CN110764124B - Efficient and reliable multi-frequency multi-mode GNSS observation value covariance matrix estimation method - Google Patents
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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
Technical Field
The invention relates to the technical field of observation value covariance matrix construction in satellite navigation and positioning technology, in particular to a high-efficiency and reliable multi-frequency multi-mode GNSS observation value covariance matrix estimation method.
Background
In GNSS (Global Navigation Satellite System) navigation positioning, it is a very important step to determine a stochastic model, i.e. to construct an observation covariance matrix. Only by constructing a correct covariance matrix, the satellite navigation positioning with high precision and high reliability can be realized. With the development of multi-frequency multi-mode GNSS, the number of observations is greatly increased, so that the dimension of the corresponding covariance matrix is multiplied, and the difficulty in constructing the multi-frequency multi-mode GNSS observations covariance matrix is increased.
Currently, the elements in the observed value covariance matrix are often estimated empirically and passively. As in Real-Time Kinematic (RTK) positioning, only mathematical correlation is considered into the covariance element, since double difference solutions may cause mathematical correlation. In order to obtain reliable Variance covariance components, particularly when there are multiple observation types, methods of Variance covariance component estimation (VCE) and the like are often used. Physical correlations, i.e., spatial, cross-correlation, and temporal correlations, also need to be considered when more realistic covariances are required.
However, for multi-frequency multi-mode GNSS observations, the corresponding covariance matrix is estimated efficiently and accurately, and there is still a need for further resolution. First, in a covariance matrix, it is difficult for a user to estimate all of these correlations due to too many physical correlations, especially in a multi-frequency multi-mode GNSS application scenario, where the estimated variances or covariance elements will be unstable or even meaningless due to the use of VCEs. Second, inverting the covariance matrix results in a significant amount of computation, and therefore the time-dependent covariance matrix needs to be converted to a non-time-dependent block diagonal matrix.
Disclosure of Invention
Aiming at the problems, the invention provides a high-efficiency and reliable multi-frequency multi-mode GNSS observation value covariance matrix estimation method, which actually improves the availability and accuracy of GNSS application.
In order to achieve the technical purpose and achieve the technical effect, the invention is realized by the following technical scheme:
an efficient and reliable multi-frequency multi-mode GNSS observation covariance matrix estimation method comprises the following steps:
acquiring a multi-frequency multi-mode GNSS observation value;
constructing a first covariance matrix according to the multi-frequency multi-mode GNSS observation value;
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 the 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;
substituting the final observed value covariance matrix into a GNSS solution mathematical model to complete navigation positioning.
As a further improvement of the present invention, the multi-frequency multi-mode GNSS observations comprise various types of raw observations 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 ＝KD 0 K T
wherein K is a coefficient matrix, D 1 As a second covariance matrix D 0 Is the first covariance matrix.
As a further improvement of the present invention, the physical correlation coefficient includes a spatial correlation, a cross correlation, and a temporal correlation coefficient.
As a further improvement of the present invention, the spatial correlation and the cross correlation between the observed values are estimated using the cross correlation coefficient, as shown in the following formula:
wherein ,ρij Is l i and lj Cross-correlation coefficient ρ of ji Is l j and li Cross-correlation coefficient, sigma i and σj Respectively is observed value l i and lj Corresponding residual v i and vj Standard deviation of (2); 'Cov' represents the covariance operator;
the time correlation between observations is estimated using autocorrelation coefficients, as shown in the following equation:
wherein τ is the time interval and satisfies
c 0 C at τ=0 τ 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 n observations residuals.
As a further improvement of the present invention, when spatial correlation is extracted:
for spatial correlation, as in the double-difference positioning mode, a single-difference residual SD of any nth satellite is obtained by adding an independent constraint n ；
wherein ,ωn Represents weighting the nth satellite by using the altitude weighting function, and theta represents the corresponding altitude and satisfies omega n ＝sin 2 (θ) and Σω n SD n ＝0；DD mn Representing the double difference residuals for satellites m and n. Based on this single difference residual, a spatial correlation is estimated that is not affected by the mathematical correlation.
As a further improvement of the present invention, the performing a significance test on the extracted physical correlation coefficient specifically includes the following sub-steps:
physical correlation coefficient { ρ } 1 ,…,ρ K The random variable satisfying the independent same distribution and the average value of the samples
Considered as normal distribution; />
By zero equalizationValue test and set original assumption H 0 And alternative hypothesis H 1 Respectively H 0 :ρ＝0，H 1 :ρ≠0；
Will be
Normalization can be performed to obtain:
wherein μ=0, and determining standard deviation σ of the physical correlation coefficient ρ And the significance level alpha, and according to the central limit theorem, estimating a corresponding confidence interval to finish the significance test.
As a further improvement of the present invention, the transforming the third covariance matrix into a block diagonal matrix by using a matrix transformation method, to obtain a final covariance matrix of the observed value specifically includes:
the function model for the adjacent GNSS observations is set as follows:
L * ＝B * X * +E *
wherein ,
B * ＝blkdiag([A i-1 ,A i ])；
l i-1 and li For observations of the i-1 th and i th epoch, A i-1 and Ai Design matrix for i-1 and i epoch, x i-1 and xi Unknown parameters including position coordinates for the i-1 th and i th epoch, e i-1 and ei Observed value noise for the i-1 th and i th epoch;
the covariance matrix of adjacent GNSS observations satisfies Q (i-1) =q (i) =q', and therefore the covariance matrix of adjacent GNSS observations is:
wherein ,
represents a crohn inner integrable operator; to obtain independent observations, the following transformations were performed:
first, let the matrix R satisfy the following equation:
URU T ＝D
wherein 
Then, the two sides of the above formula are multiplied together
Where m is the number of observations observed at once, thus yielding a transformed functional model:
wherein ,
the new covariance matrix at this time is:
obviously, the new covariance matrix is a block diagonal matrix.
Compared with the prior art, the invention has the beneficial effects that:
1. the efficient and reliable multi-frequency multi-mode GNSS observation value covariance matrix estimation method disclosed by the invention has the advantages that the constructed GNSS observation value covariance matrix fully considers the time correlation and the physical correlation coefficient, the reliability is high, and the precise satellite navigation positioning service can be provided for users.
2. The physical correlation coefficient passing the saliency test is reserved by carrying out the saliency test on the physical correlation coefficient. The scheme not only considers the physical correlation coefficients of cross correlation, spatial correlation and time correlation, but also maximally reduces the insignificant physical correlation coefficients, thereby simplifying the structure of the covariance matrix, improving the feasibility and efficiency of the following calculation, and having the advantage of high efficiency.
3. And transforming the covariance matrix into a block diagonal matrix by using a matrix transformation mode to obtain the final covariance matrix of the observed value. The scheme not only considers time correlation, but also changes the time correlation covariance matrix into a time independent covariance matrix, thereby simplifying calculation and being applicable to the field of GNSS real-time dynamic navigation positioning.
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In order that the invention may be more readily understood, a more particular description of the invention will be rendered by reference to specific embodiments that are illustrated in the appended drawings, in which:
FIG. 1 is a flow chart of a method for efficient and reliable multi-frequency and multi-mode GNSS observations covariance matrix estimation according to an embodiment of the invention.
Detailed Description
The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the detailed description and specific examples are intended for purposes of illustration only and are not intended to limit the scope of the invention.
The principle of application of the invention is described in detail below with reference to the accompanying drawings.
The invention provides a high-efficiency and reliable multi-frequency multi-mode GNSS observation value covariance matrix estimation method, which is shown in fig. 1 and specifically comprises the following steps:
(1) Acquiring a multi-frequency multi-mode GNSS observation value;
the multi-frequency multi-mode GNSS observations comprise various 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, different types of observations at different frequencies, such as GPS (Global Positioning System), BDS (BeiDou Navigation Satellite System), GLONASS (GLObal NAvigation Satellite System) and Galileo, are involved;
(2) Constructing a first covariance matrix according to the multi-frequency multi-mode GNSS observation value;
in a specific embodiment of the present invention, the main diagonal of the first covariance matrix is a variance element, and the non-main diagonal is a covariance element; the specific calculation methods of the variance element and the covariance element are all in the prior art, so that redundant description is not needed in the invention; in this embodiment, the variance element of the observed value may be estimated using an index such as a height angle, that is, a function in which the height angle is an argument.
(3) 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 the first covariance matrix through a 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 ＝KD 0 K T
wherein K is a coefficient matrix, D 1 As a second covariance matrix D 0 Is the first covariance matrix.
(4) Extracting physical correlation coefficients of the second covariance matrix, wherein the physical correlation coefficients comprise spatial correlation, cross correlation and time correlation coefficients;
the spatial correlation and the cross correlation are essentially cross correlation coefficients, but the positions of the cross correlation coefficients are different, representing the cross correlation coefficients of different properties, some are spatial correlation coefficients, some are cross correlation coefficients, for this purpose, in a specific embodiment of the invention, the cross correlation coefficients are used to estimate the spatial correlation and the cross correlation between observations, as shown in the following formula:
wherein ,ρij Is l i and lj Cross-correlation coefficient ρ of ji Is l j and li Cross-correlation coefficient, sigma i and σj Respectively is observed value l i and lj Corresponding residual v i and vj Standard deviation of (2); 'Cov' represents the covariance operator;
the time correlation between observations is estimated using autocorrelation coefficients, as shown in the following equation:
wherein τ is the time interval and satisfies
c 0 C at τ=0 τ 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 n observations residuals.
In particular, in extracting the spatial correlation, the method further comprises:
for spatial correlation, as in the double-difference positioning mode, a single-difference residual SD of any nth satellite is obtained by adding an independent constraint n ；
wherein ,ωn Represents weighting the nth satellite by using the altitude weighting function, and theta represents the corresponding altitude and satisfies omega n ＝sin 2 (θ) Sigma omega n SD n ＝0；DD mn Representing the double difference residuals for satellites m and n. Based on this single difference residual, a spatial correlation is estimated that is not affected by the mathematical correlation.
(5) Performing significance test on the extracted physical correlation coefficient;
in a specific embodiment of the present invention, the performing a saliency test on the extracted physical correlation coefficient specifically includes the following sub-steps:
physical correlation coefficient { ρ } 1 ,…,ρ K The random variable satisfying the independent same distribution and the average value of the samples
Considered as normal distribution;
by zero mean test and setting the original assumption H 0 And alternative hypothesis H 1 Respectively H 0 :ρ＝0，H 1 :ρ≠0；
Will be
Normalization can be performed to obtain:
wherein μ=0, and determining standard deviation σ of the physical correlation coefficient ρ And the significance level alpha, and according to the central limit theorem, estimating a corresponding confidence interval to finish the significance test.
(6) Preserving the physical correlation coefficients that pass the saliency test (i.e., preserving significant spatial correlation, cross correlation, and temporal correlation coefficients, and deleting insignificant spatial correlation, cross correlation, and temporal correlation coefficients), and forming a third covariance matrix based on the preserved physical correlation coefficients of the saliency test;
(7) 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;
in a specific embodiment of the present invention, the transforming the third covariance matrix into a block diagonal matrix by using a matrix transformation method to obtain a final covariance matrix of the observed value specifically includes:
the function model for the adjacent GNSS observations is set as follows:
L * ＝B * X * +E *
wherein ,
B * ＝blkdiag([A i-1 ,A i ])；
l i-1 and li For observations of the i-1 th and i th epoch, A i-1 and Ai Design matrix for i-1 and i epoch, x i-1 and xi Unknown parameters including position coordinates for the i-1 th and i th epoch, e i-1 and ei Observed value noise for the i-1 th and i th epoch;
the covariance matrix of adjacent GNSS observations satisfies Q (i-1) =q (i) =q', and therefore the covariance matrix of adjacent GNSS observations is:
wherein ,
represents a crohn inner integrable operator; to obtain independent observations, the following transformations were performed:
first, let the matrix R satisfy the following equation:
URU T ＝D
wherein 
Next, on the pairBoth sides of the formula are multiplied by
Where m is the number of observations observed at once, thus yielding a transformed functional model:
wherein ,
the new covariance matrix at this time is:
obviously, the new covariance matrix is a block diagonal matrix.
(8) Substituting the final covariance matrix of the observed value into a GNSS solution mathematical model to finish navigation positioning; the GNSS solution mathematical model may be any one of the prior arts, as long as navigation positioning can be achieved.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The embodiments of the present invention have been described above with reference to the accompanying drawings, but the present invention is not limited to the above-described embodiments, which are merely illustrative and not restrictive, and many forms may be made by those having ordinary skill in the art without departing from the spirit of the present invention and the scope of the claims, which are all within the protection of the present invention.
The foregoing has shown and described the basic principles and main features of the present invention and the advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (7)
1. An efficient and reliable multi-frequency multi-mode GNSS observation covariance matrix estimation method is characterized by comprising the following steps of:
acquiring a multi-frequency multi-mode GNSS observation value;
constructing a first covariance matrix according to the multi-frequency multi-mode GNSS observation value;
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 the 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;
substituting the final covariance matrix of the observed value into a GNSS solution mathematical model to finish navigation positioning;
the physical correlation coefficient comprises a spatial correlation, a cross correlation and a time correlation coefficient;
estimating the spatial correlation and the cross correlation between the observed values by using the cross correlation coefficient, wherein the following formula is shown:
wherein ,ρij Is l i and lj Cross-correlation coefficient ρ of ji Is l j and li Cross-correlation coefficient, sigma i and σj Respectively is observed value l i and lj Corresponding residual v i and vj Standard deviation of (2); 'Cov' represents the covariance operator;
the time correlation between observations is estimated using autocorrelation coefficients, as shown in the following equation:
wherein τ is the time interval and satisfies
c 0 C at τ=0 τ 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 n observations residuals.
2. The efficient and reliable multi-frequency multi-mode GNSS observation covariance matrix estimation method according to claim 1, wherein: the multi-frequency multi-mode GNSS observations comprise various original observations of different satellite systems and different frequencies.
3. The efficient and reliable multi-frequency multi-mode GNSS observation covariance matrix estimation method according to claim 1, wherein: the main diagonal of the first covariance matrix is a variance element, and the non-main diagonal is a covariance element.
4. The efficient and reliable multi-frequency multi-mode GNSS observation covariance matrix estimation method according to claim 1, wherein: the expression of the second covariance matrix is as follows:
D 1 ＝KD 0 K T
wherein K is a coefficient matrix, D 1 As a second covariance matrix D 0 Is the first covariance matrix.
5. The efficient and reliable multi-frequency multi-mode GNSS observation covariance matrix estimation method according to claim 1, wherein: when extracting spatial correlation:
for spatial correlation, as in the double-difference positioning mode, a single-difference residual SD of any nth satellite is obtained by adding an independent constraint n ；
wherein ,ωn Represents weighting the nth satellite by using the altitude weighting function, and theta represents the corresponding altitude and satisfies omega n ＝sin 2 (θ) and Σω n SD n ＝0；DD mn And (3) a double difference residual representing satellites m and n, and estimating the spatial correlation which is not influenced by the mathematical correlation based on the single difference residual.
6. The efficient and reliable multi-frequency multi-mode GNSS observation covariance matrix estimation method according to claim 1, wherein: the method for performing significance test on the extracted physical correlation coefficient specifically comprises the following substeps: physical correlation coefficient { ρ } 1 ，…，ρ K The random variable satisfying the independent same distribution and the average value of the samples
Considered as normal distribution;
by zero mean test and setting the original assumption H 0 And alternative hypothesis H 1 Respectively H 0 ：ρ＝0，H 1 ：ρ≠0；
Will be
Normalization can be performed to obtain:
wherein μ=0, and determining standard deviation σ of the physical correlation coefficient ρ And the significance level alpha, and according to the central limit theorem, estimating a corresponding confidence interval to finish the significance test.
7. The efficient and reliable multi-frequency multi-mode GNSS observation covariance matrix estimation method according to claim 1, wherein: the method for transforming the third covariance matrix into a block diagonal matrix by utilizing a matrix transformation mode, and obtaining the final covariance matrix of the observed value specifically comprises the following steps:
the function model for the adjacent GNSS observations is set as follows:
L * ＝B * X * +E *
wherein ,
B * ＝blkdiag([A i-1 ，A i ])；
l i-1 and li For observations of the i-1 th and i th epoch, A i-1 and Ai Design matrix for i-1 and i epoch, x i-1 and xi Unknown parameters including position coordinates for the i-1 th and i th epoch, e i-1 and ei Observed value noise for the i-1 th and i th epoch; the covariance matrix of adjacent GNSS observations satisfies Q (i-1) =q (i) =q', and therefore the covariance matrix of adjacent GNSS observations is:
wherein ,
represents a crohn inner integrable operator; to obtain independent observations, the following transformations were performed:
first, let the matrix R satisfy the following equation:
URU T ＝D
wherein 
Then, the two sides of the above formula are multiplied together
Where m is the number of observations observed at once, thus yielding a transformed functional model:
wherein ,
the new covariance matrix at this time is:
obviously, the new covariance matrix is a block diagonal matrix.
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