of a device or feature as shown in the figures to other devices or features. It should be understood that spatial relative terms are intended to encompass different orientations in use or operation beyond the orientation of the device as described in the figures. For example, if the device in the figures were inverted, a device described as "above" or "on top of" other devices or structures would subsequently be positioned as "below" or "under" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below." The device may also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatial relative descriptions used herein will be interpreted accordingly.

[0086] Furthermore, it should be noted that the use of terms such as "first" and "second" to define components is merely for the purpose of distinguishing the corresponding components. Unless otherwise stated, the above terms have no special meaning and therefore should not be construed as limiting the scope of protection of this invention.

[0087] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for integrity monitoring using a combined high, medium, and low orbit precision single-point positioning system, characterized in that, The method includes: S10. Determine the ionospheric penetration point of each satellite signal based on the position information of the receiver and each satellite; determine the initial variance of the ionospheric delay of each satellite based on the ionospheric penetration point of each satellite signal. S20. Construct the initial variance matrix of ionospheric delay based on the initial variance of ionospheric delay for each satellite; S30. Obtain the ionospheric delay variance matrix based on the initial variance matrix of the ionospheric delay and the weighting factors; S40. Establish the basic observation equations for undifferentiated carrier phase and pseudorange. Use the ionospheric delay variance matrix as the first weight matrix to perform weighted least squares calculations on the basic observation equations for undifferentiated carrier phase and pseudorange to obtain the weighted sum of squares of the post-hoc residuals. S50. Determine whether the weighted sum of squares of the post-test residuals is less than the convergence threshold. If yes, proceed to S60. Otherwise, increase the weight factor by the preset step size and proceed to S30. S60. Use the current weight factor as the optimal weight factor; S70. Based on the optimal weight factor and the initial variance of the ionospheric delay of each satellite, the optimal weight ratio coefficient of each satellite is obtained. Based on the optimal weight ratio coefficient of each satellite, the progressively relaxed constraints are added to obtain the optimized weight ratio coefficient of each satellite. S80. Construct an optimized weight ratio matrix based on the optimized weight ratio coefficients of each satellite, and use the optimized weight ratio matrix as the second weight matrix; S90. The receiver's position information and clock error are used as state vectors, and state equations are established based on the state vectors. The carrier phase and pseudorange are used as observation vectors, and observation equations are established based on the observation vectors. Kalman filter equations are established based on the state equations and observation equations. Robust adaptive Kalman filtering is performed on the Kalman filter equations based on the second weight matrix to obtain state vector estimates. Observation vector predictions are obtained based on the state vector estimates. S100. Take the difference between the measured value of the observed vector and the predicted value of the observed vector as the information, and construct a test statistic based on the information. S110. Determine whether the test statistic is less than the test threshold. If yes, determine that there is no integrity fault; otherwise, determine that there is an integrity fault.

2. The method according to claim 1, characterized in that, The initial variance of the ionospheric delay for each satellite is determined by the following formula: In the formula, Let be the initial variance of the ionospheric delay for the i-th satellite, where i = 1, 2, ..., m, and m is the total number of satellites. Let be the initial variance of the ionospheric delay. Let ele be the prior variance that varies with time and space, ele be the satellite's elevation angle, B be the geographic latitude corresponding to the ionospheric puncture point, and t be the local time at the puncture point.

3. The method according to claim 1, characterized in that, The ionospheric delay variance matrix is ​​obtained using the following formula: in, In the formula, R I Let K be the ionospheric delay variance matrix, and K be the weighting factor. The initial variance matrix of the ionospheric delay. Let be the initial variances of the ionospheric delay for the 1st, 2nd, ..., mth satellites, respectively.

4. The method according to claim 1, characterized in that, The optimized weighting coefficients for each satellite are obtained using the following formula: In the formula, K i Let K be the optimized weight ratio coefficient for the i-th satellite, and K′ be the optimal weight factor. Let be the optimal weighting coefficient for the i-th satellite, α be the variance rate of change, and Δt be the time interval between the current observation time and the initial observation time.

5. The method according to claim 1, characterized in that, The optimized weighting coefficient matrix is ​​constructed using the following formula: In the formula, R K The optimized weighting coefficient matrix, K1, K2, ..., K m These are the optimized weighting coefficients for the 1st, 2nd, ..., mth satellites, respectively.

6. The method according to claim 1, characterized in that, The new information is obtained through the following formula: In the formula, r k For new information, Y k For the observed vector measurement value, The predicted value for the observation vector.

7. The method according to claim 1, characterized in that, The test statistic is constructed using the following formula: In the formula, T k To test the statistic, D k Let be the covariance matrix of the new information.

8. The method according to claim 1, characterized in that, The preset step size is set to 1.

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