GNSS precision positioning precision prediction method based on PDOP error model
By constructing a polynomial fitting method based on the PDOP error model, the limitations of qualitative assessment of PDOP in GNSS positioning are solved, and real-time quantitative accuracy prediction at the user end is realized, which is applicable to scenarios such as autonomous driving and low-altitude drones.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- THE 54TH RESEARCH INSTITUTE OF CHINA ELECTRONICS TECHNOLOGY GROUP CORPORATION
- Filing Date
- 2026-03-26
- Publication Date
- 2026-05-05
AI Technical Summary
In traditional GNSS positioning, PDOP can only qualitatively assess geometric accuracy and cannot quantitatively predict actual errors. The resources of ground-based augmentation system monitoring stations have not been fully explored, resulting in a waste of data value. Users cannot obtain quantifiable positioning accuracy expectations in real time.
An error propagation model is constructed based on the PDOP values and true coordinate values from multiple monitoring stations during the positioning process. Lightweight coefficients are generated through polynomial fitting, and users only need the local PDOP values to calculate the expected positioning accuracy.
It enables direct prediction from geometric accuracy attenuation factor to specific error magnitude, tapping into the value of monitoring station data, and is suitable for low-power real-time accuracy prediction of mobile terminals such as drones.
Smart Images
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Abstract
Description
Technical Field
[0001] This invention relates to the field of satellite navigation and positioning technology, and in particular to a method for predicting the accuracy of GNSS precise positioning based on the PDOP error model. Background Technology
[0002] The positioning accuracy of Global Navigation Satellite Systems (GNSS) is significantly affected by the spatial geometric distribution of satellites, and the Position Precision Factor (PDOP) is a core indicator for evaluating the reliability of GNSS positioning, directly reflecting the amplification effect of satellite spatial geometry on positioning errors. In scenarios such as autonomous driving and precision agriculture, when the PDOP value exceeds a threshold, the system needs to issue timely warnings to avoid decision-making errors, highlighting its crucial role in high-reliability applications. However, in traditional positioning services, users can only roughly judge reliability through the PDOP threshold, which has the following technical shortcomings: the nonlinear relationship between PDOP and the true error is not modeled, resulting in PDOP only reflecting geometric accuracy decay and unable to predict the specific error magnitude; the spatiotemporal correlation characteristics between the coordinate true value deviation of monitoring stations and PDOP in ground-based augmentation systems (such as CORS networks) are not deeply explored, resulting in a waste of data value; although mainstream GNSS receivers can output PDOP in real time, users cannot convert it into quantifiable accuracy expectations.
[0003] With the completion of the BeiDou-3 global network and the development of emerging technologies, the demand for real-time positioning accuracy from intelligent user terminals such as autonomous driving and low-altitude drones is becoming increasingly urgent. How to utilize ground reference stations or monitoring stations to provide users with reliable positioning accuracy information is a pressing issue that needs to be addressed, and it is also the bottleneck hindering the development of GNSS high-precision positioning services to deeper and broader areas. Summary of the Invention
[0004] To address the issue that PDOP in GNSS positioning can only qualitatively assess geometric accuracy but cannot quantitatively predict actual errors, this invention proposes a GNSS precise positioning accuracy prediction method based on a PDOP error model. This method constructs an error propagation model based on PDOP values from multiple monitoring stations during the positioning process, positioning results, and the known true coordinates of the monitoring stations. It then uses a coordinate deviation dataset to invert the mapping relationship between PDOP and positioning deviation, and employs polynomial fitting to generate lightweight coefficients. Users only need local PDOP values to calculate the expected positioning accuracy.
[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:
[0006] A method for predicting the accuracy of GNSS precise positioning based on the PDOP error model includes the following steps:
[0007] Step 1: Select multiple ground monitoring stations on the service side, and use different satellite combinations to perform precise positioning calculations for the observation data of each monitoring station in a single epoch.
[0008] Step 2: Record the PDOP value and coordinate result deviation of each monitoring station for each selected satellite combination positioning under a single epoch;
[0009] Step 3: Fit all PDOP values and their corresponding coordinate deviations for a single epoch into a polynomial function, and use the coefficients of the polynomial function as the accuracy prediction parameters sent to the user.
[0010] Step 4: When the user performs precise positioning, the PDOP value is calculated, and then the positioning reference value is calculated based on the accuracy prediction parameters. The accuracy level of the positioning result is evaluated based on the reference value.
[0011] Furthermore, the specific method of step 1 is as follows:
[0012] Step 101: Select multiple GNSS ground monitoring stations, utilize the ionospheric de-isomerization PPP method, and combine precise satellite orbit and satellite clock bias information to implement real-time positioning, and construct the single-epoch dual-frequency original observation equation:
[0013]
[0014] Among them, superscript Indicates satellite number, subscript Indicates the receiver number, subscript Indicates the frequency band number. These are pseudorange observations. For carrier phase observations, For receiver To satellite geometric distance, For known satellites coordinates For unknown receivers coordinates For tropospheric dry delay, This is the tropospheric wet delay projection function. For tropospheric zenith wet delay, For receiver The clock difference, For satellite The clock difference, For satellite Ionospheric delay at the first frequency, This is the ratio between the ionospheric delay at other frequencies and the ionospheric delay at the first frequency. For the corresponding frequency The wavelength, λ1 is the wavelength of the first frequency. For receiver With satellite Frequency between The corresponding ambiguity; except and Except for the dimensionless parameter, all other parameters are in meters.
[0015] Step 102, construct the combined observation equations for ionosphere elimination:
[0016]
[0017] Among them, subscript This represents the ionosphere decomposition operator, where... , , f1 is the frequency of the first frequency band, f2 is the frequency of the second frequency band, and the subscripts 1 and 2 represent the first frequency band and the second frequency band, respectively;
[0018] Step 103, for the receiver Number of satellites observed at a certain epoch The number of satellites listed are 4, 5, ... All satellite combinations at that time, the total number of satellite combinations is Group;
[0019] Step 104, for the receiver The observation data of a single epoch from the i-th satellite group are used to substitute the satellite orbits, satellite clock products, and projection functions of the tropospheric dry delay and tropospheric wet delay into the ionospheric combined observation equation. Solving the equation yields the parameters. , , , And extract the PDOP value from the normal equation. i=1,2,..., .
[0020] Furthermore, the specific method for step 2 is as follows:
[0021] Step 201, based on all the receiver coordinates solved in step 104 and coordinate true value Calculate the deviation of the coordinate results i=1,2,..., ;
[0022] Step 202, adjust the coordinate result deviation According to the transformation method from the rectangular coordinate system to the station center coordinate system, the coordinate deviations in the east, north, and elevation directions after transformation to the station center coordinate system are... .
[0023] Furthermore, step 3 is performed as follows:
[0024] Step 301, based on the absolute value of the coordinate deviation of a single epoch. and Polynomial functions were fitted to the east, north, and elevation direction deviations and the PDOP values, respectively:
[0025]
[0026]
[0027]
[0028] in, , , Let be the coefficients of three polynomial functions, j = 0, 1, 2, ..., m. The highest power of the fitted polynomial;
[0029] Step 302, calculate the latest epoch solution from step 301. , , , This information is sent to the user as an accuracy prediction parameter.
[0030] Furthermore, step 4 is specifically implemented as follows:
[0031] Step 401: The user uses the same positioning technology as the server to perform positioning, and obtains the positioning result by solving the algorithm equation according to the corresponding positioning process calculation method. and PDOP value , The three components represent latitude, longitude, and elevation in the geodetic coordinate system, with subscripts... User identification;
[0032] Step 402, predict the accuracy based on the received parameters. , , , , combined Substitute these values into the polynomial to obtain the reference value for positioning. , and :
[0033]
[0034]
[0035]
[0036] Step 403, based on reference values , and Assess the accuracy level of the positioning results.
[0037] Due to the adoption of the above technical solution, the beneficial effects of this invention compared with the prior art are as follows:
[0038] 1. This invention establishes a nonlinear mapping relationship between the PDOP value and the actual positioning error through polynomial modeling, realizing direct prediction from the geometric precision attenuation factor (PDOP) to the specific error level, and solving the limitation of the traditional PDOP threshold method which can only provide qualitative early warning.
[0039] 2. This invention explores the spatiotemporal correlation characteristics between the true coordinates of monitoring stations and PDOP in ground-based augmentation systems (such as CORS networks). By using a multi-station, multi-satellite combined data inversion error propagation model, it deeply mines the monitoring station data and transforms it into accurate prediction parameters, thereby maximizing the value of infrastructure data.
[0040] 3. The user terminal of the present invention uses the polynomial coefficients calculated by the server as the calculation parameters. It only needs the local PDOP value to output the expected quantization accuracy in real time. It does not need to continuously rely on cloud services or increase hardware computing power, which is suitable for the low power consumption requirements of mobile terminals such as drones. Detailed Implementation
[0041] The invention will now be further described.
[0042] A method for predicting GNSS precision positioning accuracy based on the PDOP error model is proposed. On the service side, this method utilizes observation data from GNSS ground monitoring stations and external augmentation information to calculate the PDOP values and positioning results from multiple monitoring stations. Through polynomial modeling, a nonlinear mapping relationship between the PDOP values and the actual positioning error is established, enabling direct prediction from the geometric accuracy attenuation factor to the specific error magnitude. This innovatively mines the spatiotemporal correlation characteristics between the true coordinates of the monitoring stations and the PDOP, and uses multi-station, multi-satellite combined data to invert the error propagation model. At the application level, the user terminal only needs to receive the polynomial coefficient parameters calculated by the service side and combine them with the local PDOP values to output the quantified accuracy prediction in real time.
[0043] Specifically, this method includes the following steps:
[0044] Step 1: The service side selects multiple ground monitoring stations and, for the observation data of each monitoring station in a single epoch, uses different satellite combinations to perform precise positioning calculations. The specific method is as follows:
[0045] (101) Select several fixed ground-based GNSS monitoring stations and implement real-time positioning using precise positioning technology combined with precise satellite orbit and satellite clock bias information. The following single-epoch dual-frequency original observation equations are constructed using the ionospheric desiccation PPP technology as an example:
[0046]
[0047] Among them, superscript Indicates satellite number, subscript Indicates the receiver number, subscript Indicates the frequency band number. These are pseudorange observations. For carrier phase observations, For receiver To satellite geometric distance, Given the known satellite positions, For unknown station coordinates, For tropospheric dry delay, This is the tropospheric wet delay projection function. For tropospheric zenith wet delay, For receiver The clock difference, For satellite The clock difference, For satellite Ionospheric delay at the first frequency, This is the ratio between the ionospheric delay at other frequencies and the ionospheric delay at the first frequency. For the corresponding frequency wavelength, For receiver With satellite Frequency between The corresponding ambiguity; except and Except for the dimensionless parameter, all other parameters are in meters.
[0048] (102) Constructing the combined observation equations for ionospheric de-escalation:
[0049]
[0050] in, This represents the ionosphere decomposition operator, where... , , .
[0051] (103) For the station receiver Number of satellites observed at a certain epoch First, list all satellite combinations starting with the minimum of 4 satellites; similarly, list combinations starting with 5 satellites and increasing to the maximum number of satellites. All satellite combinations of , assuming different satellite combinations have Group.
[0052] (104) For the receiver The The observation data of a single epoch of satellites are combined, and the satellite orbit, satellite clock products, and projection functions of tropospheric dry delay and tropospheric wet delay are substituted into the observation equation in (102). The equation is then solved using Kalman filtering or other adjustment methods. , , , Parameters, and extract PDOP values from the normal equations. .
[0053] Step 2: Record the PDOP value and coordinate result deviation for each monitoring station, single epoch, and each selected satellite combination for positioning. The specific method is as follows:
[0054] (201) Based on the coordinates of all monitoring stations solved in step (104) and true values of monitoring station coordinates Calculate the deviation of the coordinate results .
[0055] (202) Adjust the coordinate results to be offset Following the traditional method of converting from a rectangular coordinate system to a station-centered coordinate system, the coordinate deviations in the east, north, and elevation directions are calculated in the station-centered coordinate system. .
[0056] Step 3: Fit all PDOP values and their corresponding coordinate deviations for a single epoch into a polynomial function. The polynomial coefficients are then used as accuracy prediction parameters sent to the user. Specifically:
[0057] (301) Based on the absolute value of coordinate deviation of a single epoch and Polynomial functions were fitted to the east, north, and elevation direction deviations and the PDOP values, respectively:
[0058]
[0059]
[0060]
[0061] in, , , The coefficients are polynomials in three directions. For serial number, Let be the highest power of the fitted polynomial.
[0062] (302) The latest epoch solution in (301) , , , This information is sent to the user as an accuracy prediction parameter so that they can assess the positioning level themselves.
[0063] Step 4: When the user performs precise positioning, the PDOP value is calculated, and then the accuracy level of the positioning result is calculated based on the accuracy prediction parameters in Step 3. The specific method is as follows:
[0064] (401) When the user implements positioning using the same positioning technology as the service side, the positioning result and PDOP value are obtained by solving the algorithm equation according to the corresponding positioning process calculation method, such as latitude, longitude and elevation in the geodetic coordinate system. and ,in Used as a user identifier.
[0065] (402) Based on the received accuracy prediction parameters , , , , combined Substitute the values into the polynomial to obtain a reference value for the user's positioning accuracy. , and :
[0066]
[0067]
[0068]
[0069] (403) Based on reference values , and Assess the accuracy level of the positioning results.
[0070] This invention utilizes observation data from GNSS ground monitoring stations, along with enhanced information such as satellite orbits and clock biases, on the service side to calculate the PDOP values and positioning results from multiple monitoring stations. Addressing the issue that PDOP in GNSS positioning can only qualitatively assess geometric accuracy but cannot quantify and predict actual errors, this invention quantifies the nonlinear relationship between PDOP and the actual error, providing a lightweight error propagation model based on polynomial fitting. This allows users to assess expected positioning errors in real time using only local PDOP values. This invention avoids the communication burden of continuous reliance on cloud services and requires no additional computing power for terminal hardware, making it particularly suitable for the stringent requirements of low power consumption and high real-time performance for mobile terminals such as drones.
[0071] Those skilled in the art will recognize that the described embodiments are intended to help readers understand the principles of the invention and should be understood as not limiting the scope of protection of the invention to the described embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.
Claims
1. A GNSS precise positioning accuracy prediction method based on the PDOP error model, characterized in that, Includes the following steps: Step 1: Select multiple ground monitoring stations on the service side, and use different satellite combinations to perform precise positioning calculations for the observation data of each monitoring station in a single epoch. Step 2: Record the PDOP value and coordinate result deviation of each monitoring station for each selected satellite combination positioning under a single epoch; Step 3: Fit all PDOP values and their corresponding coordinate deviations for a single epoch into a polynomial function, and use the coefficients of the polynomial function as the accuracy prediction parameters sent to the user. Step 4: When the user performs precise positioning, the PDOP value is calculated, and then the positioning reference value is calculated based on the accuracy prediction parameters. The accuracy level of the positioning result is evaluated based on the reference value.
2. The GNSS precise positioning accuracy prediction method based on the PDOP error model according to claim 1, characterized in that, The specific method for step 1 is as follows: Step 101: Select multiple GNSS ground monitoring stations, utilize the ionospheric de-isomerization PPP method, and combine precise satellite orbit and satellite clock bias information to implement real-time positioning, and construct the single-epoch dual-frequency original observation equation: Among them, superscript Indicates satellite number, subscript Indicates the receiver number, subscript Indicates the frequency band number. These are pseudorange observations. For carrier phase observations, For receiver To satellite geometric distance, For known satellites coordinates For unknown receivers coordinates For tropospheric dry delay, This is the tropospheric wet delay projection function. For tropospheric zenith wet delay, For receiver The clock difference, For satellite The clock difference, For satellite Ionospheric delay at the first frequency, This is the ratio between the ionospheric delay at other frequencies and the ionospheric delay at the first frequency. For the corresponding frequency The wavelength, λ1 is the wavelength of the first frequency. For receiver With satellite Frequency between The corresponding ambiguity; except and Except for the dimensionless parameter, all other parameters are in meters. Step 102, construct the combined observation equations for ionosphere elimination: Among them, subscript This represents the ionosphere decomposition operator, where... , , f1 is the frequency of the first frequency band, f2 is the frequency of the second frequency band, and the subscripts 1 and 2 represent the first frequency band and the second frequency band, respectively; Step 103, for the receiver Number of satellites observed at a certain epoch The number of satellites listed are 4, 5, ... All satellite combinations at that time, the total number of satellite combinations is Group; Step 104, for the receiver The observation data of a single epoch from the i-th satellite group are used to substitute the satellite orbits, satellite clock products, and projection functions of the tropospheric dry delay and tropospheric wet delay into the ionospheric combined observation equation. Solving the equation yields the parameters. , , , And extract the PDOP value from the normal equation. i=1,2,..., .
3. The GNSS precise positioning accuracy prediction method based on the PDOP error model according to claim 2, characterized in that, The specific method for step 2 is as follows: Step 201, based on all the receiver coordinates solved in step 104 and coordinate true value Calculate the deviation of the coordinate results i=1,2,..., ; Step 202, adjust the coordinate result deviation According to the transformation method from the rectangular coordinate system to the station center coordinate system, the coordinate deviations in the east, north, and elevation directions after transformation to the station center coordinate system are... .
4. The GNSS precise positioning accuracy prediction method based on the PDOP error model according to claim 3, characterized in that, The specific method for step 3 is as follows: Step 301, based on the absolute value of the coordinate deviation of a single epoch. and Polynomial functions were fitted to the east, north, and elevation direction deviations and the PDOP values, respectively: in, , , Let be the coefficients of three polynomial functions, j = 0, 1, 2, ..., m. The highest power of the fitted polynomial; Step 302, calculate the latest epoch solution from step 301. , , , This information is sent to the user as an accuracy prediction parameter.
5. The GNSS precise positioning accuracy prediction method based on the PDOP error model according to claim 4, characterized in that, The specific method for step 4 is as follows: Step 401: The user uses the same positioning technology as the server to perform positioning, and obtains the positioning result by solving the algorithm equation according to the corresponding positioning process calculation method. and PDOP value , The three components represent latitude, longitude, and elevation in the geodetic coordinate system, with subscripts... User identification; Step 402, predict the accuracy based on the received parameters. , , , , combined Substitute these values into the polynomial to obtain the reference value for positioning. , and : Step 403, based on reference values , and Assess the accuracy level of the positioning results.