Satellite navigation tight integration positioning method based on mixed frequency observation fusion

Abstract

The present invention discloses a satellite navigation tight combination positioning method based on mixed frequency observation fusion, including: constructing single-difference observation equations between pseudorange and carrier stations of mobile stations and reference stations; eliminating the rank deficiency of the model by selecting reference frequency and reparameterization, while maintaining the integer estimability of ambiguity. In the multi-epoch filtering process, the time-invariant characteristics of inter-system deviations and inter-frequency deviations are fully utilized to impose constraints, thereby improving the strength of the model. Compared with the traditional RTK loose combination model and the current RTK tight combination model based on the same frequency or the same number of frequencies, the present invention can fully integrate the observation information of each system, each satellite and each frequency point, and the positioning effect is improved in good or extreme observation environments.

Description

Technical Field

[0001] The present invention belongs to the field of GNSS (Global Navigation Satellite System) positioning and navigation technology, and in particular relates to a satellite navigation tightly combined positioning method based on mixed frequency observation fusion. Background Art

[0002] Thanks to the modernization of the Global Navigation Satellite System (GNSS), users now have access to a wider range of satellite and frequency resources. High-precision positioning requires the effective fusion of multi-frequency and multi-constellation signals. The number of satellites, the frequencies used, and the selected functional model all affect model strength. Fully integrating observations from different satellite systems in different frequency bands is crucial for improving positioning accuracy and reliability, especially when satellite observation data is limited.

[0003] Traditional RTK positioning algorithms use an intra-system differencing model, where each system selects a reference satellite for each frequency band and performs intra-system double-difference. This model is widely used because it can eliminate common errors such as inter-frequency and inter-system bias during intra-system differencing. However, in extreme environments, when only one observation is available in a frequency band within a system, it cannot be used because no other observations can be double-differenced with it, resulting in wasted observations. This is particularly true in scenarios with limited satellite availability, such as urban canyons and road sections obscured by trees. This method can lead to the loss of some observations, reducing model robustness and sometimes even causing positioning interruption. Furthermore, current research on tight RTK integration primarily focuses on overlapping frequencies or using the same number of frequencies between different systems, lacking scalability for mixed processing of heterogeneous frequency observations. Therefore, it is crucial to construct a function model that fully integrates observation information from all systems, satellites, and frequencies. Summary of the Invention

[0004] To address these issues, the present invention discloses a tightly integrated satellite navigation positioning method based on mixed-frequency observation fusion. It proposes a functional model compatible with mixed-frequency observation fusion processing and capable of leveraging time-varying characteristics such as inter-system and inter-frequency biases. This model eliminates rank deficiency by selecting a reference frequency and performing reparameterization operations. This method fully integrates observation information from various systems, satellites, and frequencies, improving positioning performance in both good and extreme observation environments.

[0005] To achieve the above object, the technical solution of the present invention is as follows:

[0006] The satellite navigation tightly integrated positioning method based on mixed frequency observation fusion includes the following steps:

[0007] Step 1: Based on the mixed-frequency GNSS observation data, construct the pseudorange and carrier-station single-difference observation equations of the rover and reference stations;

[0008] Step 2: Select the reference frequency band and re-parameterize the pseudorange and carrier inter-station single-difference observation equations to achieve full rank of the equations;

[0009] Step 3: Transform the parameters to be estimated in the filtering process.

[0010] The specific steps are:

[0011] Step 1. Based on the mixed-frequency GNSS observation data, construct the pseudorange and carrier-to-station single-difference observation equations for the rover and reference stations, as follows:

[0012] The following inter-station single-difference observation equation is established:

[0013]

[0014] where Δ(·) is the inter-station single-difference operator; P and φ represent pseudorange observations and carrier phase observations, respectively; subscripts 1 and 2 denote rover and base stations, respectively; j and k denote the corresponding satellite frequency bands; and superscripts G and C denote GPS and BDS satellites, respectively. Represents the GPS satellite index, represents the number of GPS satellites in the j-band; ρ is the geometric distance between the satellite and the receiver; dt is the receiver clock error; d and l are the pseudorange hardware delay and carrier hardware delay, respectively; λ is the wavelength of the corresponding frequency band; Z is the integer ambiguity; ξ and ε are the pseudorange and carrier observation noise, respectively.

[0015] Step 2. Select the reference frequency band and reparameterize the pseudorange and carrier inter-station single-difference observation equations to achieve full rank of the equations, as follows:

[0016] To construct a full-rank model, a solution benchmark needs to be selected to eliminate these two types of correlations. In this process, assuming the reference frequency is 1, the parameter of the pseudorange receiver clock error and hardware delay at the reference frequency is the "new clock error," which actually constitutes the inter-system bias model, that is, each system shares the same receiver clock error parameter:

[0017]

[0018] In the formula is the “new clock error”, and the subscript L1 is the frequency band corresponding to the satellite. Then the pseudorange observation equations of the reference frequency band and the pseudorange observation equations of the non-reference frequency band are transformed as follows:

[0019]

[0020] The difference in hardware delay separated by the non-reference frequency band at this time That is, the differential inter-system or differential inter-frequency deviation on the pseudorange observation value, which has time domain stability;

[0021] The selected benchmark will be further transferred to the carrier observation values ​​of each system and frequency band. The carrier observation equation at the benchmark frequency changes as follows:

[0022]

[0023] The non-reference frequency band carrier observation equation is expressed as follows:

[0024]

[0025] In the formula In order to introduce the pseudo-range clock error reference and carrier solution reference, is the carrier hardware delay between differential systems or differential frequencies, which has time domain stability. For the carrier observation equation, there is still a linear correlation between the integer ambiguity and the carrier hardware delay. Therefore, it is necessary to further select a reference in the carrier observation value to eliminate the rank deficiency problem caused by this correlation. Assuming that the ambiguity of the satellite with index 1 is selected as the reference in each system and each frequency, the carrier observation equation of the non-reference frequency band is further transformed into:

[0026]

[0027] in It constitutes the final solution reference parameters on each frequency band. is the estimable carrier differential inter-system bias or differential inter-frequency bias parameter containing the reference satellite ambiguity; so far, the full rank of the equation is achieved, and the ambiguity has restored the integer property, which is consistent with the double-difference ambiguity in form.

[0028] Step 3. The parameters to be estimated in the filtering process are transformed as follows:

[0029] From the above process of eliminating rank deficiency, we can see that the settings of some benchmark parameters are related to specific frequencies or specific satellites. In complex observation environments, when the observation values ​​of a certain frequency band of the satellite are missing, the form of the estimated parameters also changes accordingly. The basic idea is to estimate the parameters based on the previous moment and perform corresponding transformations according to the actual needs of the current moment, so that the parameter form predicted at the previous moment is consistent with the parameter state at the current moment. Parameter transformation mainly involves two situations:

[0030] The first is when the reference frequency is the GPS L1 band. When all observations on the reference band disappear and the GPS system L2 band is currently used as the reference, the predicted parameters need to implement the following inter-epoch transformations:

[0031]

[0032] In the second case, when the reference frequency does not change and the reference star corresponding to the reference frequency changes from 1 to s, the predicted parameters change as follows:

[0033]

[0034] Where t and t-1 represent two consecutive epochs, and their corresponding variances and covariances are transformed in the same way. Similar transformations are also performed when the double-difference ambiguity corresponds to the change in the corresponding observation value.

[0035] The beneficial effects of the present invention are:

[0036] The satellite navigation tight combination positioning method based on mixed frequency observation fusion proposed in the present invention avoids the problem that the conventional RTK loose combination is limited by the number of observation values ​​in the system and the current tight combination RTK only considers overlapping frequencies or the same number of frequencies. The advantages are reflected in two aspects. On the one hand, compared with the conventional method, the present invention utilizes more observation values ​​and improves the distribution of satellites; on the other hand, even if the observation values ​​used by the two are consistent, in scenarios with severe observation conditions, this model has the constraint of time-invariant parameters. During multi-epoch filtering, this parameter can be regarded as a known value. At this time, even if it is consistent with the observation values ​​involved in the solution of the conventional method, this model has higher redundancy and higher model strength. In scenarios with limited satellites, it can improve positioning accuracy and positioning continuity. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is an implementation flow chart of the present invention;

[0038] FIG2 is a comparison diagram of the positioning effects in the E, N, and U directions of the conventional RTK method (a) and the present invention (b) when the cut-off elevation angle is 40° in a static scene.

[0039] FIG3 is a comparison diagram of the positioning effects in the E, N, and U directions of the conventional RTK method (a) and the present invention (b) in a dynamic scene. DETAILED DESCRIPTION

[0040] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0041] As shown in the figure, this embodiment discloses a satellite navigation tightly integrated positioning method based on mixed frequency observation fusion, and the specific steps are as follows:

[0042] Step 1. Based on the mixed-frequency GNSS observation data, construct the pseudorange and carrier-to-station single-difference observation equations for the rover and reference stations, as follows:

[0043] The following inter-station single-difference observation equation is established:

[0044]

[0045] where Δ(·) is the inter-station single-difference operator; P and φ represent pseudorange observations and carrier phase observations, respectively; subscripts 1 and 2 denote rover and base stations, respectively; j and k denote the corresponding satellite frequency bands; and superscripts G and C denote GPS and BDS satellites, respectively. Represents the GPS satellite index, represents the number of GPS satellites in the j-band; ρ is the geometric distance between the satellite and the receiver; dt is the receiver clock error; d and l are the pseudorange hardware delay and carrier hardware delay, respectively; λ is the wavelength of the corresponding frequency band; Z is the integer ambiguity; ξ and ε are the pseudorange and carrier observation noise, respectively.

[0046] Step 2. Select the reference frequency band and reparameterize the pseudorange and carrier inter-station single-difference observation equations to achieve full rank of the equations, as follows:

[0047] To construct a full-rank model, a solution benchmark needs to be selected to eliminate these two types of correlations. In this process, assuming the reference frequency is 1, the parameter of the pseudorange receiver clock error and hardware delay at the reference frequency is the "new clock error," which actually constitutes the inter-system bias model, that is, each system shares the same receiver clock error parameter:

[0048]

[0049] In the formula is the “new clock error”, and the subscript L1 is the frequency band corresponding to the satellite. Then the pseudorange observation equations of the reference frequency band and the pseudorange observation equations of the non-reference frequency band are transformed as follows:

[0050]

[0051] The difference in hardware delay separated by the non-reference frequency band at this time That is, the differential inter-system or differential inter-frequency deviation on the pseudorange observation value, which has time domain stability;

[0052] The selected benchmark will be further transferred to the carrier observation values ​​of each system and frequency band. The carrier observation equation at the benchmark frequency changes as follows:

[0053]

[0054] The non-reference frequency band carrier observation equation is expressed as follows:

[0055]

[0056] In the formula In order to introduce the pseudo-range clock error reference and carrier solution reference, is the carrier hardware delay between differential systems or differential frequencies, which has time domain stability. For the carrier observation equation, there is still a linear correlation between the integer ambiguity and the carrier hardware delay. Therefore, it is necessary to further select a reference in the carrier observation value to eliminate the rank deficiency problem caused by this correlation. Assuming that the ambiguity of the satellite with index 1 is selected as the reference in each system and each frequency, the carrier observation equation of the non-reference frequency band is further transformed into:

[0057]

[0058] in It constitutes the final solution reference parameters on each frequency band. is the estimable carrier differential inter-system bias or differential inter-frequency bias parameter containing the reference satellite ambiguity; so far, the full rank of the equation is achieved, and the ambiguity has restored the integer property, which is consistent with the double-difference ambiguity in form.

[0059] Step 3. The parameters to be estimated in the filtering process are transformed as follows:

[0060] From the above process of eliminating rank deficiency, we can see that the settings of some benchmark parameters are related to specific frequencies or specific satellites. In complex observation environments, when the observation values ​​of a certain frequency band of the satellite are missing, the form of the estimated parameters also changes accordingly. The basic idea is to estimate the parameters based on the previous moment and perform corresponding transformations according to the actual needs of the current moment, so that the parameter form predicted at the previous moment is consistent with the parameter state at the current moment. Parameter transformation mainly involves two situations:

[0061] The first is when the reference frequency is the GPS L1 band. When all observations on the reference band disappear and the GPS system L2 band is currently used as the reference, the predicted parameters need to implement the following inter-epoch transformations:

[0062]

[0063] In the second case, when the reference frequency does not change and the reference star corresponding to the reference frequency changes from 1 to s, the predicted parameters change as follows:

[0064]

[0065] Where t and t-1 represent two consecutive epochs, and their corresponding variances and covariances are transformed in the same way. Similar transformations are also performed when the double-difference ambiguity corresponds to the change in the corresponding observation value.

Claims

1. Satellite navigation tight combination positioning method based on mixed frequency observation fusion, characterized by: include: Step 1: Based on the mixed-frequency GNSS observation data, construct the pseudorange and carrier-station single-difference observation equations of the rover and reference stations; The details are as follows: The following inter-station single-difference observation equation is established: where Δ(·) is the inter-station single difference operator; P and φ represent pseudorange observations and carrier phase observations, respectively; subscripts 1 and 2 denote rover and base stations, respectively; j and k denote the corresponding satellite frequency bands; and superscripts G and C denote GPS and BDS satellites, respectively. Represents the GPS satellite index, represents the number of GPS satellites in the j-band; ρ is the geometric distance between the satellite and the receiver; dt is the receiver clock error; d and l are the pseudorange hardware delay and carrier hardware delay, respectively; λ is the wavelength of the corresponding frequency band; Z is the integer ambiguity; ξ and ε are the pseudorange and carrier observation noise, respectively; Step 2: Select the reference frequency band and re-parameterize the pseudorange and carrier inter-station single-difference observation equations to achieve full rank of the equations; The details are as follows: To construct a full-rank model, a solution benchmark must be selected to eliminate these two types of correlations. Assuming the benchmark frequency is 1, the parameter resulting from the merging of the pseudorange receiver clock error and hardware delay at the benchmark frequency is the "new clock error," effectively forming an inter-system bias model. This means that all systems share the same receiver clock error parameter: In the formula is the "new clock error", and the subscript L1 is the frequency band corresponding to the satellite; then the pseudorange observation equation of the reference frequency band and the pseudorange observation equation of the non-reference frequency band are transformed as follows: The difference in hardware delay separated by the non-reference frequency band at this time That is, the differential inter-system or differential inter-frequency deviation on the pseudorange observation value, which has time domain stability; The selected benchmark will be further transferred to the carrier observation values ​​of each system and each frequency band. The carrier observation equation at the benchmark frequency changes as follows: The non-reference frequency band carrier observation equation is expressed as follows: In the formula In order to introduce the pseudo-range clock error reference and carrier solution reference, is the carrier hardware delay between differential systems or differential frequencies, which has time domain stability. For the carrier observation equation, there is still a linear correlation between the integer ambiguity and the carrier hardware delay. Therefore, it is necessary to further select a reference in the carrier observation value to eliminate the rank deficiency problem caused by this correlation. Assuming that the ambiguity of the satellite with index 1 is selected as the reference in each system and each frequency, the carrier observation equation of the non-reference frequency band is further transformed into: in It constitutes the final solution reference parameters on each frequency band. is the estimable carrier differential inter-system bias or differential inter-frequency bias parameter containing the reference satellite ambiguity. At this point, the full rank of the equation is achieved, and the ambiguity has restored the integer property, which is consistent with the double-difference ambiguity in form. Step 3: Transform the parameters to be estimated in the filtering process.

2. The satellite navigation tightly integrated positioning method based on mixed frequency observation fusion according to claim 1, characterized in that: The parameters to be estimated in the filtering process described in step 3 are transformed as follows: From the process of eliminating rank deficiency, we can see that the settings of some benchmark parameters are related to specific frequencies or specific satellites. In complex observation environments, when the observation values ​​of a certain frequency band of the satellite are missing, the form of the estimated parameters also changes accordingly. The method is to estimate the parameters based on the previous moment and perform corresponding transformations according to the actual needs of the current moment, so that the parameter form predicted at the previous moment is consistent with the parameter state at the current moment. Parameter transformation involves two situations: The first is when the reference frequency is the GPS L1 band. When all observations on the reference band disappear and the GPS system L2 band is currently used as the reference, the predicted parameters need to implement the following inter-epoch transformations: In the second case, when the reference frequency does not change and the reference star corresponding to the reference frequency changes from 1 to s, the predicted parameters change as follows: Where t and t-1 represent two consecutive epochs, and their corresponding variances and covariances are also transformed in the same way; similar transformations are also performed when the double-difference ambiguity corresponding to the observation value changes.

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