CN110764124B - Efficient and reliable multi-frequency multi-mode GNSS observation value covariance matrix estimation method - Google Patents

Abstract

The invention discloses a high-efficiency and reliable multi-frequency multi-mode GNSS observation value covariance matrix estimation method, which comprises the steps of obtaining multi-frequency multi-mode GNSS observation values; constructing a first covariance matrix according to the multi-frequency multi-mode GNSS observation values; according to the relation between the type of the observed value and the multi-frequency multi-mode GNSS observed value during positioning, introducing mathematical correlation into a first covariance matrix through a covariance propagation law to obtain a second covariance matrix; extracting a physical correlation coefficient of the second covariance matrix; performing significance test on the extracted physical correlation coefficient; reserving the physical correlation coefficient passing the saliency test, and forming a third covariance matrix based on the reserved physical correlation coefficient of the saliency test; transforming the third covariance matrix into a block diagonal matrix by utilizing a matrix transformation mode to obtain a final covariance matrix of the observed value; the final covariance matrix of observations is substituted into the GNSS solution mathematical model. The invention has the advantages of high calculation efficiency, high reliability and the like, and provides precise satellite navigation positioning service for users.

Description

An efficient and reliable method for estimating the covariance matrix of multi-frequency and multi-mode GNSS observations

Technical Field

The present invention relates to the technical field of observation value covariance matrix construction in satellite navigation and positioning technology, and in particular to an efficient and reliable multi-frequency and multi-mode GNSS observation value covariance matrix estimation method.

Background Art

In GNSS (Global Navigation Satellite System) navigation and positioning, determining the random model, that is, constructing the observation covariance matrix, is a very important step. Only by constructing the correct covariance matrix can high-precision and high-reliability satellite navigation and positioning be achieved. With the development of multi-frequency and multi-mode GNSS, the number of observations has greatly increased, resulting in the exponential expansion of the corresponding covariance matrix dimension, which is bound to increase the difficulty of constructing the covariance matrix of multi-frequency and multi-mode GNSS observations.

At present, the elements in the observation covariance matrix are often estimated empirically and passively. For example, in real-time kinematic (RTK) positioning, since the double difference solution will cause mathematical correlation, only the mathematical correlation is taken into account in the covariance elements. In order to obtain reliable variance covariance components, especially when there are multiple types of observations, the variance covariance component estimation (VCE) method is often used. When a more realistic covariance matrix is needed, physical correlations, namely spatial correlations, cross correlations and temporal correlations, need to be considered.

However, there are still problems to be solved in order to efficiently and accurately estimate the corresponding covariance matrix for multi-frequency and multi-mode GNSS observations. First, since there are too many physical correlations to be estimated in the covariance matrix, it is difficult for users to estimate all of these correlations, especially in multi-frequency and multi-mode GNSS application scenarios. Since VCE may be required, these estimated variance or covariance elements will be unstable or even meaningless. Second, inverting the covariance matrix will result in a huge amount of calculations, so the time-dependent covariance matrix needs to be converted to a non-time-dependent block diagonal matrix.

Summary of the invention

In view of the above problems, the present invention proposes an efficient and reliable multi-frequency and multi-mode GNSS observation covariance matrix estimation method, which effectively improves the availability and accuracy of GNSS applications.

In order to achieve the above technical objectives and the above technical effects, the present invention is implemented through the following technical solutions:

An efficient and reliable method for estimating the covariance matrix of multi-frequency and multi-mode GNSS observations, comprising:

Obtain multi-frequency and multi-mode GNSS observations;

Constructing a first covariance matrix based on the multi-frequency and multi-mode GNSS observations;

According to the relationship between the observation value type during positioning and the multi-frequency multi-mode GNSS observation value, mathematical correlation is introduced into the first covariance matrix through the covariance propagation law to obtain a second covariance matrix;

extracting a physical correlation coefficient of the second covariance matrix;

Conduct significance test on the extracted physical correlation coefficients;

Retain the physical correlation coefficients that pass the significance test, and form a third covariance matrix based on the retained physical correlation coefficients of the significance test;

By means of matrix transformation, the third covariance matrix is transformed into a block diagonal matrix to obtain a final covariance matrix of the observed values;

The covariance matrix of the final observation value is substituted into the GNSS solution mathematical model to complete the navigation positioning.

As a further improvement of the present invention, the multi-frequency and multi-mode GNSS observation values include various types of original observation values of different satellite systems and different frequencies.

As a further improvement of the present invention, the first covariance matrix has variance elements on the main diagonal and covariance elements on the non-main diagonal.

As a further improvement of the present invention, the expression of the second covariance matrix is:

D ₁ ＝K D ₀ K ^T

Where K is the coefficient matrix, _D1 is the second covariance matrix, and _D0 is the first covariance matrix.

As a further improvement of the present invention, the physical correlation coefficient includes spatial correlation, cross correlation and time correlation coefficient.

As a further improvement of the present invention, the spatial correlation and cross-correlation between the observations are estimated using the mutual correlation coefficient, as shown in the following formula:

Where ρ _ij is the correlation coefficient between l _i and l _j , ρ _ji is the correlation coefficient between l _j and l _i , σ _i and σ _j are the standard deviations of the residuals _vi and v _j corresponding to the observations l _i and l _j, respectively; 'Cov' represents the covariance operator;

The time correlation between observations is estimated using the autocorrelation coefficient, as shown below:

c₀为τ＝0时的c_τ，n为观测值残差个数，v(k)和v(k+τ)为第k和k+τ个的观测值残差，

为n个观测值残差的均值。Where τ is the time interval and satisfies

c ₀ is c _τ when τ = 0, n is the number of observation residuals, v(k) and v(k+τ) are the k-th and k+τ-th observation residuals,

is the mean of the residuals of the n observations.

As a further improvement of the present invention, when extracting spatial correlation:

For spatial correlation, such as in the double-difference positioning mode, an independent restriction condition is added to obtain the single-difference residual SD ⁿ of any n-th satellite;

Where ω _n represents the weighting of the nth satellite using the altitude weighting function, θ represents the corresponding altitude angle, and satisfies ω _n = sin ² (θ) and ∑ω _n SD ⁿ = 0; DD ^mn represents the double difference residual of satellites m and n. Based on this single difference residual, the spatial correlation that is not affected by the mathematical correlation is estimated.

As a further improvement of the present invention, the significance test of the extracted physical correlation coefficient specifically includes the following sub-steps:

视为正态分布；The physical correlation coefficients {ρ ₁ ,…,ρ _K } are random variables that satisfy independent and identical distribution, and the sample mean

Considered as normally distributed;

Use the zero mean test, and set the null hypothesis H ₀ and alternative hypothesis H ₁ to be H ₀ :ρ＝0, H ₁ :ρ≠0 respectively;

进行标准化，可以得到：Will

After standardization, we can get:

Among them, μ = 0. At the same time, the standard deviation σ _ρ and the significance level α of the physical correlation coefficient are determined, and the corresponding confidence interval is estimated according to the central limit theorem to complete the significance test.

As a further improvement of the present invention, the third covariance matrix is transformed into a block diagonal matrix by means of matrix transformation to obtain the final covariance matrix of the observed value, specifically including:

Assume that the function model of adjacent GNSS observations is as follows:

L ^* ＝B ^* X ^* +E ^*

B^*＝blkdiag([A_i-1,A_i])；

l_i-1和l_i为第i-1和i个历元的观测值，A_i-1和A_i为第i-1和i个历元的设计矩阵，x_i-1和x_i为第i-1和i个历元的含位置坐标的未知参数，e_i-1和e_i为第i-1和i个历元的观测值噪声；in,

B ^* =blkdiag([A _i-1 ,A _i ]);

l _i-1 and l _i are the observations of the i-1th and i epochs, Ai _-1 and _Ai are the design matrices of the i-1th and i epochs, x _i-1 and x _i are the unknown parameters including position coordinates of the i-1th and i epochs, e _i-1 and e _i are the observation noise of the i-1th and i epochs;

The covariance matrix of adjacent GNSS observations satisfies Q(i-1)=Q(i)=Q′. Therefore, the covariance matrix of adjacent GNSS observations is:

代表克罗内可积算子；为了获得独立观测值，进行如下变换：in,

represents the Krone integrable operator; to obtain independent observations, the following transformation is performed:

First, assume that the matrix R satisfies the following equation:

URU ^T = D

in

其中m是一次性观测到的观测值数量，因此，得到转换后的函数模型：Next, multiply both sides of the above formula by

Where m is the number of observations observed at one time, so the converted function model is obtained:

此时新的协方差阵为：in,

At this time, the new covariance matrix is:

Obviously, the new covariance matrix is a block diagonal matrix.

Compared with the prior art, the present invention has the following beneficial effects:

1. The present invention discloses an efficient and reliable multi-frequency and multi-mode GNSS observation value covariance matrix estimation method. The constructed GNSS observation value covariance matrix fully considers the time correlation and physical correlation coefficients, has the advantage of high reliability, and can provide users with precise satellite navigation and positioning services.

2. Perform a significance test on the physical correlation coefficients and retain the physical correlation coefficients that pass the significance test. This scheme not only takes into account the physical correlation coefficients such as cross-correlation, spatial correlation and temporal correlation, but also minimizes the insignificant physical correlation coefficients, thereby simplifying the structure of the covariance matrix, improving the feasibility and efficiency of subsequent calculations, and has the advantage of high efficiency.

3. Using matrix transformation, the covariance matrix is transformed into a block diagonal matrix to obtain the final covariance matrix of the observation value. This scheme not only takes into account the time correlation, but also transforms the time-correlated covariance matrix into a time-independent covariance matrix, thereby simplifying the calculation and can be used in the field of GNSS real-time dynamic navigation and positioning.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to make the content of the present invention more clearly understood, the present invention is further described in detail below according to specific embodiments and in conjunction with the accompanying drawings, wherein:

FIG1 is a schematic flow chart of an efficient and reliable multi-frequency and multi-mode GNSS observation covariance matrix estimation method according to an embodiment of the present invention.

DETAILED DESCRIPTION

In order to make the purpose, technical solution and advantages of the present invention more clear, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the scope of protection of the present invention.

The application principle of the present invention is described in detail below in conjunction with the accompanying drawings.

The present invention provides an efficient and reliable method for estimating the covariance matrix of multi-frequency and multi-mode GNSS observation values, as shown in FIG1 , which specifically includes the following steps:

(1) Obtain multi-frequency and multi-mode GNSS observations;

The multi-frequency and multi-mode GNSS observations include various types of original observations of different satellite systems and different frequencies. In a specific embodiment of the present invention, taking the RTK positioning mode as an example, it involves observations of different frequencies and types such as GPS (Global Positioning System), BDS (BeiDou Navigation Satellite System), GLONASS (GLObal NAvigation Satellite System) and Galileo.

(2) constructing a first covariance matrix based on the multi-frequency and multi-mode GNSS observations;

In a specific embodiment of the present invention, the main diagonal of the first covariance matrix contains variance elements, and the non-main diagonal contains covariance elements; the specific calculation methods of the variance elements and covariance elements are all existing technologies, so they are not described in detail in the present invention; in this specific implementation, the variance elements of the observed values can be estimated using indicators such as altitude angle, that is, the variance elements of the observed values are estimated using a function with altitude angle as the independent variable.

(3) according to the relationship between the observation value type during positioning and the multi-frequency multi-mode GNSS observation value, mathematical correlation is introduced into the first covariance matrix through the covariance propagation law to obtain a second covariance matrix;

In a specific embodiment of the present invention, the expression of the second covariance matrix is:

D ₁ ＝K D ₀ K ^T

Where K is the coefficient matrix, _D1 is the second covariance matrix, and _D0 is the first covariance matrix.

(4) extracting physical correlation coefficients of the second covariance matrix, wherein the physical correlation coefficients include spatial correlation, cross correlation and time correlation coefficients;

Spatial correlation and cross-correlation are essentially mutual correlation coefficients, but the positions of the mutual correlation coefficients are different, representing mutual correlation coefficients of different properties, some are spatial correlation coefficients, and some are cross-correlation coefficients. Therefore, in a specific embodiment of the present invention, the spatial correlation and cross-correlation between the observations are estimated using the mutual correlation coefficients, as shown in the following formula:

Where ρ _ij is the correlation coefficient between l _i and l _j , ρ _ji is the correlation coefficient between l _j and l _i , σ _i and σ _j are the standard deviations of the residuals _vi and v _j corresponding to the observations l _i and l _j, respectively; 'Cov' represents the covariance operator;

The time correlation between observations is estimated using the autocorrelation coefficient, as shown below:

c₀为τ＝0时的c_τ，n为观测值残差个数，v(k)和v(k+τ)为第k和k+τ个的观测值残差，

为n个观测值残差的均值。Where τ is the time interval and satisfies

c ₀ is c _τ when τ = 0, n is the number of observation residuals, v(k) and v(k+τ) are the k-th and k+τ-th observation residuals,

is the mean of the residuals of the n observations.

In particular, when extracting the spatial correlation, the method further comprises:

For spatial correlation, such as in the double-difference positioning mode, an independent restriction condition is added to obtain the single-difference residual SD ⁿ of any n-th satellite;

Where ω _n represents the weighting of the nth satellite using the altitude weighting function, θ represents the corresponding altitude angle, and satisfies ω _n = sin ² (θ) and ∑ω _n SD ⁿ = 0; DD ^mn represents the double difference residual of satellites m and n. Based on this single difference residual, the spatial correlation that is not affected by the mathematical correlation is estimated.

(5) Conduct significance test on the extracted physical correlation coefficients;

In a specific embodiment of the present invention, the significance test of the extracted physical correlation coefficient specifically includes the following sub-steps:

视为正态分布；The physical correlation coefficients {ρ ₁ ,…,ρ _K } are random variables that satisfy independent and identical distribution, and the sample mean

Considered as normally distributed;

Use the zero mean test, and set the null hypothesis H ₀ and alternative hypothesis H ₁ to be H ₀ :ρ＝0, H ₁ :ρ≠0 respectively;

进行标准化，可以得到：Will

After standardization, we can get:

Among them, μ = 0. At the same time, the standard deviation σ _ρ and the significance level α of the physical correlation coefficient are determined, and the corresponding confidence interval is estimated according to the central limit theorem to complete the significance test.

(6) retaining the physical correlation coefficients that pass the significance test (i.e., retaining the significant spatial correlation, cross-correlation, and time correlation coefficients, and deleting the insignificant spatial correlation, cross-correlation, and time correlation coefficients), and forming a third covariance matrix based on the retained physical correlation coefficients of the significance test;

(7) transforming the third covariance matrix into a block diagonal matrix by means of matrix transformation to obtain the final covariance matrix of the observed values;

In a specific embodiment of the present invention, the third covariance matrix is transformed into a block diagonal matrix by means of matrix transformation to obtain the final covariance matrix of the observed value, specifically including:

Assume that the function model of adjacent GNSS observations is as follows:

L ^* ＝B ^* X ^* +E ^*

B^*＝blkdiag([A_i-1,A_i])；

l_i-1和l_i为第i-1和i个历元的观测值，A_i-1和A_i为第i-1和i个历元的设计矩阵，x_i-1和x_i为第i-1和i个历元的含位置坐标的未知参数，e_i-1和e_i为第i-1和i个历元的观测值噪声；in,

B ^* =blkdiag([A _i-1 ,A _i ]);

l _i-1 and l _i are the observations of the i-1th and i epochs, Ai _-1 and _Ai are the design matrices of the i-1th and i epochs, x _i-1 and x _i are the unknown parameters including position coordinates of the i-1th and i epochs, e _i-1 and e _i are the observation noise of the i-1th and i epochs;

The covariance matrix of adjacent GNSS observations satisfies Q(i-1)=Q(i)=Q′. Therefore, the covariance matrix of adjacent GNSS observations is:

代表克罗内可积算子；为了获得独立观测值，进行如下变换：in,

represents the Krone integrable operator; to obtain independent observations, the following transformation is performed:

First, assume that the matrix R satisfies the following equation:

URU ^T = D

in

其中m是一次性观测到的观测值数量，因此，得到转换后的函数模型：Next, multiply both sides of the above formula by

Where m is the number of observations observed at one time, so the converted function model is obtained:

此时新的协方差阵为：in,

At this time, the new covariance matrix is:

Obviously, the new covariance matrix is a block diagonal matrix.

(8) Substituting the covariance matrix of the final observation value into the GNSS solution mathematical model to complete navigation positioning; the GNSS solution mathematical model can be any one of the existing technologies as long as it can achieve navigation positioning.

Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

The present application is described with reference to the flowchart and/or block diagram of the method, device (system) and computer program product according to the embodiment of the present application. It should be understood that each process and/or box in the flowchart and/or block diagram, and the combination of the process and/or box in the flowchart and/or block diagram can be realized by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device produce a device for realizing the function specified in one process or multiple processes in the flowchart and/or one box or multiple boxes in the block diagram.

These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory produce a manufactured product including an instruction device that implements the functions specified in one or more processes in the flowchart and/or one or more boxes in the block diagram.

These computer program instructions may also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, whereby the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one or more processes in the flowchart and/or one or more boxes in the block diagram.

The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the enlightenment of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the purpose of the present invention and the claims, which all fall within the protection of the present invention.

The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims (7)

1. An efficient and reliable method for estimating the covariance matrix of multi-frequency and multi-mode GNSS observations, characterized by comprising: Obtain multi-frequency and multi-mode GNSS observations; Constructing a first covariance matrix based on the multi-frequency and multi-mode GNSS observations; According to the relationship between the observation value type during positioning and the multi-frequency multi-mode GNSS observation value, mathematical correlation is introduced into the first covariance matrix through the covariance propagation law to obtain a second covariance matrix; extracting a physical correlation coefficient of the second covariance matrix; Conduct significance test on the extracted physical correlation coefficients; Retain the physical correlation coefficients that pass the significance test, and form a third covariance matrix based on the retained physical correlation coefficients of the significance test; By means of matrix transformation, the third covariance matrix is transformed into a block diagonal matrix to obtain a final covariance matrix of the observed values; Substituting the covariance matrix of the final observation value into the GNSS solution mathematical model to complete navigation positioning; The physical correlation coefficients include spatial correlation, cross-correlation and time correlation coefficients; The spatial correlation and cross-correlation between observations are estimated using the mutual correlation coefficient, as shown in the following formula:

Where ρ _ij is the correlation coefficient between l _i and l _j , ρ _ji is the correlation coefficient between l _j and l _i , σ _i and σ _j are the standard deviations of the residuals _vi and v _j corresponding to the observations l _i and l _j, respectively; 'Cov' represents the covariance operator; The time correlation between observations is estimated using the autocorrelation coefficient, as shown below:

Where τ is the time interval and satisfies

c ₀ is c _τ when τ = 0, n is the number of observation residuals, v(k) and v(k+τ) are the k-th and k+τ-th observation residuals,

is the mean of the residuals of the n observations. 2. According to claim 1, an efficient and reliable multi-frequency multi-mode GNSS observation value covariance matrix estimation method is characterized in that the multi-frequency multi-mode GNSS observation values include various types of original observation values of different satellite systems and different frequencies. 3. According to the efficient and reliable multi-frequency and multi-mode GNSS observation value covariance matrix estimation method described in claim 1, it is characterized in that: the main diagonal of the first covariance matrix is the variance element, and the non-main diagonal is the covariance element. 4. The efficient and reliable multi-frequency multi-mode GNSS observation value covariance matrix estimation method according to claim 1, characterized in that: the expression of the second covariance matrix is: D ₁ ＝K D ₀ K ^T Where K is the coefficient matrix, _D1 is the second covariance matrix, and _D0 is the first covariance matrix. 5. The efficient and reliable multi-frequency and multi-mode GNSS observation covariance matrix estimation method according to claim 1 is characterized in that when extracting spatial correlation: For spatial correlation, such as in the double-difference positioning mode, an independent restriction condition is added to obtain the single-difference residual SD ⁿ of any n-th satellite;

Wherein, ω _n represents the weighting of the nth satellite using the altitude angle weighting function, θ represents the corresponding altitude angle, and satisfies ω _n = sin ² (θ) and ∑ω _n SD ⁿ = 0; DD ^mn represents the double difference residual of satellites m and n. Based on this single difference residual, the spatial correlation that is not affected by mathematical correlation is estimated. 6. The efficient and reliable multi-frequency and multi-mode GNSS observation covariance matrix estimation method according to claim 1 is characterized in that: the extracted physical correlation coefficient is subjected to a significance test, specifically comprising the following sub-steps: the physical correlation coefficient {ρ ₁ , ..., ρ _K } is a random variable that satisfies independent and identical distribution, and the sample mean

Considered as normally distributed; Use the zero mean test, and set the null hypothesis H ₀ and alternative hypothesis H ₁ as H ₀ : ρ = 0, H ₁ : ρ ≠ 0; Will

After standardization, we can get:

Among them, μ = 0. At the same time, the standard deviation σ _ρ and the significance level α of the physical correlation coefficient are determined, and the corresponding confidence interval is estimated according to the central limit theorem to complete the significance test. 7. The efficient and reliable multi-frequency multi-mode GNSS observation value covariance matrix estimation method according to claim 1 is characterized in that: the third covariance matrix is transformed into a block diagonal matrix by matrix transformation to obtain the final observation value covariance matrix, specifically comprising: Assume that the function model of adjacent GNSS observations is as follows: L ^* ＝B ^* X ^* +E ^* in,

B ^* =blkdiag([A _i-1 ,A _i ]);

Li _-1 and _Li are the observation values of the i-1th and i-th epochs, Ai _-1 and _Ai are the design matrices of the i-1th and i-th epochs, Xi _-1 and _Xi are the unknown parameters containing position coordinates of the i-1th and i-th epochs, and Ei _-1 and _Ei are the observation value noises of the i-1th and i-th epochs. The covariance matrix of adjacent GNSS observations satisfies Q(i-1) = Q(i) = Q′. Therefore, the covariance matrix of adjacent GNSS observations is:

in,

represents the Krone integrable operator; to obtain independent observations, the following transformation is performed: First, assume that the matrix R satisfies the following equation: URU ^T = D in

Next, multiply both sides of the above formula by

Where m is the number of observations observed at one time, so the converted function model is obtained:

in,

At this time, the new covariance matrix is:

Obviously, the new covariance matrix is a block diagonal matrix.

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