CN105629278A - GNSS pseudo-range single-point positioning-based high-precision mutual difference value median weighted positioning method - Google Patents

Abstract

The invention discloses a GNSS pseudo-range single-point positioning-based high-precision mutual difference value median weighted positioning method. According to the method, the weighted diagonal matrix of a positioning error equation is constructed according to the pseudo-range error of satellites. In satellite positioning, compared with the least square method, the mutual difference weighted median positioning method can make positioning accuracy improved by more than 30%, and at the same time, the method has the advantages of favorable anti-multipath performance, suitability for single-epoch solution and the like, while, a satellite measurement error-based variance weighting method is not suitable for single-epoch solution. The difference value median weighted positioning method can be popularized and applied to user receiver positioning performance improvement.

Description

A kind of mutual deviation intermediate value weighting localization method of high-precision GNSS pseudorange One-Point Location

Technical field

The present invention relates to the mutual deviation intermediate value weighting localization method in GNSS (GlobalNavigationSatelliteSystem, GPS) pseudorange One-Point Location field, particularly a kind of high-precision GNSS pseudorange One-Point Location.

Background technology

At present, the commonly used WLS of GNSS pseudorange One-Point Location (WeightedLeastSquare, weighted least-squares) localization method improves positioning precision. Conventional WLS method has the WLS method based on elevation of satellite, WLS method based on Satellite observation error variance. Needing the elevation angle of real-time resolving satellite based on the WLS method of elevation of satellite, then adjust satellite according to elevation angle size and participate in resolving the weight of receiver user position, the elevation angle of satellites in view is required by the method; And the WLS method based on Satellite observation error variance needs according to one piece of data, Satellite observation error variance to be solved, then carrying out the setting of weights according to the inverse of Satellite observation error variance, the method is not suitable for single epoch real-time resolving.

Summary of the invention

It is an object of the invention to for the deficiencies in the prior art, the mutual deviation intermediate value weighting localization method of a kind of high-precision GNSS pseudorange One-Point Location is provided, the method positioning precision is high, has good anti-multipath performance, applicable simple epoch solution, can improve the positioning performance of receiver user.

Realize the technical scheme of the object of the invention:

The mutual deviation intermediate value weighting localization method of a kind of high-precision GNSS pseudorange One-Point Location, comprises the steps:

(1) the pseudorange correction value of all satellites in view is obtained;

(2) according to iteration initial value, deduction station star obtains the pseudorange error of all satellites in view from, receiver clock-offsets;

(3) pseudorange error of all satellites in view is sorted, seek the intermediate value of pseudorange error;

(4) with intermediate value for benchmark, carry out difference between satellites with all satellites in view, obtain relative pseudorange error, i.e. mutual deviation, using the absolute value of the mutual deviation weighting diagonal matrix as weights tectonic location error equation reciprocal;

(5) utilize weighting diagonal matrix, solve the position coordinates of receiver user according to weighted least-squares method.

In step (1): the pseudorange to same moment epoch all satellites in view, i.e. code phase observationCarry out pretreatment, time delay error that deduction tropospheric delay error, ionosphere delay error, satellite clock correction cause and the error that relativistic effect causes, hardware corridor delay error, obtain revised pseudorange ��_i��

In step (2): according to (x_u,y_u,z_u,��_t) iteration initial value (x₀,y₀,z₀,B₀), calculate the pseudorange error �� �� of pseudorange after all satellites in view corrections_i, ${\mathrm{\Δ\ρ}}_i=\sqrt{{(x_i-x_0)}^2+{(y_i-y_0)}^2+{(z_i-z_0)}^2}+c\×B_0-{\mathrm{\ρ}}_i.$

Wherein (x_i,y_i,z_i) for satellite coordinate in ECEF coordinate system, i is satellites in view numbering, (i=0,1 ..., n), (x_u,y_u,z_u) refer to receiver coordinate in ECEF coordinate system, ��_tRepresent the time delay that receiver clock-offsets causes.

In step (3): to the pseudorange error �� �� of pseudorange after all satellites in view corrections_iSequence, obtains intermediate value �� ��_mid��

Define arrays �� ��=[�� ��₁����₂...����_n], obtain �� �� after array �� �� ascending order is arranged_asc, namelyMid=fix ((n+1)/2) makes, and wherein fix (.) is bracket function, peek group �� ��_ascIntermediate value �� ��_mid=�� ��_asc(mid)��

In step (4): with �� ��_midAs intermediate value, with intermediate value for benchmark, with other each satellite �� ��_iCarry out difference between satellites, obtain relative pseudorange error, i.e. mutual deviation, using the absolute value of the mutual deviation weighting diagonal matrix �� as weights tectonic location error equation reciprocal

Because | �� ��_i-����_mid| in there will be the number that is 0, be set to ��_mid=| �� ��_i-����_mid|=0, take ��_mid=0.001.

In step (5): adopting weighted least-squares method to resolve and obtain positioning result, its ultimate principle can be expressed as

�� x=(H^T��H)^-1H^T�ئ���

Wherein H represents Direct cosine matrix, and �� is weighting diagonal matrix, and �� �� represents the pseudorange error vector of satellite, �� x=[�� x_u,��y_u,��z_u,����_t] ' it is (x_u,y_u,z_u,��_t) ' iteration renewal amount, make x₀=x₀+��x_u, y₀=y₀+��y_u, z₀=z₀+��z_u, B₀=B₀+����_t, repeat step (3), (4), (5), until �� x_u,��y_u,��z_uSufficiently small, the value that now resolves out is the position coordinates of receiver user and receiver clock-offsets should be: x_��=x₀+��x_u,y_��=y₀+��y_u,z_��=z₀+��z_u,B₀=B₀+����_t��

The method weighting diagonal matrix according to the pseudorange error tectonic location error equation of satellite, it can be effectively improved positioning precision and applicable single epoch real-time resolving.

The invention has the beneficial effects as follows: (1), in satellite fix, compared with least square method, mutual deviation intermediate value weighting localization method can make positioning precision improve more than 30%. (2) the method has the advantages such as good anti-multipath performance, applicable simple epoch solution, can be applied to receiver user positioning performance and improve.

Accompanying drawing explanation

Fig. 1: MDMWLS algorithm (MutualDifferenceMedianWeightedLeastSquares, mutual deviation intermediate value weighting algorithm) and LS (LeastSquare, method of least square) algorithm positioning precision comparison diagram;

Fig. 2: MDMWLS algorithm and the WLS algorithm positioning precision comparison diagram based on Satellite observation error variance weighting.

Detailed description of the invention

Below in conjunction with embodiment and accompanying drawing, present invention is further described, but is not limitation of the invention.

Embodiment:

The mutual deviation intermediate value weighting localization method of a kind of high-precision GNSS pseudorange One-Point Location, comprises the steps:

(1) the pseudorange correction value of all satellites in view is obtained:

Pseudorange to same moment epoch all satellites in view, i.e. code phase observationCarry out pretreatment, time delay error that deduction tropospheric delay error, ionosphere delay error, satellite clock correction cause and the error that relativistic effect causes, hardware corridor delay error, obtain revised pseudorange ��_i;

(2) according to iteration initial value, deduction station star obtains the pseudorange error of all satellites in view from, receiver clock-offsets:

According to (x_u,y_u,z_u,��_t) iteration initial value (x₀,y₀,z₀,B₀), calculate the pseudorange error �� �� of pseudorange after all satellites in view corrections_i, ${\mathrm{\Δ\ρ}}_i=\sqrt{{(x_i-x_0)}^2+{(y_i-y_0)}^2+{(z_i-z_0)}^2}+c\×B_0-{\mathrm{\ρ}}_i.$ Wherein (x_i,y_i,z_i) for satellite coordinate in ECEF coordinate system, i be satellites in view numbering (i=0,1 ..., n), (x_u,y_u,z_u) refer to receiver coordinate in ECEF coordinate system, ��_tRepresent the time delay that receiver clock-offsets causes.

Order reasoning:

The observational equation of pseudorange is:

${\widetilde{\mathrm{\ρ}}}_i=\sqrt{{(x_i-x_u)}^2+{(y_i-y_u)}^2+{(z_i-z_u)}^2}+c\×{\mathrm{\δ}}_t-c\×{{\mathrm{\δ}}_{t_s}}^{\left(i\right)}+c\×\mathrm{tgd}+I^i+T^i+{\mathrm{\ϵ}}_{\mathrm{rmult}}^i+{\mathrm{\ϵ}}_{\mathrm{rel}}^i+{\mathrm{\ϵ}}_{\mathrm{noise}}+{\mathrm{\ϵ}}_{\mathrm{rand}}^i---\left(1\right)$

(1) in formula (i=1,2 ... n, n >=4);It it is the survey code Pseudo-range Observations of i-th satellite; (x_i,y_i,z_i) it is the ECEF coordinate of i-th satellite, (x_u,y_u,z_u) for the ECEF coordinate of receiver to be asked; C is the light velocity; ��_tFor the time delay that receiver clock-offsets causes;For the time delay that satellite clock correction causes; Tgd is hardware corridor time delay; IⁱFor ionosphere delay error; TⁱFor tropospheric delay error;For multipath effect error;For the error that relativistic effect causes; ��_noiseFor receiver noise error;For other random error. WhereinEphemeris parameter can be utilized to be modified, Iⁱ��TⁱMathematical model modeling and ephemeris parameter correction can be passed through. AssumeIⁱ��TⁱRevise completely, orderThen pseudorange equation can be reduced to

$.\left\{\begin{array}{c}{\mathrm{\Δ\ρ}}_i=\sqrt{{(x_1-x_u)}^2+{(y_1-y_u)}^2+{(z_1+z_u)}^2}+c\×{\mathrm{\δ}}_t-{\mathrm{\ρ}}_1\\ \·\\ \·\\ \·\\ {\mathrm{\Δ\ρ}}_n=\sqrt{{(x_n-x_u)}^2+{(y_n-y_u)}^2+{(z_n-z_u)}^2}+c\×{\mathrm{\δ}}_t-{\mathrm{\ρ}}_n\end{array}\right.---\left(2\right)$

(wherein $({\mathrm{\ρ}}_i={\widetilde{\mathrm{\ρ}}}_i-(I^i+T^i-c\×{\mathrm{\δ}}_{t_s}^i+c\×\mathrm{tgd}+{\mathrm{\ϵ}}_{\mathrm{rel}}^i))$

If (x_u,y_u,z_u,��_t) iteration initial value (x₀,y₀,z₀,B₀), calculate the pseudorange biases amount �� �� of all satellites in view_i, ${\mathrm{\Δ\ρ}}_i=\sqrt{{(x_i-x_0)}^2+{(y_i-y_0)}^2+{(z_i-z_0)}^2}+c\×B_0-{\mathrm{\ρ}}_i.$ First �� �� is analyzed_iConstituent, whereinFor the pseudorange value that linearisation point is corresponding, it can change along with the carrying out of iteration, ��_iFor revised pseudorange value, it is constant, although ��_iRevise not exclusively in a practical situation, contain some errors, including multipath effect error, receiver observation noise error, have or not and revise ionosphere and tropospheric error and do not revise satellite orbital error etc. completely completely, but the relative �� of these errors_iIt is a minimum amount, then ��_iRefer to the pseudorange value containing less error that i-th satellite is corresponding with user's physical location, then �� ��_iRefer to the deviation contained between less error pseudorange value and the corresponding pseudorange value of linearisation point that i-th satellite is corresponding with receiver physical location;

(3) pseudorange error of all satellites in view is sorted, seeks the intermediate value of pseudorange error:

To the pseudorange error �� �� of pseudorange after all satellites in view corrections_iSequence, obtains intermediate value �� ��_mid. Define arrays �� ��=[�� ��₁����₂...����_n], obtain �� �� after array �� �� ascending order is arranged_asc, namelyMid=fix ((n+1)/2) makes, and wherein fix (.) is bracket function, peek group �� ��_ascIntermediate value �� ��_mid=�� ��_asc(mid);

(4) with intermediate value for benchmark, carry out difference between satellites with all satellites in view, obtain relative pseudorange error, i.e. mutual deviation, using the absolute value of mutual deviation inverse as the weighting diagonal matrix of weights tectonic location error equation:

With �� ��_midAs intermediate value, with intermediate value for benchmark, with other each satellite �� ��_iCarry out difference between satellites, obtain relative pseudorange error, i.e. mutual deviation, using the absolute value of the mutual deviation weighting diagonal matrix �� as weights tectonic location error equation reciprocal.

Each element in former array �� �� is deducted �� �� successively_midAnd take absolute value, obtain new array ��=[��₁��₂...��_n], wherein

$\left\{\begin{array}{c}{\mathrm{\α}}_1=|{\mathrm{\Δ\ρ}}_1-{\mathrm{\Δ\ρ}}_{\mathrm{mid}}|\\ {\mathrm{\α}}_2=|{\mathrm{\Δ\ρ}}_2-{\mathrm{\Δ\ρ}}_{\mathrm{mid}}|\\ \·\\ \·\\ \·\\ {\mathrm{\α}}_n=|{\mathrm{\Δ\ρ}}_n-{\mathrm{\Δ\ρ}}_{\mathrm{mid}}|\end{array}\right.---\left(3\right)$

Here we analyze ��_i=| �� ��_i-����_mid|, it should be the absolute value that the deviation between pseudorange value and the corresponding pseudorange value of linearisation point containing less error that satellite is corresponding with receiver physical location seeks mutual deviation. For same linearisation point, after seeking mutual deviation, we eliminate the total receiver clock-offsets of same moment epoch difference satellite, receiver noise error equal error. We construct weight coefficient matrix �� and are now

Here to do a process, because �� array there will be the number that is 0, be set to ��_mid=0, so taking ��_mid=0.001, then, be equivalent to the power of deviation that satellite interjacent between pseudorange value and the corresponding pseudorange value of linearisation point containing less error corresponding with receiver physical location to be set to maximum, and according to ��_i=| �� ��_i-����_mid| size the weight of other satellites is set. Why so setting, we are referring initially to a special case, if (x₀,y₀,z₀) it is exactly the physical location of receiver now, corresponding (2) formula, then��ⁱIt is ionosphere, tropospheric error and the satellite orbital error do not revised completely of i-th satellite. So �� ��_iShould be the smaller the better, but in practice due to the impact of various errors, �� ��_iBe have just have negative, so we take the �� �� mediated in �� �� array_midThe weight of that corresponding satellite is maximum. If ��_iMore big, then the multipath effect error of this satellite and other random error are also very big, and mutual deviation is more big, and its weight is more little, can effectively suppress the mutual deviation higher value contribution rate to position error, improve stationarity and the positioning precision of location.

It is emphasized that this �� matrix be one from weighting matrix, it can along with the carrying out of iterative process, and the position coordinates of receiver is once update, and it also can update simultaneously, utilize this weight matrix can greatly reduce the impact of problem satellite, improve the weight of healthy satellite;

(5) utilize weighting diagonal matrix, solve the position coordinates of receiver user according to weighted least-squares method:

Adopting weighted least-squares method to resolve and obtain positioning result, its ultimate principle can be expressed as

�� x=(H^T��H)^-1H^T�ئ���(5)

Wherein H represents Direct cosine matrix, and �� is weighting diagonal matrix, and �� �� represents the pseudorange error vector of satellite, �� x=[�� x_u,��y_u,��z_u,����_t] ' it is (x_u,y_u,z_u,��_t) ' iteration renewal amount, make x₀=x₀+��x_u, y₀=y₀+��y_u, z₀=z₀+��z_u, B₀=B₀+����_t, repeat step (3), (4), (5), until �� x_u,��y_u,��z_uSufficiently small, the value that now resolves out is the position coordinates of receiver user and receiver clock-offsets should be: x_��=x₀+��x_u,y_��=y₀+��y_u,z_��=z₀+��z_u,B₀=B₀+����_t��

As shown in Figure 1, mutual deviation intermediate value weighting location algorithm and common pseudorange One-Point Location method comparison, mutual deviation weighting location algorithm can make positioning precision improve more than 30%, in figure, common location algorithm refers to least-squares algorithm (LS algorithm), Fig. 2 illustrates that the positioning precision of mutual deviation intermediate value weighting location algorithm is also higher than the positioning precision of the location algorithm based on Satellite observation error variance weighting, it is seen that mutual deviation intermediate value weighting location algorithm is effective for the raising of positioning precision; It addition, mutual deviation intermediate value weighting location algorithm has the advantages such as good anti-multipath performance, applicable simple epoch solution, receiver user positioning performance can be applied to and improve.

Claims (7)

1. the mutual deviation intermediate value weighting localization method of a high-precision GNSS pseudorange One-Point Location, it is characterised in that comprise the steps:

(1) the pseudorange correction value of all satellites in view is obtained;

(2) according to iteration initial value, deduction station star obtains the pseudorange error of all satellites in view from, receiver clock-offsets;

(3) pseudorange error of all satellites in view is sorted, seek the intermediate value of pseudorange error;

(4) with intermediate value for benchmark, carry out difference between satellites with all satellites in view, obtain relative pseudorange error, i.e. mutual deviation, using the absolute value of the mutual deviation weighting diagonal matrix as weights tectonic location error equation reciprocal;

(5) utilize weighting diagonal matrix, solve the position coordinates of receiver user according to weighted least-squares method.

2. the mutual deviation intermediate value localization method of high-precision GNSS pseudorange One-Point Location according to claim 1, it is characterised in that in step (1), the pseudorange to same moment epoch all satellites in view, i.e. code phase observationCarry out pretreatment, time delay error that deduction tropospheric delay error, ionosphere delay error, satellite clock correction cause and the error that relativistic effect causes, hardware corridor delay error, obtain revised pseudorange ��_i��

3. the mutual deviation intermediate value localization method of high-precision GNSS pseudorange One-Point Location according to claim 1, it is characterised in that in step (2), according to (x_u,y_u,z_u,��_t) iteration initial value (x₀,y₀,z₀,B₀), calculate the pseudorange error �� �� of pseudorange after all satellites in view corrections_i, $\mathrm{\Δ}{\mathrm{\ρ}}_i=\sqrt{{(x_i-x_0)}^2+{(y_i-y_0)}^2+{(z_i-z_0)}^2}+c\×B_0-{\mathrm{\ρ}}_i.$ Wherein (x_i,y_i,z_i) for satellite coordinate in ECEF coordinate system, i be satellites in view numbering (i=0,1 ..., n), (x_u,y_u,z_u) refer to receiver coordinate in ECEF coordinate system, ��_tRepresent the time delay that receiver clock-offsets causes.

4. the mutual deviation intermediate value localization method of high-precision GNSS pseudorange One-Point Location according to claim 1, it is characterised in that in step (3), to the pseudorange error �� �� of pseudorange after all satellites in view corrections_iSequence, obtains intermediate value �� ��_mid. Define arrays �� ��=[�� ��₁����₂...����_n], obtain �� �� after array �� �� ascending order is arranged_asc, namely

$\mathrm{\Δ}{\mathrm{\ρ}}_{\mathrm{asc}}=\left[\begin{array}{cccc}\mathrm{\Δ}{\mathrm{\ρ}}_{\mathrm{asc}}^{\left(1\right)}& {\mathrm{\Δ\ρ}}_{\mathrm{asc}}^{\left(2\right)}& ...& {\mathrm{\Δ\ρ}}_{\mathrm{asc}}^{\left(n\right)}\end{array}\right],$ Mid=fix ((n+1)/2) makes, and wherein fix (.) is bracket function, peek group �� ��_ascIntermediate value �� ��_mid=�� ��_asc(mid)��

5. the mutual deviation intermediate value localization method of high-precision GNSS pseudorange One-Point Location according to claim 1, it is characterised in that in step (4), with �� ��_midAs intermediate value, with intermediate value for benchmark, with other each satellite �� ��_iCarry out difference between satellites, obtain relative pseudorange error, i.e. mutual deviation, using the absolute value of the mutual deviation weighting diagonal matrix �� as weights tectonic location error equation reciprocal

6. the mutual deviation intermediate value localization method of high-precision GNSS pseudorange One-Point Location according to claim 5, it is characterised in that because | �� ��_i-����_mid| in there will be the number that is 0, be set to ��_mid=| �� ��_i-����_mid|=0, take ��_mid=0.001.

7. the mutual deviation intermediate value localization method of high-precision GNSS pseudorange One-Point Location according to claim 1, it is characterised in that in step (5), adopts weighted least-squares method to resolve and obtains positioning result, and its ultimate principle can be expressed as

�� x=(H^T��H)^-1H^T�ئ���

Wherein H represents Direct cosine matrix, and �� is weighting diagonal matrix, and �� �� represents the pseudorange error vector of satellite,

�� x=[�� x_u,��y_u,��z_u,����_t] ' it is (x_u,y_u,z_u,��_t) ' iteration renewal amount, make x₀=x₀+��x_u, y₀=y₀+��y_u, z₀=z₀+��z_u, B₀=B₀+����_t, repeat step (3), (4), (5), until �� x_u,��y_u,��z_uSufficiently small, the value now resolving out is receiver user coordinate and receiver clock-offsets should be:

x_��=x₀+��x_u,y_��=y₀+��y_u,z_��=z₀+��z_u,B₀=B₀+����_t��