A single-frequency real-time precise point positioning method

Abstract

The present invention relates to a single-frequency real-time precise point positioning method, belonging to the technical field of single-frequency real-time precise point positioning observation data processing. First, preprocess the acquired multi-epoch observation data; then, use the preprocessed multi-epoch observation data to establish an observation equation and a state equation; then determine the prior variance-covariance matrix of the parameters and the observations; finally, according to the equivalence of the parameters between epochs, establish an inter-epoch parameter constraint equation, add the constraint equation to the square root information filtering algorithm for parameter solution, obtain the coordinate correction value and correct the single-point probability coordinates to achieve precise point positioning. According to the equivalence of the parameters in the multi-epoch observation data, the present invention performs precise point positioning, solves the rank deficiency problem caused by taking the ionospheric delay as a parameter in the single-frequency precise point positioning calculation, does not need to introduce external ionospheric delay information and additional errors, and improves the positioning accuracy and convergence speed of single-frequency precise point positioning.

Description

Technical Field

[0001] The present invention relates to a single-frequency real-time precise point positioning method, belonging to the technical field of single-frequency real-time precise point positioning observation data processing. Background Technique

[0002] Precise Point Positioning (PPP) is a research hotspot in the field of navigation and positioning currently. In recent years, scholars at home and abroad have conducted a large number of studies on it and solved many key problems. Single-frequency receivers have been widely used in deformation monitoring, low-orbit satellite orbit determination, and ground network solution and other fields due to their low price and convenience of use. However, there is still a certain gap in the positioning accuracy between single-frequency PPP and multi-frequency PPP. The biggest difficulty is the correction of ionospheric delay. Finding a more effective ionospheric processing method can greatly improve the positioning accuracy of single-frequency PPP.

[0003] Among the existing ionospheric delay processing methods for single-frequency real-time precise point positioning, there are methods using ionospheric model correction, constructing semi-combined observations to eliminate the low-order terms of the ionosphere, and establishing an ionospheric slant delay parameter model to describe the simple activities of the ionosphere; there are also processing methods that require external ionospheric information, and the established models are relatively rough, and there are still large ionospheric delay residual errors, which greatly affect the positioning accuracy of single-frequency PPP. The existing research focuses on the single-frequency PPP estimation method of ionospheric model correction and additional ionospheric constraints. The positioning accuracy of single-frequency precise points directly depends on the accuracy of the established model. When estimating the ionospheric slant delay, taking the ionospheric parameters as parameter estimation will lead to rank deficiency problems and result in low positioning accuracy. Summary of the Invention

[0004] The purpose of the present invention is to provide a single-frequency real-time precise point positioning method to solve the problem of low positioning accuracy of current single-frequency real-time precise point positioning.

[0005] The present invention provides a single-frequency real-time precise point positioning method, which is characterized in that the method includes the following steps:

[0006] 1) Obtain multi-epoch satellite observation data of the target position; and perform data preprocessing on the obtained data to obtain preprocessed single-point multi-epoch observation data;

[0007] 2) Use the preprocessed multi-epoch observation data to construct an observation equation and a state equation for the inter-epoch observation data;

[0008] 3) Use the autocorrelation coefficient method to determine the variance-covariance matrix between multi-epoch observations, and use the single-frequency PPP algorithm to determine the prior variance-covariance matrix between multi-epoch parameters;

[0009] 4) Set the first sliding window size, and adopt the sliding window single-frequency PPP algorithm according to the set first sliding window size. Establish the epoch-to-epoch constraint equation of the parameters based on the equivalence between the parameters, add this constraint equation to the square root information filtering model, and perform parameter calculation according to the variance-covariance matrix between the generated observations and the prior variance-covariance matrix between the multi-epoch parameters to obtain the coordinate correction value. Correct the single-point approximate coordinates according to the coordinate correction value to achieve precise point positioning; wherein the square root information filtering model includes an observation equation and a state equation.

[0010] The present invention proposes a single-frequency real-time precise point positioning method, which uses single-point multi-epoch observation data for single-frequency precise point positioning calculation, avoids the rank deficiency problem caused by taking the ionospheric delay as a parameter, and takes into account the correlation between the epoch observations and the parameters between epochs. Construct the variance-covariance matrix between the observations and the variance-covariance matrix between the parameters between epochs. Finally, considering the equivalence of the parameters between epochs, establish the epoch-to-epoch constraint equation according to the sliding window algorithm, and solve the single-point coordinate correction value to achieve single-point precise positioning. According to the equivalence of the parameters in the multi-epoch satellite observation data, the present invention performs single-frequency precise point positioning calculation, solves the rank deficiency problem caused by estimating the ionospheric delay as a parameter in the single-frequency precise point positioning calculation, does not need to introduce external ionospheric delay information and additional errors, and improves the accuracy and reliability of the single-frequency precise point positioning for parameter estimation of the ionospheric delay.

[0011] Further, the calculation formula for the variance-covariance matrix between the observations in step 3) is:

[0012] ρ τ =ρ ij =ρ ji , τ = |i - j|, i, j = 1, …, m

[0013]

[0014] In the formula, ρ is the correlation coefficient between two observations; m is the number of epochs participating in the calculation; is the deviation of the i-th epoch, σ i and σ i+τ are respectively the mean square errors of the observations in the i-th and the (i + τ)-th epochs; τ is the number of epochs between two observations; r i and r i+τ are respectively the residuals of the observations in the i-th and the (i + τ)-th epochs, and satisfy r i =r i+τ =n - 1, n is the number of observable satellites in the multi-epoch observation.

[0015] Further, in order to obtain accurate single-point multi-epoch observation data, the data preprocessing in step 1) includes detecting and repairing gross errors and clock jumps through data detection methods; detecting and repairing cycle slips through Doppler integration method and phase pseudorange combination method.

[0016] Further, in order to obtain accurate single-point multi-epoch observation data, the preprocessing further includes eliminating invalid time periods in satellite data.

[0017] Further, in order to quickly establish the observation equation between epochs, before establishing the observation equation in step 2), a second sliding window size is set, and a sliding window of epoch observation values is established according to the second sliding window size, and the observation equation of the epoch observation values under each window is calculated.

[0018] Further, for the convenience of calculation, step 2) also includes linearizing the observation equation and the state equation.

[0019] Further, in order to make the calculation result more accurate, before parameter solution in step 4), the ambiguity of the first group under the first sliding window is selected as the reference value, and the ambiguity is obtained by subtracting the pseudorange observation value from the single-frequency phase observation value and correcting the ionospheric delay.

[0020] Further, when performing parameter solution in step 4), an observation error equation needs to be established, and the error equation is:

[0021] V j =A j x j +B j y j -l j

[0022] In the formula, V is the observation error matrix; j is the combined number of epochs; x j are the j unconstrained epoch parameters; y j are the j constrained epoch parameters; A j and B j are the coefficient full row rank matrices of x j and y j respectively; l j is the error vector. Description of the Drawings

[0023] Figure 1 is the flowchart of the single-frequency real-time precise point positioning method of the present invention. Detailed Embodiments

[0024] The following further describes the detailed embodiments of the present invention with reference to the accompanying drawings.

[0025] The present invention proposes a single-frequency real-time precise point positioning method, and the specific process is as Figure 1 shown. First, the single-point multi-epoch observation data obtained is preprocessed; then, using the preprocessed multi-epoch observation data, the observation equation and state equation of the square root information filtering model of the inter-epoch observation data are constructed; then, the autocorrelation coefficient method is used to determine the variance-covariance matrix between multi-epoch observations, and the single-frequency PPP algorithm is used to determine the prior variance-covariance matrix between multi-epoch parameters; finally, the inter-epoch constraint equation of the parameters is established according to the equivalence between the parameters, and this constraint equation is added to the square root information filtering model for parameter solution, obtaining the coordinate correction value and correcting the single-point approximate coordinates to achieve precise point positioning. The present invention performs single-frequency precise point positioning calculation according to the equivalence between the parameters in the multi-epoch satellite observation data, solves the rank deficiency problem caused by estimating the ionospheric delay as a parameter in single-frequency precise point positioning, does not require introducing external ionospheric delay information and additional errors, and improves the accuracy and reliability of single-frequency precise point positioning for parameter estimation of the ionospheric delay.

[0026] Step 1. Data acquisition and data preprocessing

[0027] The present invention uses a single-frequency receiver to obtain multi-epoch satellite observation data. During the satellite observation process, the satellite, receiver, and signal propagation will all cause certain errors to the measured values, mainly affected by factors such as satellite clock error, receiver clock error, ionospheric delay, tropospheric delay, and multipath effect during the satellite signal propagation process. Therefore, after obtaining the multi-epoch observation data, it is first necessary to preprocess the multi-epoch satellite observation data. The preprocessing methods include: using the data detection method to detect and repair gross errors and clock jumps in the epoch data; using the Doppler integration method and the phase pseudorange combination method to detect and repair cycle slips, and at the same time eliminating some invalid time periods in the satellite data, such as invalid data caused by multipath reflection and satellite signal blockage.

[0028] Among them, the method for detecting and repairing cycle slips is: calculating the Doppler integration between epochs, smoothing the pseudorange observation value through the Doppler integration, and then combining the smoothed pseudorange observation value with the phase observation value to detect the cycle slips occurring in the satellite observation value. When the cycle slip value is within a certain range, it is considered that the cycle slip detection is accurate, determining the cycle slip value by rounding, and then correcting it in the observation data.

[0029] Step 2. Construct the observation equation and state equation

[0030] Based on the multiple epoch data preprocessed in step 1, establish the observation equation and state equation between the preprocessed multi-epoch observation data, which serve as the observation equation and state equation of the subsequent square root information filtering model. For the convenience of subsequent calculations, linearize the obtained observation equation and state equation. Among them, before establishing the observation equation, set the second sliding window size, establish a sliding window of epoch observation values according to the second sliding window size, and calculate the observation equation of the epoch observation values under each window. In this embodiment, take two or more epoch observation values as the sliding window. After each calculation is completed, the sliding window slides down once. The receiver clock error, tropospheric delay, ionospheric delay, and ambiguity are set the same for both static and dynamic conditions. However, in static observations, the receiver remains stationary at a single point position, and in dynamic observations, the receiver observes different single-point information. Therefore, three parameters (X, Y, Z) are set for multiple epochs in the static case, and three parameters (X i , Y i , Z i ) are set for each epoch in the dynamic case, where i represents the i-th epoch, and the observation equation of the epoch observation values under each sliding window is obtained.

[0031] Step 3. Determine the variance-covariance matrices of the observations and parameters

[0032] Based on the multi-epoch observation data preprocessed in step 1, determine the variance-covariance matrix between multi-epoch observation values and the prior variance-covariance matrix between multi-epoch parameters.

[0033] Among them, the variance-covariance matrix between the observations is determined by the autocorrelation coefficient method, and its calculation formula is:

[0034] ρ τ =ρ ij =ρ ji , τ = |i - j|, i, j = 1, …, m

[0035]

[0036] In the formula, ρ is the correlation coefficient between two observations; m is the number of epochs participating in the calculation; is the deviation of the i-th epoch, σ i and σ i+τ are the mean square errors of the observations at the i-th and (i + τ)-th epochs respectively; τ is the number of epochs between two observations; r i and r i+τ are the residuals of the observations at the i-th and (i + τ)-th epochs respectively, and satisfy r i =r i+τ =n - 1, where n is the number of observable satellites in multi-epoch observations.

[0037] Among them, the prior variance-covariance matrix of the parameters is determined by the calculation results of the ionospheric single-frequency PPP algorithm for T epoch data. In this embodiment, T is set to 100. As other implementation manners, the value of T can be determined according to the specific number of epochs.

[0038] Step 4. Parameter solution and observation value correction

[0039] The present invention adopts a sliding window single-frequency PPP algorithm, establishes an epoch-interval constraint equation for parameters according to the equivalence between parameters, adds the constraint equation to the square root information filtering model, and performs parameter solution according to the variance-covariance matrix between the observation values generated in step 3 and the prior variance-covariance matrix between parameters, obtains the coordinate correction value of a single point, corrects the approximate coordinate of the single point, obtains the accurate single-point positioning coordinate, and realizes single-point precise positioning. Among them, the square root information filtering algorithm model includes the observation equation and the state equation generated in step 2; the epoch-interval parameters can be divided into constrained parameters and unconstrained parameters. Among them, whether a parameter is selected to be constrained can be determined by the user according to the actual situation of the observation data.

[0040] When constructing the epoch-interval constraint equation for parameters, set the size of the first sliding window, adopt the sliding window single-frequency PPP algorithm with a determined size, and according to the correlation between the observation values and parameters under each sliding window, there is equivalence between parameters in the theoretical previous and subsequent calculations, and the corresponding epoch-interval constraint equation can be established by using this equivalence.

[0041] In the process of parameter solution in the square root information filtering model, it is necessary to continuously adjust the weights of the constraint equation and the observation equation. The weights of the constraint equation and the observation equation are adjusted accordingly according to the convergence degree. If it has converged, the weight of the constraint equation is higher, and if it has not converged, the weight of the observation equation is higher. When the convergence accuracy reaches 1 - 3 decimeters, the solution accuracy is satisfied, and the weights of the constraint equation and the observation equation are adjusted according to the results calculated by each sliding window. At this time, the weight of the constraint equation is higher, and the weight of the observation equation is lower.

[0042] Before performing parameter solution, in order to solve the rank deficiency problem caused by the ionospheric delay as an estimated parameter, the ambiguity of the first group of observation data under the first sliding window is used as the reference value, that is, the ambiguity of the first group of observation data in the window under the determined size of the first sliding window is constrained to an approximate value. This approximate value is obtained by subtracting the pseudorange observation value from the single-frequency phase observation value and correcting the ionospheric delay, which can make the calculation result more accurate and improve the single-point positioning accuracy.

[0043] Meanwhile, an observation value error equation needs to be established before performing parameter solution. The error equation is:

[0044] V j =A j xj +B j y j -l j

[0045] wherein, V is the observation value error matrix; j is the combined number of epochs; x j are the parameters of j epochs that are not constrained; y j are the constrained parameters; A j and B j are respectively the full row rank matrices of the coefficients of x j and y j ; l j is the error vector.

[0046] To prove the reliability of the present invention in single-frequency precise point positioning, the observation data of 15 reference stations distributed globally for 14 days and the shipborne data collected at Lake Moritz in Germany are used for calculation. Through testing, compared with the traditional single-frequency PPP calculation method, the sliding window single-frequency PPP calculation method with additional epoch-to-epoch constraints proposed by the present invention greatly shortens the convergence time, improves the calculation accuracy. The accuracy of the static positioning solution is better than 3 cm, and the accuracy of the simulated dynamic solution can reach 1.5 dm. Compared with the traditional single-frequency PPP method, the convergence speed of this method is increased by about 24%, and the positioning accuracy is increased by about 30%. In particular, the improvement of the positioning accuracy of the elevation component is more obvious.

Claims

1. A single-frequency real-time precise point positioning method, characterized in that, The method includes the following steps: 1) Obtain multi-epoch satellite observation data at a target location; and perform data preprocessing on the obtained data to obtain preprocessed single-point multi-epoch observation data; 2) Use the preprocessed multi-epoch observation data to construct an observation equation and a state equation for the inter-epoch observation data; 3) Use the autocorrelation coefficient method to determine the variance-covariance matrix between multi-epoch observations, and use the single-frequency PPP algorithm to determine the prior variance-covariance matrix between multi-epoch parameters; 4) Set the size of the first sliding window, and use the sliding window single-frequency PPP algorithm according to the set size of the first sliding window. Establish an inter-epoch constraint equation for the parameters based on the equivalence between the parameters, add this constraint equation to the square root information filtering model, and perform parameter solution according to the generated variance-covariance matrix between the observations and the prior variance-covariance matrix between the multi-epoch parameters to obtain a coordinate correction value. Correct the single-point approximate coordinates according to the coordinate correction value to achieve precise point positioning; wherein the square root information filtering model includes an observation equation and a state equation.

2. The single-frequency real-time precise point positioning method according to claim 1, wherein In step 1), the data preprocessing is to detect and repair gross errors and clock jumps through the data detection method, and detect and repair cycle slips through the Doppler integration method and the phase pseudorange combination method.

3. The single-frequency real-time precise point positioning method according to claim 2, characterized in that, The preprocessing further includes removing invalid time periods in the satellite data.

4. The single-frequency real-time precise point positioning method according to claim 1, characterized in that In step 2), the process of establishing the observation equation is: set the size of the second sliding window, and establish a sliding window of epoch observations according to the size of the second sliding window to obtain the observation equation of the epoch observations under each window.

5. The single-frequency real-time precise point positioning method according to claim 1 or 4, characterized in that Step 2) also includes linearizing the observation equation and the state equation.

6. The single-frequency real-time precise point positioning method according to claim 1, wherein In step 4), before parameter solution, select the ambiguity of the first group under the first sliding window as the reference value, and the ambiguity is obtained by subtracting the pseudorange observation value from the single-frequency phase observation value and correcting the ionospheric delay.

7. The single-frequency real-time precise point positioning method according to claim 1, wherein When performing parameter solution in step 4), an observation error equation also needs to be established, and the error equation is: V j = A j x j + B j y j - l j In the formula, V is the observed value error matrix; j is the combined number of epochs; x j is the unconstrained j parameters of the epochs; y j is the constrained j parameters of the epochs; A j and B j are respectively x j and y j coefficient row full-rank matrices; l j is the error vector.

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