A multi-frequency GNSS step-by-step full-probability integer ambiguity resolution method

Abstract

The present invention discloses a multi-frequency GNSS step-by-step full-probability integer ambiguity resolution method. First, a multi-frequency GNSS non-combination geometry correlation function model is established, and the basic ambiguity is reparameterized in the parameter domain of the observation equation to obtain the ultra-wide lane, wide lane, and narrow lane ambiguity parameter forms. Then, based on the floating-point solutions of each level of ambiguity, the ambiguity candidate values are selected with a high confidence level as the threshold condition, reducing the problem of infinite candidate values with full probability to a finite calculation problem, thereby obtaining the full-probability integer solution based on a finite number of integer candidate vectors. Furthermore, based on the weighted average criterion, the variance of the full-probability integer solution of the ambiguity is calculated to evaluate the accuracy of the solution of each level of ambiguity. Finally, according to the conditional variance formula, the next level of ambiguity is constrained to achieve the solution of each level of ambiguity. This method changes the conventional step-by-step integer fixing mode to a step-by-step full-probability solution mode, effectively improving the positioning utilization efficiency while avoiding the risk of incorrect ambiguity fixing.

Description

Technical Field

[0001] The present invention belongs to the technical field of GNSS (Global Navigation Satellite System) positioning and navigation, relates to the technology of GNSS integer ambiguity resolution, and mainly relates to a multi-frequency GNSS step-by-step full-probability integer ambiguity resolution method. Background Art

[0002] In recent years, with the development of emerging intelligent industries such as driverless and intelligent robots, the connotation of modern position service requirements has also changed significantly. On the premise of meeting the accuracy, the environmental adaptability of the positioning system and the credibility of the results have become increasingly important performance indicators; especially in fields related to life safety such as driverless and aircraft approach, the reliability of positioning is particularly important. High-precision satellite positioning mainly relies on carrier observations, restores the integer characteristics of the ambiguity through a mixed integer model, and then calculates the high-precision positioning result through precise carrier ranging information. At present, the mixed integer estimation theory based on the assumption of unbiased errors (i.e., the observation errors conform to Gaussian white noise) has been relatively mature. However, under complex observation conditions such as urban environments, satellite signals are easily affected by obstacles such as buildings and tree canopies, as well as reflection and refraction, resulting in problems such as insufficient visible satellites, frequent observation gross errors, and strong multipath effects. The problem of unmodeled errors is serious, making it difficult to meet the assumption of unbiased observation errors. In this case, according to the currently commonly used integer ambiguity resolution system (i.e., fixing the floating-point solution of the ambiguity to an integer vector), an ideal fixing effect cannot be obtained, and it is difficult to objectively evaluate the effect of ambiguity fixing.

[0003] From a probability perspective, any set of integer vectors of the same dimension may be the true value of the ambiguity. Therefore, starting from a rigorous statistical theory, all possible integer vectors that may be the ambiguity should be used to obtain the full-probability integer solution of the ambiguity according to probability. Compared with fixing the ambiguity to a specific integer vector, the full-probability integer solution is more rigorous theoretically, without losing the possibility that other integer vectors are the true value of the ambiguity. Therefore, theoretically, no two types of errors, namely false acceptance and false rejection, are introduced, which is an ideal solution that takes into account both the high-precision positioning utilization rate and reliability.

[0004] Regardless of the integer ambiguity resolution method, the restoration effect of the integer characteristics of the ambiguity depends on the accuracy (i.e., variance) of the floating-point solution of the ambiguity. The higher the accuracy of the floating-point solution, the closer the restored integer solution is to the objective true value. The accuracy of the floating-point solution of the ambiguity mainly depends on the strength of the parameter resolution model. Currently, many studies have shown that it is relatively easy to resolve ultra-wide-lane / wide-lane ambiguities by using multi-frequency observation combinations, which can better resist the influence of observation noise and systematic errors. The fixing of the upper-level ambiguity can play an integer constraint role in the fixing of the lower-level ambiguity. On the premise of step-by-step resolution, using the all-probability integer solution method to ensure the reliability of the positioning solutions at all levels will further balance the real-time performance, utilization rate, and reliability of positioning. Currently, a practical method system for the all-probability integer solution has not been established. In particular, there is a lack of method support for the reasonable reduction of the integer candidate vector from infinity to finiteness and the accuracy evaluation of the all-probability integer solution. Further research and deepening are required to apply it to the multi-frequency GNSS ambiguity resolution system. Summary of the Invention

[0005] The present invention precisely aims at the problems in the prior art and provides a multi-frequency GNSS step-by-step all-probability integer ambiguity resolution method. First, a multi-frequency GNSS non-combined geometric correlation function model is established, and the basic ambiguity is re-parameterized in the parameter domain of the observation equation to obtain the parameter forms of ultra-wide-lane, wide-lane, and narrow-lane ambiguities. Then, based on the floating-point solutions of ambiguities at all levels, the ambiguity candidate values are selected with a high confidence level as the threshold condition, and the problem of infinite candidate values with all probabilities is reduced to a finite calculation problem, thereby obtaining an all-probability integer solution based on a finite number of integer candidate vectors. Secondly, based on the weighted average criterion, the variance of the all-probability integer solution of the ambiguity is calculated to realize the accuracy evaluation of the ambiguity resolution at all levels. Finally, after the all-probability integer solutions of ambiguities at all levels are completed, the ambiguity at the next level is constrained according to the conditional variance formula, and finally the resolution of ambiguities at all levels is realized. The method proposed by the present invention changes the conventional step-by-step integer fixing mode to a step-by-step all-probability resolution mode, which can effectively improve the positioning utilization efficiency while avoiding the risk of incorrect ambiguity fixing.

[0006] To achieve the above object, the technical solution adopted by the present invention is: a multi-frequency GNSS step-by-step all-probability integer ambiguity resolution method, including the following steps:

[0007] S1. Establish a multi-frequency GNSS non-combined geometric correlation function model, and re-parameterize the basic ambiguity in the parameter domain of the observation equation to obtain the parameter forms of ultra-wide-lane, wide-lane, and narrow-lane ambiguities;

[0008] S2. Based on the floating-point solutions of ambiguities at all levels, select the ambiguity candidate values with a high confidence level as the threshold condition, reduce the problem of infinite candidate values with all probabilities to a finite calculation problem, and obtain an all-probability integer solution based on a finite number of integer candidate vectors;

[0009] S3. Calculate the variances of the full-probability integer solutions of ambiguities at all levels based on the weighted average criterion to achieve the accuracy evaluation of ambiguity resolution.

[0010] S4. After the full-probability integer solutions of ambiguities at all levels are completed, constrain the ambiguities at the next level according to the conditional variance formula, and finally achieve the resolution of all ambiguities.

[0011] Compared with the prior art, the multi-frequency GNSS step-by-step full-probability integer ambiguity resolution method proposed by the present invention is based on the non-combination function model with the most sufficient utilization of observation information, gives full play to the advantage that the multi-frequency signal combined ambiguity is easy to fix, and through the full-probability integer solution process, changes the conventional step-by-step integer fixing mode into a step-by-step full-probability resolution mode, so that the integer resolution of ambiguities is no longer limited by the fact that the ambiguity at the previous level has been fixed to a specific integer vector. While avoiding the risk of incorrect fixing, it can effectively improve the positioning utilization efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 is a schematic flow chart of the multi-frequency GNSS step-by-step full-probability integer ambiguity resolution method of the present invention;

[0013] Figure 2 is a positioning accuracy map obtained by using the Beidou-3 ultra-wide lane and wide lane combinations for a single epoch in the case of a long baseline (50.8 km) by the method of the present invention;

[0014] Figure 3 is a positioning accuracy map obtained by using the Beidou-3 narrow lane combination through multi-epoch filtering in the case of a long baseline (50.8 km) by the method of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0015] The present invention will be further illustrated below in conjunction with the drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and not to limit the scope of the present invention.

[0016] Embodiment 1

[0017] A multi-frequency GNSS step-by-step full-probability integer ambiguity resolution method, the specific steps are as follows:

[0018] Step S1. Use multi-frequency GNSS observations to construct a non-combination observation equation, and re-parameterize the basic ambiguity in the parameter domain of the observation value equation to obtain the ultra-wide lane, wide lane, and narrow lane ambiguity parameter forms.

[0019] The multi-frequency GNSS non-combination geometric correlation function model is expressed as:

[0020]

[0021] where ν represents the observation residual vector; the subscript △P i and △φ i represent the differential pseudorange and carrier observation values at frequency point i, respectively; β1, β2, and β3 are the ionospheric delay factors at three frequencies; I is the identity matrix; λ1, λ2, and λ3 are the carrier wavelengths at three frequencies, respectively; and Ion represent the baseline parameter and ionospheric parameter vectors, respectively; A is the design matrix of the baseline parameter ; denotes the ambiguity vector, and the subscripts (0, -1, 1), (1, -1, 0), and (1, 0, 0) represent the combined observation value coefficients of the ultra-wide lane, wide lane, and narrow lane, respectively; l represents the vector of the difference between the observation value and the calculated value (OMC).

[0022] The model shown in Equation (1) adopts independent non-combined observation equations, without introducing observation correlation due to the combination of observation values. Therefore, the observation values are independent of each other, which is convenient for constructing the stochastic model and for sequential solution of the observation values. At the same time, based on the non-combined observation equations, through the ambiguity re-parameterization in the parameter domain, the forms of the ultra-wide lane, wide lane, and narrow lane ambiguities are directly obtained.

[0023] Step S2: Based on the floating-point solutions of ambiguities at all levels, select the candidate values of ambiguities with a high confidence level as the threshold condition, reduce the problem of infinite candidate values with full probability to a finite calculation problem, and obtain the full-probability integer solution based on a finite number of integer candidate vectors.

[0024] During the solution process of the full-probability integer solution based on a finite number of integer candidate vectors, according to the observation model described in Step S1, the floating-point solutions of ambiguities at all levels obtained by the Kalman filter floating-point solution and their variance-covariance matrix are considered. Considering that any set of integer vectors of the same dimension n may be the true value a corresponding to the ambiguity, that is where z i represents any set of n-dimensional integer vectors. According to the probability weighted model, the full-probability integer solution of the ambiguity vector can be obtained that is

[0025]

[0026] where

[0027]

[0028] Among them, is the quadratic form expression of, and its expansion is

[0029] To solve the formula shown in Equation (2), the range of values of \(i\) in Equation (2) is restricted (i.e., \(1\leq i\leq t\)), transforming the infinite problem into a finite problem. When solving the problem of infinity to finiteness, it is inevitable to introduce reduction errors. To control the reduction errors within an acceptable range, the selected finite number of ambiguity candidate vectors need to satisfy the condition that the sum of their probabilities meets the given confidence level condition. That is

[0030]

[0031] The selection process of the \(t\) candidate vectors is as follows: According to the probability Determine the size of the hyper-ellipsoid Within Search to obtain the \(t\) required integer vectors.

[0032] Step S3: Based on the weighted average criterion, calculate the variance of the full probability integer solution of each level of ambiguity, and realize the accuracy evaluation of the ambiguity resolution.

[0033] According to the idea of internal consistency accuracy, calculate according to the weighted average formula to obtain The corresponding variance

[0034]

[0035] Among them, \(w\) i Represents the weight when the true value of the ambiguity is the \(i\)-th ambiguity candidate value \(z\) i Based on Equation (5), the accuracy evaluation of each level of ambiguity is completed.

[0036] Step S4: After the full probability integer solutions of each level of ambiguity are completed, constrain the ambiguity of the next level according to the conditional variance formula, and finally realize the resolution of all ambiguities.

[0037] After the full probability integer solutions of each level of ambiguity are completed, constrain the ambiguity of the next level according to the conditional variance formula, and perform according to Equation (6)

[0038]

[0039] In the formula, Respectively represent And As well as And The covariance matrices between them, and the corresponding subscripts 1 and 2 respectively represent the ambiguity-related quantities that have been solved and to be solved.

[0040] According to Equation (6), the fixation of each level of ambiguity can be realized step by step. That is, when the full probability integer solution of the ultra-wide lane ambiguity is completed, the constrained wide lane ambiguity solution can be obtained. Figure 2This is the positioning accuracy map obtained by using the Beidou-3 ultra-wide lane and wide lane combinations with a single epoch under the condition of a long baseline (50.8 km) for the method of the present invention. Figure 3 This is the positioning accuracy map obtained by using the Beidou-3 narrow lane combination with multi-epoch filtering under the condition of a long baseline (50.8 km) for the method of the present invention. As shown in the appendix Figure 2 As can be seen, under the condition of a long baseline, decimeter-level accuracy can be obtained by using the Beidou-3 ultra-wide lane and wide lane combinations with a single epoch; after the full-probability integer solution of the wide lane ambiguity is completed, the constrained narrow lane ambiguity solution can be obtained, and the positioning effect is as shown in the appendix Figure 3 As can be seen, centimeter-level accuracy can be obtained for the narrow lane solution.

[0041] It should be noted that the above content only illustrates the technical idea of the present invention, and the protection scope of the present invention cannot be limited thereby. For those of ordinary skill in the art of this technology, without departing from the principle of the present invention, several improvements and retouches can be made, and these improvements and retouches all fall within the protection scope of the claims of the present invention.

Claims

1. A multi-frequency GNSS step-by-step full-probability integer ambiguity resolution method, characterized in that, It includes the following steps: S1. Establish a multi-frequency GNSS non-combined geometry correlation function model, re-parameterize the basic ambiguity in the parameter domain of the observation equation, and obtain the ultra-wide lane, wide lane, and narrow lane ambiguity parameter forms; S2. Based on the floating-point solutions of each level of ambiguity, select ambiguity candidate values with a high confidence level as the threshold condition, reduce the infinite candidate value problem with full probability to a finite calculation problem, and obtain the full-probability integer solution based on a finite number of integer candidate vectors; S3. Based on the weighted average criterion, calculate the variances of the full-probability integer solutions of each level of ambiguity, and realize the accuracy evaluation of the ambiguity resolution; S4. After the full-probability integer solutions of each level of ambiguity are completed, constrain the next-level ambiguity according to the conditional variance formula, and finally realize the resolution of all ambiguities.

2. The multi-frequency GNSS step-by-step full-probability integer ambiguity resolution method according to claim 1, wherein: The multi-frequency GNSS non-combined geometry correlation function model in step S1 is: where ν represents the observation residual vector; the subscript △P i and △φ i respectively represent the differential pseudorange and carrier observation value at frequency point i; β1, β2, and β3 are the ionospheric delay factors at three frequencies; I is the identity matrix; λ1, λ2, and λ3 are the carrier wavelengths of the three frequencies respectively; and Ion respectively represent the baseline parameter and ionospheric parameter vectors; A is the design matrix of the baseline parameter ; represents the ambiguity vector, and the subscripts (0, -1, 1), (1, -1, 0), and (1, 0, 0) respectively represent the combined observation value coefficients of the ultra-wide lane, wide lane, and narrow lane; l represents the vector of the observed value minus the calculated value (OMC).

3. The multi-frequency GNSS step-by-step full probability integer ambiguity resolution method according to claim 2, characterized in that: The high confidence threshold condition in step S2 is that the sum of probabilities of a finite number of ambiguity candidate vectors selected satisfies a given confidence condition That is where t represents the number of candidate ambiguities; denotes the probability that under the condition of the current floating solution of the ambiguity i the true value of the ambiguity is the i-th ambiguity candidate value z is the conditional threshold of the given confidence level; The selection process of t candidate vectors is as follows: According to the probability Determine the size of the hyper-ellipsoid Within t required integer vectors are obtained through search.

4. The multi-frequency GNSS step-by-step full probability integer ambiguity resolution method according to claim 2 or 3, characterized in that: In the process of solving the all - probability integer solution based on a finite number of integer candidate vectors in step S2, through the function model of step S1, the floating - point ambiguity solutions at all levels obtained by the Kalman filter floating - point solution and its variance - covariance matrix after that, any set of integer vectors of the same dimension n may be the true value a corresponding to the ambiguity, that is where z i represents any set of n - dimensional integer vectors, and the all - probability integer solution of the ambiguity vector can be obtained according to the probability - weighted model that is In the formula Among them, is the quadratic form expression of, and its expansion is Limit the value range of i, that is, 1 ≤ i ≤ t, and reduce the infinite candidate value problem with full probability to a finite calculation problem.

5. The multi-frequency GNSS step-by-step full probability integer ambiguity resolution method according to claim 4, characterized in that: In the calculation of the ambiguity full probability integer solution variance in step S3, according to the idea of internal consistency accuracy, it is calculated according to the weighted average formula The corresponding variance Complete the accuracy evaluation of each level of ambiguity, and the calculation formula is: where w i represents the weight value when the ambiguity true value is the i-th ambiguity candidate value z i .

6. The multi-frequency GNSS step-by-step full probability integer ambiguity resolution method according to claim 5, characterized in that: In step S4, the ultra-wide lane, wide lane, and narrow lane ambiguity solutions are obtained step by step. That is, after the full-probability integer solution of the ultra-wide lane ambiguity is calculated, the constrained wide lane ambiguity solution can be obtained, and after the full-probability integer solution of the wide lane ambiguity is calculated, the constrained narrow lane ambiguity solution can be obtained.

7. The multi-frequency GNSS step-by-step full-probability integer ambiguity resolution method according to claim 6, characterized in that: In step S4, the conditional variance formula is specifically: In the formula, respectively represent and as well as and The covariance matrix between them, and the corresponding subscripts 1 and 2 respectively represent the ambiguity-related quantities that have been solved and to be solved.

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