CN112835079B - GNSS self-adaptive weighted positioning method based on edge sampling consistency - Google Patents
GNSS self-adaptive weighted positioning method based on edge sampling consistency Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/42—Determining position
Abstract
The invention relates to a GNSS self-adaptive weighted positioning method based on edge sampling consistency, which comprises the following steps: s1, acquiring an initial position solution vector of a user receiver and an initial receiver clock error by using all available GNSS satellites and pseudo-range measurement values thereof, and setting all weight values of all the GNSS satellites to be zero in an initialized mode; s2, calculating a pseudo-range residual after positioning according to the initial position solution vector, the initial receiver clock error and the pseudo-range measured value; s3, acquiring a standard deviation estimated value of the GNSS satellite according to the positioned pseudo-range residues; s4, constructing a probability distribution density function and carrying out edge sampling processing to obtain the probability that the GNSS satellite has consistency with the initial position solution vector; s5, updating the weight by using the probability; s6, acquiring a new position solution vector of the user receiver and a receiver clock error by using the updated weight; s7, repeating the steps S2 to S6 until the position solution vector converges or the number of repeated iterations reaches a preset number. The invention has high positioning precision and strong anti-poor capability.
Description
Technical Field
The invention relates to the field of satellite navigation and positioning, in particular to a GNSS self-adaptive weighted positioning method based on edge sampling consistency.
Background
The concept of autonomous integrity algorithms (ReceiverAutonomous Integrity Monitoring, RAIM) of global satellite navigation systems (GlobalNavigation Satellite System, GNSS) receivers was first developed and developed in the civil aviation field, with the aim of autonomously monitoring the health of the navigation satellite signals and of giving a warning to the user in time in the event of anomalies or faults. For design and service assurance, GNSS constellations such as the global positioning system (GlobalPositioning System, GPS) generally have at most only one satellite to fail, and the probability of simultaneous failure of two or more satellites is almost zero, and meanwhile, since an aircraft flies at high altitude and is not affected by Multipath Effect (Multipath Effect) errors, early RAIM algorithm is relatively simple and is proposed based on single-failure assumption conditions.
However, when the receiver is applied to urban vehicle-mounted, pedestrian navigation and other conditions, the receiver is shielded by objects such as high buildings, forests and the like, users can be frequently affected by multipath errors, and meanwhile, a plurality of satellite measurement values are greatly abnormal. At this time, it has been difficult for the conventional RAIM algorithm based on Single Fault assumption (Single Fault) to meet the usage requirements.
Thus, some modified RAIM algorithms based on multiple Fault hypothesis (Multi-Fault) have also been proposed. The improved RAIM algorithm can remove more abnormal or coarse and poor measured values, and better ensures positioning accuracy and reliability. However, they still have some common problems. Firstly, a detection threshold value is usually required to be 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 the correct satellite is rejected, and the situation of error rejection exists; thirdly, when a plurality of satellites are removed, the geometric precision factors (Dilutionof Precision, DOP) of the satellite constellation are easy to deteriorate, so that the comprehensive optimal solution is not necessarily obtained.
Disclosure of Invention
The invention aims to provide a GNSS self-adaptive weighted 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, including:
s1, acquiring a user receiver by using all available GNSS satellites and pseudo-range measurement values thereofInitial position solution vector X 0 From the initial receiver clock difference δt 0 And weighting ω for all of the GNSS satellites i (i=1, 2, …, n) all initializations are set to zero;
s2, solving the vector X according to the initial position 0 Said initial receiver clock difference δt 0 And calculating the pseudo-range residual delta rho after the pseudo-range measurement value is positioned i ；
S3, according to the positioned pseudo range residual delta rho i Acquiring a standard deviation estimation value sigma of the GNSS satellite i ；
S4, constructing a probability distribution density function and carrying out edge sampling processing to obtain a solution vector X of the GNSS satellite and the initial position 0 Probability of having consistency L i ；
S5, using the probability L i For the weight omega i (i=1, 2, …, n) update;
s6, utilizing the updated weight omega i (i=1, 2, …, n) obtaining the new position solution vector X of the user receiver and the receiver clock difference δt.
S7, repeating the steps S2 to S6 until the position solution vector X converges or the repeated iteration number reaches the preset number.
According to one aspect of the invention, in step S1, an initial position solution vector X for a user receiver is obtained using all available GNSS satellites and their pseudorange measurements 0 From the initial receiver clock difference δt 0 In the step (a), the least square method or the weighted least square method is used for calculating by utilizing all available GNSS satellites and pseudo-range measurement values thereof to obtain the initial position solution vector X 0 And the initial receiver clock difference δt 0 。
According to one aspect of the invention, in step S2, the vector X is solved according to the initial position 0 Said initial receiver clock difference δt 0 And calculating the pseudo-range residual delta rho after the pseudo-range measurement value is positioned i In the step (a), according to the initial position solution vector X 0 Said initial receiver clock difference δt 0 Calculating a geometry between the GNSS satellite and the user receiverA distance value, and calculating the positioned pseudo-range residual delta rho by using the geometric distance value and the pseudo-range measured value i 。
According to one aspect of the invention, in step S3, a residual Deltaρ is derived from the post-positioning pseudoranges i Acquiring a standard deviation estimation value sigma of the GNSS satellite i In the step (a), according to the post-positioning pseudo-range residual Deltaρ i And obtaining the standard deviation sigma corresponding to the Gaussian distribution under the preset quantile based on the Gaussian distribution, and obtaining the pseudo-range residual delta rho after positioning i And the standard deviation sigma obtains the standard deviation estimation value sigma i 。
According to one aspect of the invention, in step S1, an initial position solution vector X for a user receiver is obtained using all available GNSS satellites and their pseudorange measurements 0 From the initial receiver clock difference δt 0 Comprises the following steps:
constructing an observation equation for the GNSS satellite: gΔx=b, where G is a satellite direction cosine matrix of the GNSS satellite, Δx is a correction vector of the position and clock error unknowns of the user receiver, and b is a residual vector of the satellite pseudo-range observation value;
when the equation set is positive, the observation equation has a Gaussian-Newton iterative solution form: Δx=g -1 b；
When the equation set is over-time, solving by using a least square method to obtain an equation: Δx= (G) T G) -1 G T b；
If further consider the different weights omega between the GNSS satellites i (i=1, 2, …, n), a diagonal weight matrix W of size n×n can be constructed: w=diag (ω) 1 ,ω 2 ,…,ω n ) Wherein n is the number of GNSS satellites; then a weighted least square method is adopted to solve, and an equation is obtained: Δx= (G) T CG) -1 G T Cb，C＝W T W；
Starting from an approximate coordinate position of the user receiver, adopting a least square method or a weighted least square method to iteratively solve the equation set to obtain an initial position solution vector X of the user receiver 0 From the initial receiver clock difference δt 0 。
According to one aspect of the invention, in step S2, the post-positioning pseudorange residual Δρ i Expressed as: Δρ i ＝ρ i -||X i -X 0 ||-δt 0 Wherein X is i An orbital position coordinate vector, ρ, for the ith (i=1, 2, …, n) of the GNSS satellites i Pseudo-range measurements for the i (i=1, 2, …, n) th of the GNSS satellites.
According to an aspect of the present invention, in step S3, the standard deviation estimate σ i Expressed as:
according to one aspect of the invention, in step S4, the probability L i Expressed as:
wherein Γ (a) is a gamma function and has a>0，σ 0 ＝0。
According to one aspect of the present invention, in step S5, the updated weight ω i Expressed as: omega i ＝ω i +L i 。
According to the scheme of the invention, the noise of the measured value is marginalized in a certain range, and the noise value is not directly estimated, so that the problem that the traditional RAIM algorithm relies on manual setting of the coarse difference threshold value can be solved. And the probability function superposition quantity after the marginalization can be used as a satellite weight which is continuously and adaptively adjusted to optimize a weighted least square (Weighted Least Squares, WLS) resolving process. Meanwhile, the satellite is not directly removed by the method, so that the goodness of the constellation DOP value can be ensured, the comprehensive optimal solution can be obtained more easily, and the robust positioning capability is better.
Drawings
FIG. 1 is a block diagram schematically illustrating 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 will be described in detail below with reference to the drawings and the specific embodiments, which are not described in detail herein, but the embodiments of the present invention are not limited to the following embodiments.
The present invention proposes a GNSS adaptive weighted positioning method based on marginalized sample consistency to solve the above-mentioned problems. Marginalization (marginaling) is a common mathematical method in probability that determines the edge contribution of one variable by summing the possible values of another variable; sometimes it is also called "integrate nuisance variable" to eliminate the effect of certain specific variables in probability calculations.
Referring to fig. 1 and 2, according to an embodiment of the present invention, a GNSS adaptive weighted positioning method based on edge sampling consistency includes:
s1, acquiring an initial position solution vector X of a user receiver by using all available GNSS satellites and pseudo-range measurement values thereof 0 From the initial receiver clock difference δt 0 And weighting ω for all GNSS satellites i (i=1, 2, …, n) all initializations are set to zero;
s2, solving the vector X according to the initial position 0 Initial receiver clock difference δt 0 And calculating pseudo-range residual delta rho after the pseudo-range measurement value is positioned i ；
S3, according to the pseudo-range residual delta rho after positioning i Obtaining standard deviation estimation value sigma of GNSS satellite i ；
S4, constructing a probability distribution density function and carrying out edge sampling processing to obtain a GNSS satellite and initial position solution vector X 0 Probability of having consistency L i ；
S5, using probability L i For weight omega i (i＝1,2,…N) updating;
s6, utilizing the updated weight omega i (i=1, 2, …, n) obtaining a new position solution vector X of the user receiver and the receiver clock difference δt;
s7, repeating the steps S2 to S6 until the position solution vector X converges or the number of repeated iterations reaches the preset number.
Referring to fig. 1 and 2, in step S1, an initial position solution vector X of a user receiver is obtained using all available GNSS satellites and pseudorange measurements thereof according to an embodiment of the invention 0 From the initial receiver clock difference δt 0 In the step (a), all available n GNSS satellites i (i=1, 2, …, n) and their pseudo-range measurements are used to perform least square method or weighted least square method to obtain an initial position solution vector X 0 And initial receiver clock skew δt 0 。
In the present embodiment, the initial position solution vector X of the user receiver is obtained by using all available GNSS satellites and their pseudo-range measurements 0 From the initial receiver clock difference δt 0 Comprises the following steps:
an observation equation for a GNSS satellite is constructed in a matrix form as follows:
GΔx＝b，
wherein G is a satellite direction cosine matrix of the GNSS satellite, deltax is a correction vector of the position and clock error unknowns of the user receiver, and b is a residual vector of satellite pseudo-range observation values; in this embodiment, b is related to the pseudorange measurements, but b is not exactly the pseudorange measurements, which is the difference between the pseudorange measurements and the pseudorange geometry calculation, referred to as the "pseudorange observation residue".
When the system of equations is positive (there are n unknowns to solve, and the system of equations has just n independent equations, this case is called "system of equations positive"), the observation equation has a gaussian-newton iterative solution: Δx=g -1 b；
When the system of equations is overdetermined (n unknowns are provided to be solved and the number of independent equations of the system of equations is greater than n (i.e. redundancy exists), this is called "overdetermined system of equations"), a least squares method (LeastSquares, LS) is used to performSolving the rows to obtain the equation: Δx= (G) T G) -1 G T b；
If further consider the different weights ω between the respective 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 ,ω 2 ,…,ω n ) Wherein n is the number of GNSS satellites; then a Weighted Least Squares (WLS) method is used to solve to obtain the equation: Δx= (G) T CG) -1 G T Cb，C＝W T W；
Starting from an approximate coordinate position of the user receiver, adopting a least square method or a weighted least square method to iteratively solve the equation set to obtain an initial position solution vector X of the user receiver 0 From the initial receiver clock difference δt 0 。
In the present embodiment, the initial position solution vector X is completed 0 From the initial receiver clock difference δt 0 After solving, weights ω of all satellites i (i=1, 2, …, n) is initialized to zero for subsequent updates.
As shown in fig. 1 and 2, in step S2, according to an embodiment of the present invention, the vector X is solved according to the initial position 0 Initial receiver clock difference δt 0 And calculating pseudo-range residual delta rho after the pseudo-range measurement value is positioned i In the step (a), the vector X is solved according to the initial position 0 Initial receiver clock difference δt 0 Calculating to obtain a geometrical distance value between the GNSS satellite and the user receiver, and calculating to obtain a pseudo-range residual delta rho after positioning by using the geometrical distance value and the pseudo-range measured value i 。
In the present embodiment, the pseudorange residual Δρ after positioning i Expressed as: Δρ i ＝ρ i -||X i -X 0 ||-δt 0 Wherein X is i An orbital position coordinate vector, ρ, for the i (i=1, 2, …, n) th GNSS satellite i Pseudo-range measurements for the i (i=1, 2, …, n) th GNSS satellite.
As shown in fig. 1 and 2, in step S3, according to one embodiment of the present invention, the pseudorange residuals Δ after positioningρ i Obtaining standard deviation estimation value sigma of GNSS satellite i In the step (a), according to the pseudo range residual Deltaρ after positioning i And based on Gaussian distribution, obtaining the standard deviation sigma corresponding to the Gaussian distribution under the preset quantile, and according to the positioned pseudo-range residual delta rho i And standard deviation sigma obtaining standard deviation estimation value sigma i . In the present embodiment, the standard deviation estimation value σ i Expressed as:
as shown in conjunction with fig. 1 and 2, in step S4, probability L is determined according to an embodiment of the present invention i Expressed as:
wherein Γ (a) is a gamma function and has a>0，σ 0 ＝0。
In the present embodiment, probability L in step S4 i Obtained by the following steps:
(1) Constructing a probability distribution density function:
by considering the generic form, the set of measurements is defined as:where p is each single measurement value and k is the spatial dimension of the measurement value; the model determined from the measurements is: θ ε Θ, whereA collection of individual models.
For a model θ in a given k-dimensional space, the residual D (θ, p) of the measured value p is typically calculated from its euclidean distance (Eucledian Distance) to the model θ. If further assume that the measurement residuals along the respective axes in the k-dimensional space are independent of each other and all have the same variance σ 2 ThenD (θ, p) corresponds to chi-square (χ) with degree of freedom k 2 ) Distribution. Thus, the measured valueThe probability distribution density function (Probability Density) conforming to a given model θ is:
wherein:
and is also provided with
Wherein Γ (a) is a gamma function and has a >0.
(2) Marginalized sampling process
Without prior probability information, it is assumed that the error (standard deviation) σ of the measured value p is within a large range (0, σ max ) Is uniformly distributed in, i.e. sigma-U (0, sigma) max ). Thus, the probability distribution density function L (p|θ, σ) can be subjected to an edge sampling process to obtain a measured valueThe probability of conforming to a given model θ is:
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 into:
wherein n represents the number of all measured values, σ i Representing the measured value p i Standard deviation estimates of (i=1, 2, …, n); in particular, sigma 0 =0. Sigma can be determined according to different quantile values of the distribution model i Is of a size of (a) and (b). For example, when χ 2 For the measurement p, the distribution score was 0.99 i (i=1, 2, …, n) has:
the method comprises the following steps:
to this end, a probability function L (p|θ) from which the measured standard deviation parameter sigma is eliminated is constructed by discretizing by means of an edge sampling process.
(3) Solving GNSS satellite consistency probabilities
For GNSS satellites, the pseudorange measurements and their post-positioning residuals are in fact only one-dimensional (although from three-dimensional space, we do not use the satellite pseudorange measurements and their residuals as three-dimensional vectors). Therefore, D (θ, p) thereof conforms to a gaussian distribution (Gaussian Distribution) with a degree of freedom of 1, and has:
the marginalized samples have the following form:
wherein sigma i Values are taken with different quantile requirements of the gaussian distribution. For example, when the Gaussian distribution takes the quantile 0.99, for the measurement p i (i=1, 2, …, n) has:
sigma is taken out i The maximum value in (i=1, 2, …, n) is σ max Then for each satellite pseudorange measurement p i (i=1, 2, …, n) and the initial position solution vector X can be calculated by using the formula (16) 0 Probability of consistency L (p i I θ), abbreviated as L i ：
L i ＝L(p i |θ)
Finally, probability L i Expressed as: wherein Γ (a) is a gamma function and has a>0，σ 0 ＝0，Δρ i Namely D (theta, p) i )。
As shown in conjunction with fig. 1 and 2, in step S5, L is utilized in accordance with an embodiment of the present invention i Weight ω for satellite i i Updating, and the updated weight omega i Expressed as: omega i ＝ω i +L i . Thus, the aforementioned diagonal weight matrix W, w=diag (ω 1 ,ω 2 ,…,ω n )。
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 measurement values for WLS calculation, and a new position solution vector X is obtained.
As shown in conjunction with fig. 1 and 2, according to one embodiment of the present invention, the above is repeatedThe processing process is carried out until the position solution vector meets the convergence condition of X-X 0 +.epsilon.where ε is a given convergence threshold), or the number of iterative computations is repeated until a certain number is reached.
The foregoing is merely exemplary of embodiments of the invention and, as regards devices and arrangements not explicitly described in this disclosure, it should be understood that this can be done by general purpose devices and methods known in the art.
The above description is only one embodiment of the present invention, and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (8)
1. A GNSS self-adaptive weighted positioning method based on edge sampling consistency comprises the following steps:
s1, acquiring an initial position solution vector X of a user receiver by using all available GNSS satellites and pseudo-range measurement values thereof 0 From the initial receiver clock difference δt 0 And weighting ω for all of the GNSS satellites i All initializations are set to zero; wherein i=1, 2, …, n;
s2, solving the vector X according to the initial position 0 Said initial receiver clock difference δt 0 And calculating the pseudo-range residual delta rho after the pseudo-range measurement value is positioned i ；
S3, according to the positioned pseudo range residual delta rho i Acquiring a standard deviation estimation value sigma of the GNSS satellite i ；
S4, constructing a probability distribution density function and carrying out edge sampling processing to obtain a solution vector X of the GNSS satellite and the initial position 0 Probability of having consistency L i The method comprises the steps of carrying out a first treatment on the surface of the Wherein the probability L i Expressed as:
wherein Γ (a) is a gamma function and has a>0，σ 0 ＝0；
S5, using the probability L i For the weight omega i Updating;
s6, utilizing the updated weight omega i Acquiring a new position solution vector X of the user receiver and a receiver clock difference delta t;
s7, repeating the steps S2 to S6 until the position solution vector X converges or the repeated iteration number reaches the preset number.
2. The method according to claim 1, wherein in step S1, the initial position solution vector X of the user receiver is obtained by using all available GNSS satellites and their pseudo-range measurements 0 From the initial receiver clock difference δt 0 In the step (a), the least square method or the weighted least square method is used for calculating by utilizing all available GNSS satellites and pseudo-range measurement values thereof to obtain the initial position solution vector X 0 And the initial receiver clock difference δt 0 。
3. The method according to claim 2, wherein in step S2, according to the initial position solution vector X 0 Said initial receiver clock difference δt 0 And calculating the pseudo-range residual delta rho after the pseudo-range measurement value is positioned i In the step (a), according to the initial position solution vector X 0 Said initial receiver clock difference δt 0 Calculating a geometrical distance value between the GNSS satellite and the user receiver, and utilizing the geometrical distance valueCalculating a geometric distance value and the pseudo-range measured value to obtain a pseudo-range residual delta rho after positioning i 。
4. The method according to claim 2, wherein in step S3, according to the post-positioning pseudo-range residual Δρ i Acquiring a standard deviation estimation value sigma of the GNSS satellite i In the step (a), according to the post-positioning pseudo-range residual Deltaρ i And obtaining the standard deviation sigma corresponding to the Gaussian distribution under the preset quantile based on the Gaussian distribution, and obtaining the pseudo-range residual delta rho after positioning i And the standard deviation sigma obtains the standard deviation estimation value sigma i 。
5. The method according to claim 2, wherein in step S1, the initial position solution vector X of the user receiver is obtained by using all available GNSS satellites and their pseudo-range measurements 0 From the initial receiver clock difference δt 0 Comprises the following steps:
constructing an observation equation for the GNSS satellite: gΔx=b, where G is a satellite direction cosine matrix of the GNSS satellite, Δx is a correction vector of the position and clock error unknowns of the user receiver, and b is a residual vector of the satellite pseudo-range observation value;
when the equation set is positive, the observation equation has a Gaussian-Newton iterative solution form: Δx=g -1 b；
When the equation set is over-time, solving by using a least square method to obtain an equation: Δx= (G) T G) -1 G T b；
If further consider the different weights omega between the GNSS satellites i Then a diagonal weight matrix W of size n×n can be constructed: w=diag (ω) 1 ,ω 2 ,…,ω n ) Wherein n is the number of GNSS satellites; then a weighted least square method is adopted to solve, and an equation is obtained: Δx= (G) T W T WG) -1 G T W T Wb；
Starting from an approximate coordinate position of the user receiver, adopting a least square method or a weighted least square method to iteratively solve the equation set to obtain an initial position solution vector X of the user receiver 0 From the initial receiver clock difference δt 0 。
6. The method according to claim 5, wherein in step S2, the post-positioning pseudo-range residual Δρ is i Expressed as: Δρ i ＝ρ i -||X i -X 0 ||-δt 0 Wherein X is i For the ith orbital position coordinate vector of the GNSS satellite, ρ i And (5) obtaining pseudo-range measurement values of the ith GNSS satellite.
7. The method according to claim 4, wherein in step S3, the standard deviation estimate σ i Expressed as:
8. the method according to claim 7, wherein in step S5, the updated weight ω i Expressed as: omega i ＝ω i +L i 。
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