CN112835079A - GNSS self-adaptive weighting positioning method based on edge sampling consistency - Google Patents
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Abstract
The invention relates to a GNSS self-adaptive weighting positioning method based on edge sampling consistency, which comprises the following steps: s1, acquiring initial position solution vectors and initial receiver clock errors of a user receiver by using all available GNSS satellites and pseudo-range measurement values thereof, and initializing all weights of all the GNSS satellites to zero; s2, calculating to obtain a pseudo range residue after positioning according to the initial position solution vector, the initial receiver clock error and the pseudo range measurement value; s3, obtaining a standard deviation estimation value of the GNSS satellite according to the pseudo-range residue after positioning; s4, constructing a probability distribution density function and performing marginalized sampling treatment to obtain the probability that the GNSS satellite and the initial position solution vector have consistency; s5, updating the weight by using the probability; s6, acquiring a new position solution vector and a receiver clock error of the user receiver by using the updated weight; s7, repeating S2-S6 until the position solution vector converges or the repeated iteration number reaches a preset number. The invention has high positioning precision and strong tolerance capability.
Description
Technical Field
The invention relates to the field of satellite navigation and positioning, in particular to a GNSS self-adaptive weighting positioning method based on edge sampling consistency.
Background
The concept of the autonomous Integrity Monitoring (RAIM) of a Global Navigation Satellite System (GNSS) receiver was first generated and developed in the field of civil aviation, and the purpose of the concept is to autonomously monitor the health condition of navigation Satellite signals and timely send an alarm to a user when an abnormality or a fault occurs. Due to design and service guarantee, GNSS constellations such as Global Positioning System (GPS) generally have only one satellite at most, and the probability of two or more satellites failing simultaneously is almost zero, and because the aircraft flies at high altitude and does not have the problem of being influenced by Multipath Effect (Multipath Effect) errors, the early RAIM algorithm is simpler and is proposed based on the single-failure assumption condition.
However, when the receiver is applied to urban vehicle-mounted and pedestrian navigation, the receiver is shielded by objects such as high buildings and trees, users are frequently influenced by multipath errors, and meanwhile, the measured values of a plurality of satellites are greatly abnormal. At this time, the traditional RAIM algorithm based on Single Fault assumption (Single Fault) has difficulty in meeting the use requirement.
Therefore, some improved RAIM algorithms based on multiple-Fault assumption (Multi-Fault) are also proposed in succession. The improved RAIM algorithm can eliminate more abnormal or gross error measurement values, and better ensure the positioning precision and reliability. However, they still have some common problems. Firstly, a detection threshold value is usually set manually according to experience, so that the algorithm is difficult to adapt to different positioning environments and scenes; secondly, the method cannot ensure that correct satellites are removed certainly, and the situation of mistaken removal exists; thirdly, when a plurality of satellites are rejected, the geometric Precision factor (DOP) of the satellite constellation is easily deteriorated, so that a comprehensive optimal solution cannot be necessarily obtained.
Disclosure of Invention
The invention aims to provide a GNSS self-adaptive weighting positioning method based on edge sampling consistency.
In order to achieve the above object, the present invention provides a GNSS adaptive weighted positioning method based on edge sampling consistency, which includes:
s1, obtaining initial position solution vector X of user receiver by utilizing all available GNSS satellites and pseudo-range measurement values thereof0Clock difference delta t from initial receiver0And the weight values omega of all the GNSS satellitesi(i ═ 1,2, …, n) all initializations are set to zero;
s2, solving the vector X according to the initial position0The initial receiver clock difference δ t0And calculating the pseudo-range measurement value to obtain the residual delta rho of the pseudo-range after positioningi；
S3, according to the pseudo range residue delta rho after positioningiObtaining the standard deviation estimated value sigma of the GNSS satellitei；
S4, constructing a probability distribution density function and performing marginalized sampling processing to obtain the GNSS satellite and an initial position solution vector X0Probability of consistency Li；
S5, using the probability LiFor the weight ωi(i ═ 1,2, …, n) update;
s6, utilizing the updated weight omegai(i ═ 1,2, …, n) obtains the new position solution vector X and receiver clock difference δ t for the user receiver.
S7, repeating S2-S6 until the position solution vector X converges or the repeated iteration number reaches a preset number.
In step S1, according to one aspect of the present invention, the initial position solution X of the user receiver is obtained using all available GNSS satellites and their pseudorange measurements0Clock difference delta t from initial receiver0Step (2) ofIn the method, all available GNSS satellites and pseudo-range measurement values thereof are utilized to carry out least square method or weighted least square method solution to obtain the initial position solution vector X0And said initial receiver clock difference δ t0。
According to one aspect of the invention, in step S2, vector X is solved according to the initial position0The initial receiver clock difference δ t0And calculating the pseudo-range measurement value to obtain the residual delta rho of the pseudo-range after positioningiIn the step (2), the vector X is solved according to the initial position0The initial receiver clock difference δ t0Calculating to obtain a geometric distance value between the GNSS satellite and the user receiver, and calculating to obtain the residual delta rho of the positioned pseudo range by using the geometric distance value and the pseudo range measured valuei。
According to an aspect of the invention, in step S3, the pseudorange residuals Δ ρ are determined according to the positioningiObtaining the standard deviation estimated value sigma of the GNSS satelliteiAccording to the residual delta rho of the pseudo range after positioningiAnd acquiring a standard deviation sigma corresponding to the positioning pseudo range under a preset quantile based on Gaussian distribution, and according to the positioned pseudo range residue delta rhoiAnd obtaining the standard deviation estimated value sigma by the standard deviation sigmai。
In step S1, according to one aspect of the present invention, the initial position solution X of the user receiver is obtained using all available GNSS satellites and their pseudorange measurements0Clock difference delta t from initial receiver0In the step (2), comprising:
constructing an observation equation for the GNSS satellite: g Δ x ═ b, where G is a satellite direction cosine matrix of the GNSS satellite, Δ x is a user receiver position and clock error unknown correction vector, and b is a satellite pseudorange observed value residual vector;
when the system of equations is positive, the observation equation has the form of a gaussian-newton iterative solution: Δ x ═ G-1b；
When the equation set is over-timing, solving by using a least square method to obtain an equation: Δ x ═ GTG)-1GTb；
If different weights omega among the GNSS satellites are further consideredi(i ═ 1,2, …, n), a diagonal weight matrix W of size n × n can be constructed: w ═ diag (ω)1,ω2,…,ωn) Wherein n is the number of GNSS satellites; then, a weighted least square method is adopted for solving, and an equation is obtained: Δ x ═ GTCG)-1GTCb，C＝WTW；
Starting from an approximate coordinate position of the user receiver, carrying out iterative solution on the equation set by adopting a least square method or a weighted least square method to obtain an initial position solution vector X of the user receiver0Clock difference delta t from initial receiver0。
According to an aspect of the invention, in step S2, the pseudorange residuals Δ ρ are determinediExpressed as: Δ ρi＝ρi-||Xi-X0||-δt0Wherein X isiAn orbital position coordinate vector, ρ, for the ith (i ═ 1,2, …, n) GNSS satelliteiThe measured pseudoranges are measured for the ith (i ═ 1,2, …, n) GNSS satellite.
According to one aspect of the invention, in step S3, the standard deviation estimate σiExpressed as:
according to an aspect of the invention, in step S4, the probability LiExpressed as:
wherein Γ (a) is a gamma function and has a>0，σ0＝0。
According to an aspect of the invention, in step S5, the updated weight ωiExpressed as: omegai＝ωi+Li。
According to one scheme of the invention, the problem that the traditional RAIM algorithm relies on manual setting of the gross error threshold value can be solved by marginalizing the noise of the measured value within a certain range instead of directly estimating the noise value. And the marginalized probability function superposition quantity can be used as a satellite weight value which is continuously subjected to self-adaptive adjustment, and a Weighted Least Square (WLS) resolving process is optimized. Meanwhile, the method does not directly eliminate the satellite, so that the method can ensure the goodness of the DOP value of the constellation, thereby being easier to obtain a comprehensive optimal solution and having better poor-tolerance positioning capability.
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FIG. 1 is a block diagram schematically illustrating the steps of a GNSS adaptive weighted positioning method according to an embodiment of the present invention;
fig. 2 is a flow chart schematically illustrating a GNSS adaptive weighted positioning method according to an embodiment of the present invention.
Detailed Description
The present invention is described in detail below with reference to the drawings and the specific embodiments, which are not repeated herein, but the embodiments of the present invention are not limited to the following embodiments.
The invention provides a GNSS self-adaptive weighting positioning method based on marginalized sampling consistency to solve the problems. Marginalization (Marginalizing) is a common mathematical method in probability that determines the marginal contribution of one variable by summing the possible values of another variable; sometimes, it is also called "integral on nuisance variable" to eliminate the effect of certain variables in the probability calculation.
Referring to fig. 1 and fig. 2, according to an embodiment of the present invention, a GNSS adaptive weighted positioning method based on edge sample consistency includes:
s1, obtaining initial position solution vector X of user receiver by utilizing all available GNSS satellites and pseudo-range measurement values thereof0Clock difference delta t from initial receiver0And the weight values omega of all GNSS satellitesi(i ═ 1,2, …, n) all initializations are set to zero;
s2, according to the initial positionSolve vector X0Initial receiver clock difference deltat0And calculating the pseudo-range measurement value to obtain the residual delta rho of the pseudo-range after positioningi；
S3, according to the pseudo range residue delta rho after positioningiObtaining standard deviation estimated value sigma of GNSS satellitei；
S4, constructing a probability distribution density function and performing marginalized sampling processing to obtain a GNSS satellite and an initial position solution vector X0Probability of consistency Li；
S5, using probability LiFor the weight value omegai(i ═ 1,2, …, n) update;
s6, utilizing the updated weight omegai(i is 1,2, …, n) acquiring a new position solution vector X of the user receiver and a receiver clock difference deltat;
s7, repeating S2-S6 until the position solution vector X converges or the repeated iteration number reaches a preset number.
Referring to fig. 1 and 2, in step S1, according to an embodiment of the present invention, an initial position solution vector X of the user receiver is obtained by using all available GNSS satellites and their pseudorange measurements0Clock difference delta t from initial receiver0In the step (a), all available n GNSS satellites i (i ═ 1,2, …, n) and pseudo-range measurement values thereof are used for performing least square method or weighted least square method solution to obtain an initial position solution vector X0And initial receiver clock difference deltat0。
In this embodiment, all available GNSS satellites and their pseudorange measurements are used to obtain the initial position solution vector X for the user receiver0Clock difference delta t from initial receiver0In the step (2), comprising:
an observation equation for the GNSS satellite is constructed in the form of a matrix as shown below:
GΔx＝b，
g is a satellite direction cosine matrix of a GNSS satellite, delta x is a correction vector of the position and clock error unknown number of the user receiver, and b is a residual vector of a satellite pseudo-range observed value; in the present embodiment, b is related to the pseudorange measurement, but b is not exactly the pseudorange measurement, and is the difference between the pseudorange measurement and the pseudorange geometry calculation, referred to as the "pseudorange observation residual".
When the system of equations is positive (with n unknowns to be solved, and the system of equations has exactly n independent equations, this case is called "system of equations positive"), the observation equation has the form of a gaussian-newton iterative solution: Δ x ═ G-1b；
When the system of equations is overdetermined (there are n unknowns to be solved, and the number of independent equations in the system of equations is greater than n (i.e., there is redundancy), which is called "overdetermination of the system of equations"), the solution is performed using a least squares method (LS) to obtain the equations: Δ x ═ GTG)-1GTb；
If we further consider different weights ω between GNSS satellites i (i ═ 1,2, …, n)i(i ═ 1,2, …, n), a diagonal weight matrix W of size n × n can be constructed: w ═ diag (ω)1,ω2,…,ωn) Wherein n is the number of GNSS satellites; then a Weighted Least Squares (WLS) method is used to solve, resulting in the equation: Δ x ═ GTCG)-1GTCb，C＝WTW；
Starting from an approximate coordinate position of the user receiver, the equation set is iteratively solved by adopting a least square method or a weighted least square method to obtain an initial position solution vector X of the user receiver0Clock difference delta t from initial receiver0。
In the present embodiment, the initial position solution vector X is completed0Clock difference delta t from initial receiver0After solving, the weight omega of all satellites is obtainediThe (i ═ 1,2, …, n) initialization is set to zero for subsequent updates.
Referring to fig. 1 and 2, according to an embodiment of the present invention, in step S2, the vector X is solved according to the initial position0Initial receiver clock difference deltat0And calculating the pseudo-range measurement value to obtain the residual delta rho of the pseudo-range after positioningiIn the step (2), the vector X is solved according to the initial position0Initial receiver clock difference deltat0Calculating to obtain the geometric distance value between the GNSS satellite and the user receiver, and using the geometryCalculating the distance value and the pseudo-range measurement value to obtain the residual delta rho of the pseudo-range after positioningi。
In the present embodiment, the pseudorange residuals Δ ρ after positioningiExpressed as: Δ ρi＝ρi-||Xi-X0||-δt0Wherein X isiIs the orbital position coordinate vector of the ith (i ═ 1,2, …, n) GNSS satellite, rhoiThe measured pseudoranges are measured for the ith (i ═ 1,2, …, n) GNSS satellite.
Referring to fig. 1 and 2, according to an embodiment of the present invention, in step S3, the pseudorange residue Δ ρ is determined according to the positioniObtaining standard deviation estimated value sigma of GNSS satelliteiAccording to the residual delta rho of the pseudo range after positioningiAnd acquiring a standard deviation sigma corresponding to the positioning pseudo range under a preset quantile based on Gaussian distribution, and according to the residual delta rho of the positioned pseudo rangeiObtaining standard deviation estimated value sigma by standard deviation sigmai. In the present embodiment, the standard deviation estimated value σiExpressed as:
referring to fig. 1 and 2, according to an embodiment of the present invention, in step S4, the probability LiExpressed as:
wherein Γ (a) is a gamma function and has a>0，σ0＝0。
In the present embodiment, the probability L in step S4iObtained by the following steps:
(1) constructing a probability distribution density function:
by considering the general form, a set of measurements is defined as:
where p is the individual measurement values and k is the spatial dimension of the measurement values; according to measurementThe model determined by the values is: theta is equal to theta, wherein
As a collection of individual models.
For a given model θ in k-dimensional space, the residual D (θ, p) of the measurement p is usually calculated from its euclidean Distance (euclidean Distance) to the model θ. If it is further assumed that the residuals of the measurements along the various axes in the k-dimensional space are independent of each other and all have the same variance σ2D (theta, p) corresponds to chi-square with a degree of freedom k2) And (4) distribution. Thus, measured value
The Probability distribution Density function (Proavailability Density) that fits a given model θ is:
in the formula:
and is
Wherein Γ (a) is a gamma function and has a > 0.
(2) Marginalized sampling processing
Without prior probability information, assume that the error (standard deviation) σ of the measured value p is in a larger range (0, σ)max) Inner uniform distribution, i.e. sigma-U (0, sigma)max). Thus, the probability distribution density function L (p | theta, sigma) can be subjected to marginalized sampling processing, and further measured values can be obtained
Accord with givingThe probability of the model θ is determined as:
wherein f (sigma) is a probability distribution density function of the error sigma, and satisfies the following conditions under a uniform distribution model:
thus, the probability formula L (p | θ) can be converted to:
where n denotes the number of all measured values, σiRepresenting the measured value pi(i-1, 2, …, n) standard deviation estimate; in particular, σ00. According to the values of different quantiles of the distribution model, sigma can be determinediThe size of (2). For example, when x2For a measured value p when the distribution is 0.99 quantilei(i ═ 1,2, …, n) has:
namely, the method comprises the following steps:
to this end, a probability function L (p | θ) from which the measured value standard deviation parameter σ is eliminated is constructed by discretization in the manner of edge sampling processing.
(3) Solving for GNSS satellite consistency probability
For GNSS satellites, the pseudorange measurements and their post-positioning residuals are actually only one-dimensional distributions (although from three-dimensional space, we do not use the satellite pseudorange measurements and their residuals as three-dimensional vectors). Therefore, D (θ, p) is in accordance with Gaussian Distribution (Gaussian Distribution) with a degree of freedom of 1, and has:
the marginalized sampling process has the form:
wherein σiValues are taken with different quantiles of the gaussian distribution. For example, when the Gaussian distribution takes a quantile of 0.99, for the measured value pi(i ═ 1,2, …, n) has:
take sigmaiThe maximum value of (i ═ 1,2, …, n) is σmaxFor each satellite pseudo-range measurement pi(i is 1,2, …, n), which is calculated from equation (16) to obtain a solution vector X with the initial position0Probability of consistency L (p)i| θ), abbreviated as Li：
Li＝L(pi|θ)
Finally, the probability LiExpressed as:
wherein Γ (a) is a gamma function and has a>0，σ0＝0，ΔρiI.e. D (theta, p)i)。
Referring to fig. 1 and 2, according to an embodiment of the present invention, L is used in step S5iWeight ω to satellite iiUpdating the weight omegaiExpressed as: omegai＝ωi+Li. Thus, the diagonal weight matrix W, W ═ diag (ω) can be obtained1,ω2,…,ωn)。
Referring to fig. 1 and 2, according to an embodiment of the present invention, the diagonal weight matrix W obtained in the previous step is used to reuse all available satellites and their distance measurements for WLS solution, and obtain a new position solution vector X.
Referring to fig. 1 and 2, according to an embodiment of the present invention, the above process is repeated until the position solution vector satisfies the convergence condition | | X-X0And | ≦ epsilon (epsilon is a given convergence threshold), or until the number of repeated iterative computations reaches a certain number.
The foregoing is merely exemplary of particular aspects of the present invention and devices and structures not specifically described herein are understood to be those of ordinary skill in the art and are intended to be implemented in such conventional ways.
The above description is only one embodiment of the present invention, and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (9)
1. A GNSS self-adaptive weighted positioning method based on edge sampling consistency comprises the following steps:
s1, obtaining initial position solution vector X of user receiver by utilizing all available GNSS satellites and pseudo-range measurement values thereof0Clock difference delta t from initial receiver0And the weight values omega of all the GNSS satellitesi(i ═ 1,2, …, n) all initializations are set to zero;
s2, solving the vector X according to the initial position0The initial receiver clock difference δ t0And calculating the pseudo-range measurement value to obtain the residual delta rho of the pseudo-range after positioningi；
S3, according to the pseudo range residue delta rho after positioningiObtaining the standard deviation estimated value of the GNSS satelliteσi；
S4, constructing a probability distribution density function and performing marginalized sampling processing to obtain the GNSS satellite and an initial position solution vector X0Probability of consistency Li；
S5, using the probability LiFor the weight ωi(i ═ 1,2, …, n) update;
s6, utilizing the updated weight omegai(i ═ 1,2, …, n) to obtain a new position solution vector X and a receiver clock difference δ t for the user receiver;
s7, repeating S2-S6 until the position solution vector X converges or the repeated iteration number reaches a preset number.
2. The GNSS adaptive weighted positioning method based on edge sample consistency as claimed in claim 1, wherein in step S1, all available GNSS satellites and their pseudo-range measurements are used to obtain the initial position solution vector X of the user receiver0Clock difference delta t from initial receiver0In the step (2), all available GNSS satellites and pseudo-range measurement values thereof are utilized to carry out least square method or weighted least square method solution to obtain the initial position solution vector X0And said initial receiver clock difference δ t0。
3. The GNSS adaptive weighted positioning method based on edge sample consistency as claimed in claim 2, wherein in step S2, the vector X is solved according to the initial position0The initial receiver clock difference δ t0And calculating the pseudo-range measurement value to obtain the residual delta rho of the pseudo-range after positioningiIn the step (2), the vector X is solved according to the initial position0The initial receiver clock difference δ t0Calculating to obtain a geometric distance value between the GNSS satellite and the user receiver, and calculating to obtain the residual delta rho of the positioned pseudo range by using the geometric distance value and the pseudo range measured valuei。
4. An edge-based according to claim 2GNSS adaptive weighted positioning method based on sampling consistency, characterized in that in step S3, the pseudo-range residue Δ ρ is determined according to the positioniObtaining the standard deviation estimated value sigma of the GNSS satelliteiAccording to the residual delta rho of the pseudo range after positioningiAnd acquiring a standard deviation sigma corresponding to the positioning pseudo range under a preset quantile based on Gaussian distribution, and according to the positioned pseudo range residue delta rhoiAnd obtaining the standard deviation estimated value sigma by the standard deviation sigmai。
5. The GNSS adaptive weighted positioning method based on edge sample consistency as claimed in claim 2, wherein in step S1, all available GNSS satellites and their pseudo-range measurements are used to obtain the initial position solution vector X of the user receiver0Clock difference delta t from initial receiver0In the step (2), comprising:
constructing an observation equation for the GNSS satellite: g Δ x ═ b, where G is a satellite direction cosine matrix of the GNSS satellite, Δ x is a user receiver position and clock error unknown correction vector, and b is a satellite pseudorange observed value residual vector;
when the system of equations is positive, the observation equation has the form of a gaussian-newton iterative solution: Δ x ═ G-1b；
When the equation set is over-timing, solving by using a least square method to obtain an equation: Δ x ═ GTG)-1GTb；
If different weights omega among the GNSS satellites are further consideredi(i ═ 1,2, …, n), a diagonal weight matrix W of size n × n can be constructed: w ═ diag (ω)1,ω2,…,ωn) Wherein n is the number of GNSS satellites; then, a weighted least square method is adopted for solving, and an equation is obtained: Δ x ═ GTCG)-1GTCb，C＝WTW；
Starting from an approximate coordinate position of the user receiver, carrying out iterative solution on the equation set by adopting a least square method or a weighted least square method to obtain an initial position solution vector X of the user receiver0Clock difference delta t from initial receiver0。
6. The GNSS adaptive weighted positioning method based on edge sample consistency as claimed in claim 5, wherein in step S2, the pseudo-range residue Δ ρ after positioning is performediExpressed as: Δ ρi＝ρi-||Xi-X0||-δt0Wherein X isiAn orbital position coordinate vector, ρ, for the ith (i ═ 1,2, …, n) GNSS satelliteiThe measured pseudoranges are measured for the ith (i ═ 1,2, …, n) GNSS satellite.
7. The GNSS adaptive weighted positioning method based on edge sample consistency according to claim 4, wherein in step S3, the estimated value of standard deviation σ isiExpressed as:
8. the GNSS adaptive weighted positioning method based on edge sample consistency as claimed in claim 6, wherein in step S4, the probability L isiExpressed as:
9. The GNSS adaptive weighted positioning method based on edge sample consistency according to claim 6, wherein in step S5, the updated weight ω isiExpressed as: omegai＝ωi+Li。
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