CN104536023A - Non-delayed sub-meter differential positioning method of high and low frequency error shunting prediction - Google Patents

Abstract

The invention discloses a non-delayed sub-meter differential positioning method of high and low frequency error shunting prediction. By adopting the strategy of high and low frequency error shunting, high frequency receiver clock errors are separated from low frequency slow-changing errors such as troposphere and ionosphere errors, satellite orbit errors, and satellite clock errors, and the slow-changing errors are used for prediction so as to achieve the purpose of sending correction data to a user in advance and achieve the non-delayed sub-meter differential positioning of a user end. By means of the method, the problem of time delay in sub-meter differential positioning is thoroughly solved. It is error correction instead of original observational value that is sent to the user, and therefore the size of the data sent to the user is greatly decreased, and the stability of wireless communication is improved.

Description

A kind of low-and high-frequency error shunting prediction without time delay sub-meter grade Differential positioning method

Technical field

The present invention relates to field of satellite location, particularly relate to the application of satnav in sub-meter grade Kinematic Positioning.

Background technology

In sub_meter position application, usually adopt pseudo range difference location model, existing pseudo range difference model mainly contains Pseudo-range Observations Differential positioning model and Coordination difference location model two kinds of methods.Pseudo-range Observations Differential positioning model belongs to tight difference model, need the Pseudo-range Observations combination carrying out simultaneous observation, need reference station that real-time observed data is transferred to mobile station user by the method for wireless transmission, the data delay of wireless transmission causes when Differential positioning realizes exists regular hour delay, under normal circumstances between 1-3 second, for vehicle-mounted real-time consumer positioning (real-time dynamic subscriber), this time delay causes sub_meter position result without any using value, and this model needs to transmit raw observation, make transmitted data amount larger, cause the instability of data communication.

Coordination difference location model adopts reference station and terminal user to carry out One-Point Location respectively, then reference station is according to known true coordinate, the coordinate result calculate One-Point Location and the difference of true coordinate send to terminal user, after terminal user receives coordinate correction information, correction is carried out to the One-Point Location coordinate of self and obtains Coordination difference positioning result.The technical bottleneck of this models applying is that reference station and terminal user must select same group of satellite to calculate, and reference station and terminal user use same set of One-Point Location to resolve model, different resolve model because different manufacturers uses in actual applications, cause the more difficult realization of which.

Summary of the invention

Goal of the invention: for above-mentioned prior art, propose a kind of low-and high-frequency error shunting prediction without time delay sub-meter grade Differential positioning method, solution sub_meter position in time delay problem.

Technical scheme: a kind of low-and high-frequency error shunting prediction without time delay sub-meter grade Differential positioning method, comprise the steps:

First, use standard One-Point Location model, isolate reference station receiver clock-offsets, and according to reference station accurate coordinate inverting low frequency aberration, it is poor that described low frequency aberration comprises tropospheric delay, ionosphere delay, the orbit error of satellite and satellite clock mistake;

Then, the low frequency aberration separated is sent to terminal user as forecast information;

Finally, when terminal user carries out the calculation of One-Point Location solution to model, the forecast information received from reference station is used for eliminating the low frequency aberration terminal user's location model.

As preferred version of the present invention, what described a kind of low-and high-frequency error shunting was predicted comprises following concrete steps without time delay sub-meter grade Differential positioning method:

Step (1), single reference station continuous acquisition Satellite Observations, and carry out real time data pre-service; Wherein said Satellite Observations comprises satellite L1, L2 carrier phase observation data and C1, P2 Pseudo-range Observations;

Step (2), uses standard One-Point Location model, computing reference station receiver clock-offsets:

(21), if current time is t, t is made ₁=t-t ₀, t ₀get the arbitrary value between 10 ~ 100 seconds, then t ₁the pseudorange observation equation of moment reference station to i satellite is:

$P_B^i\left(t_1\right)={\mathrm{\ρ}}_B^i\left(t_1\right)+c\·\mathrm{\δ}{t}_B\left(t_1\right)-c\·\mathrm{\δ}{t}^i\left(t_1\right)-c\·{\mathrm{dt}}^i\left(t_1\right)+{\mathrm{\δ}}_{\mathrm{trop}}^i\left(t_1\right)+{\mathrm{\δ}}_{\mathrm{ion}}^i\left(t_1\right)+{\mathrm{\δ}}_{\mathrm{others}}^i\left(t_1\right)---\left(1\right)$

Wherein: for t ₁moment reference station is to the Pseudo-range Observations of i satellite; for t ₁moment reference station is to the geometric distance of i satellite; δ t _b(t ₁) be t ₁moment reference station receiver clock-offsets; δ t ⁱ(t ₁) be t ₁the satellite clock correction of moment i satellite; Dt ⁱ(t ₁) be t ₁the satellite clock mistake of moment i satellite is poor; for t ₁the tropospheric delay of moment i satellite; for t ₁the ionosphere delay of moment i satellite; for t ₁the orbit error of moment i satellite; for t ₁other errors in moment; C is the light velocity;

(22), hypothetical reference station receives n satellite, then obtain the pseudorange observation equation of described reference station to n satellite, then construct t ₁the error equation of moment reference station One-Point Location model:

V _B(t ₁)＝B _B(t ₁)X _B(t ₁)-L _B(t ₁) (2)

Wherein:

$V_B\left(t_1\right)=\left[\begin{array}{c}{V}_B^1\left(t_1\right)\\ V_B^2\left(t_1\right)\\ .\\ .\\ .\\ V_B^n\left(t_1\right)\end{array}\right]B_B\left(t_1\right)=\left[\begin{array}{cccc}{l}_B^1\left(t_1\right)& m_B^1\left(t_1\right)& n_B^1\left(t_1\right)& -1\\ l_B^2\left(t_1\right)& m_B^2\left(t_1\right)& n_B^2\left(t_1\right)& -1\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ l_B^n\left(t_1\right)& m_B^n\left(t_1\right)& n_B^n\left(t_1\right)& -1\end{array}\right]$

$X_B=\left[\begin{array}{c}\mathrm{\δ}{x}_B\left(t_1\right)\\ \mathrm{\δ}{y}_B\left(t_1\right)\\ \mathrm{\δ}{z}_B\left(t_1\right)\\ \mathrm{\δ}{t}_B\left(t_1\right)\end{array}\right]L_B\left(t_1\right)=\left[\begin{array}{c}{L}_B^1\left(t_1\right)\\ L_B^2\left(t_1\right)\\ .\\ .\\ .\\ L_B^n\left(t_1\right)\end{array}\right]$

If reference station coordinates is (X _b, Y _b, Z _b), for t ₁moment coordinate is (X ⁱ(t ₁), Y ⁱ(t ₁), Z ⁱ(t ₁)) i-th satellite:

$l_B^i\left(t_1\right)=\frac{X_B-X^i\left(t_1\right)}{{\mathrm{\ρ}}_B^i\left(t_1\right)},m_B^i\left(t_1\right)=\frac{Y_B-Y^i\left(t_1\right)}{{\mathrm{\ρ}}_B^i\left(t_1\right)},n_B^i\left(t_1\right)=\frac{Z_B-Z^i\left(t_1\right)}{{\mathrm{\ρ}}_B^i\left(t_1\right)}$

$L_B^i\left(t_1\right)=P_B^i\left(t_1\right)-{\mathrm{\ρ}}_B^i\left(t_1\right)+c\·\mathrm{\δ}{t}^i\left(t_1\right)$

Wherein, for t ₁moment reference station is to the geometric distance of i satellite; Use least-squares estimation criterion to described t ₁the moment error equation of reference station One-Point Location model solves, and can obtain:

${\hat{X}}_B\left(t_1\right)={\left(B_B^T\left(t_1\right)P_B\left(t_1\right)B_B\left(t_1\right)\right)}^{-1}{B}_B^T\left(t_1\right)P_B\left(t_1\right)L_B\left(t_1\right)---\left(3\right)$

Wherein, Quan Zhen P _b(t ₁) be:

Wherein, (δ x _b(t ₁), δ y _b(t ₁), δ z _b(t ₁)) be reference station One-Point Location coordinate corrective value, its valuation is δ t _b(t ₁) be t ₁moment terminal receiver clock correction, its valuation is for t ₁moment satellite i is relative to the elevation angle of reference station B;

(3) according to t ₁the reference station observation data in moment, inverting obtains t ₁the reference station low frequency aberration in moment described low frequency aberration comprise the tropospheric delay of satellite ionosphere delay the orbit error of satellite satellite clock mistake difference dt ⁱ(t ₁) and other errors wherein:

$\begin{array}{c}{\mathrm{dL}}_B^i\left(t\right)=-c\·{\mathrm{dt}}^i\left(t_1\right)+{\mathrm{\δ}}_{\mathrm{trop}}^i\left(t_1\right)+{\mathrm{\δ}}_{\mathrm{ion}}^i\left(t_1\right)+{\mathrm{\δ}}_{\mathrm{others}}^i\left(t_1\right)\\ =P_B^i\left(t_1\right)-{\mathrm{\ρ}}_B^i\left(t_1\right)-c\·d{\hat{t}}_B\left(t_1\right)+c\·\mathrm{\δ}{t}^i\left(t_1\right)\end{array}---\left(4\right)$

By t ₁the reference station low frequency aberration in moment terminal user is sent to as forecast information, described in as terminal user at the low frequency aberration calculated value of t to i satellite observation

(4) One-Point Location of terminal user:

Suppose that user receives m satellite, and n >=m, i.e. the satellite that receives of terminal user, reference station also can ensure to receive;

(41) terminal user's One-Point Location model, is constructed: the pseudorange observation equation of t terminal user to i satellite is:

$P_r^i\left(t\right)={\mathrm{\ρ}}_r^i\left(t\right)+c\·\mathrm{\δ}{t}_r\left(t\right)-c\·\mathrm{\δ}{t}^i\left(t\right)-c\·{\mathrm{dt}}^i\left(t\right)+{\mathrm{\δ}}_{\mathrm{trop}}^i\left(t\right)+{\mathrm{\δ}}_{\mathrm{ion}}^i\left(t\right)+{\mathrm{\δ}}_{\mathrm{orbit}}^i\left(t\right)+{\mathrm{\δ}}_{\mathrm{others}}^i\left(t\right)$

Wherein: for t terminal user is to the Pseudo-range Observations of i satellite; for t terminal user is to the geometric distance of i satellite; δ t _rt () is t terminal user receiver clock-offsets; δ t ⁱt satellite clock correction that () is t i satellite; Dt ⁱt satellite clock mistake that () is t i satellite is poor; for the tropospheric delay of t i satellite; for the ionosphere delay of t i satellite; for the orbit error of t i satellite; for other errors of t; C is the light velocity;

(42), obtain the pseudorange observation equation of t terminal user to a described m satellite according to described step (41), the error equation of structure t terminal user One-Point Location model is:

V _r(t)＝B _r(t)X _r(t)-L _r(t) (5)

Wherein:

$V_r\left(t\right)=\left[\begin{array}{c}{V}_r^1\left(t\right)\\ V_r^2\left(t\right)\\ .\\ .\\ .\\ V_r^m\left(t\right)\end{array}\right]B_r\left(t\right)=\left[\begin{array}{cccc}{l}_r^1\left(t\right)& m_r^1\left(t\right)& n_r^1\left(t\right)& -1\\ l_r^2\left(t\right)& m_r^2\left(t\right)& n_r^2\left(t\right)& -1\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ l_r^m\left(t\right)& m_r^m\left(t\right)& n_r^m\left(t\right)& -1\end{array}\right]$

$X_r\left(t\right)=\left[\begin{array}{c}\mathrm{\δ}{x}_r\left(t\right)\\ \mathrm{\δ}{y}_r\left(t\right)\\ \mathrm{\δ}{z}_r\left(t\right)\\ \mathrm{\δ}{t}_r\left(t\right)\end{array}\right]L_r\left(t\right)=\left[\begin{array}{c}{L}_r^1\left(t\right)\\ L_r^2\left(t\right)\\ .\\ .\\ .\\ L_r^m\left(t\right)\end{array}\right]$

If the initial coordinate of terminal user is (X _r0(t), Y _r0(t), Z _r0(t)), be (X for t coordinate ⁱ(t), Y ⁱ(t), Z ⁱ(t)) i-th satellite:

$l_r^i\left(t\right)=\frac{X_{r0}\left(t\right)-X^i\left(t\right)}{{\mathrm{\ρ}}_r^i\left(t\right)},m_r^i\left(t\right)=\frac{Y_{r0}\left(t\right)-Y^i\left(t\right)}{{\mathrm{\ρ}}_r^i\left(t\right)},n_r^i\left(t\right)=\frac{Z_{r0}\left(t\right)-Z^i\left(t\right)}{{\mathrm{\ρ}}_r^i\left(t\right)}$

Can obtain according to the forecast information received from reference station:

$\begin{array}{c}{L}_r^i\left(t\right)=P_r^i\left(t\right)-{\mathrm{\ρ}}_r^i\left(t\right)+c\·\mathrm{\δ}{t}^i\left(t\right)-{\mathrm{dL}}_B^i\left(t\right)\\ =P_r^i\left(t\right)-{\mathrm{\ρ}}_r^i\left(t\right)+c\·\mathrm{\δ}{t}^i\left(t\right)+P_B^i\left(t_1\right)-{\mathrm{\ρ}}_B^i\left(t_1\right)-c\·{\hat{t}}_B\left(t_1\right)+c\·\mathrm{\δ}{t}^i\left(t_1\right)\end{array}---\left(6\right)$

Wherein, for t i satellite is to the geometric distance of terminal user;

(43), use the error equation of least-squares estimation criterion to described t terminal user One-Point Location model to solve, can obtain:

${\hat{X}}_r\left(t\right)={\left(B_r^T\left(t\right)P_r\left(t\right)B_r\left(t\right)\right)}^{-1}{B}_r^T\left(t\right)P_r\left(t\right)L_r\left(t\right)---\left(7\right)$

Wherein weigh battle array P _r(t) be:

Wherein, (δ x _r(t), δ y _r(t), δ z _r(t)) be t terminal user One-Point Location coordinate corrective value, its valuation is δ t _rt () is t terminal receiver clock correction, its valuation is for t ₁moment satellite i is relative to the elevation angle of terminal user r;

(5) described in basis computing terminal user coordinates (X _r(t), Y _r(t), Z _r(t)):

$\left[\begin{array}{c}{X}_r\left(t\right)\\ Y_r\left(t\right)\\ Z_r\left(t\right)\end{array}\right]=\left[\begin{array}{c}{X}_{r0}\left(t\right)\\ Y_{r0}\left(t\right)\\ Z_{r0}\left(t\right)\end{array}\right]+\left[\begin{array}{c}\mathrm{\δ}{\hat{x}}_r\left(t\right)\\ \mathrm{\δ}{\hat{y}}_r\left(t\right)\\ \mathrm{\δ}{\hat{z}}_r\left(t\right)\end{array}\right]---\left(8\right).$

Beneficial effect: the inventive method is by shunting the error in reference station observation data, error is divided into other errors such as the orbit error of the tropospheric delay of the reference station receiver clock-offsets of high frequency and low frequency, ionosphere delay, satellite and satellite clock mistake difference, uses the HF receiver clock correction separated to estimate troposphere ionospheric error, satellite clock correction, the satellite orbital error of low frequency.Because low frequency aberration changes not obvious at short notice, so the error estimated also can as the predicated error in coming few minutes, this predicated error is sent to terminal user, user can the observed reading of usage forecastings error correction self, then One-Point Location calculating is carried out, although One-Point Location is now identical with One-Point Location on model, eliminate low frequency aberration part in observed reading, calculation result is suitable with Differential positioning.By being sent to terminal user using resolving the low frequency aberration that reference station One-Point Location model obtains as warning signal, reference station will be without the need to comprising tropospheric delay, ionosphere delay, other errors such as the orbit error of satellite and satellite clock mistake difference are all transferred to mobile station user by the method for wireless transmission in interior real-time original observed data, thus greatly reduce volume of transmitted data, improve the stability of radio communication, eliminate the data delay in Differential positioning, make Differential positioning really can be used for real-time dynamic subscriber, especially the location, sub-meter grade track in intelligent transportation.

Accompanying drawing explanation

Fig. 1 is system composition structural drawing;

Fig. 2 is flow chart of data processing figure;

Fig. 3 is the Satellite empty graph of hourly observation data;

Fig. 4 is reference station receiver clock-offsets (high frequency error part);

Fig. 5 is gps system G02 and G10 two satellite low frequency aberrations;

Fig. 6 is BDS system C04 and C06 two satellite low frequency aberrations;

Fig. 7 is one hour Calculation Plane error;

Fig. 8 calculates vertical error in one hour;

Fig. 9 is one day Calculation Plane error;

Figure 10 calculates vertical error in one day.

Embodiment

Below in conjunction with accompanying drawing the present invention done and further explain.

A kind of low-and high-frequency error shunting prediction without time delay sub-meter grade Differential positioning method: first, use standard One-Point Location model, isolate reference station receiver clock-offsets, and according to reference station accurate coordinate inverting low frequency aberration, it is poor that described low frequency aberration comprises tropospheric delay, ionosphere delay, the orbit error of satellite and satellite clock mistake; Then, the low frequency aberration separated is sent to terminal user as forecast information; Finally, when terminal user carries out the calculation of One-Point Location solution to model, the forecast information received from reference station is used for eliminating the low frequency aberration terminal user's location model.The method comprises following concrete steps:

Step (1), single reference station continuous acquisition Satellite Observations, and be real-time transmitted to central server and carry out real time data pre-service; Wherein said Satellite Observations comprises satellite L1, L2 carrier phase observation data and C1, P2 Pseudo-range Observations;

Step (2), uses standard One-Point Location model, computing reference station receiver clock-offsets:

(21), if current time is t, t is made ₁=t-t ₀, t ₀get the arbitrary value between 10 ~ 100 seconds, then t ₁the pseudorange observation equation of moment reference station to i satellite is:

$P_B^i\left(t_1\right)={\mathrm{\ρ}}_B^i\left(t_1\right)+c\·\mathrm{\δ}{t}_B\left(t_1\right)-c\·\mathrm{\δ}{t}^i\left(t_1\right)-c\·{\mathrm{dt}}^i\left(t_1\right)+{\mathrm{\δ}}_{\mathrm{trop}}^i\left(t_1\right)+{\mathrm{\δ}}_{\mathrm{ion}}^i\left(t_1\right)+{\mathrm{\δ}}_{\mathrm{others}}^i\left(t_1\right)---\left(1\right)$

Wherein: for t ₁moment reference station is to the Pseudo-range Observations of i satellite; for t ₁moment reference station is to the geometric distance of i satellite; δ t _b(t ₁) be t ₁moment reference station receiver clock-offsets; δ t ⁱ(t ₁) be t ₁the satellite clock correction of moment i satellite, calculates by radio news program and obtains; Dt ⁱ(t ₁) be t ₁the satellite clock mistake of moment i satellite is poor, i.e. t ₁the satellite clock correction calculated value δ t of moment i satellite ⁱ(t ₁) and the true clock correction of i satellite between difference, namely broadcast ephemeris calculates the error component of satellite clock correction; for t ₁the tropospheric delay of moment i satellite; for t ₁the ionosphere delay of moment i satellite; for t ₁the orbit error of moment i satellite; for t ₁other errors in moment, as observed reading noise etc.; C is the light velocity;

(22), hypothetical reference station receives n satellite, then obtain the pseudorange observation equation of described reference station to n satellite, then construct t ₁the error equation of moment reference station One-Point Location model:

V _B(t ₁)＝B _B(t ₁)X _B(t ₁)-L _B(t ₁) (2)

Wherein:

$V_B\left(t_1\right)=\left[\begin{array}{c}{V}_B^1\left(t_1\right)\\ V_B^2\left(t_1\right)\\ .\\ .\\ .\\ V_B^n\left(t_1\right)\end{array}\right]B_B\left(t_1\right)=\left[\begin{array}{cccc}{l}_B^1\left(t_1\right)& m_B^1\left(t_1\right)& n_B^1\left(t_1\right)& -1\\ l_B^2\left(t_1\right)& m_B^2\left(t_1\right)& n_B^2\left(t_1\right)& -1\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ l_B^n\left(t_1\right)& m_B^n\left(t_1\right)& n_B^n\left(t_1\right)& -1\end{array}\right]$

$X_B=\left[\begin{array}{c}\mathrm{\δ}{x}_B\left(t_1\right)\\ \mathrm{\δ}{y}_B\left(t_1\right)\\ \mathrm{\δ}{z}_B\left(t_1\right)\\ \mathrm{\δ}{t}_B\left(t_1\right)\end{array}\right]L_B\left(t_1\right)=\left[\begin{array}{c}{L}_B^1\left(t_1\right)\\ L_B^2\left(t_1\right)\\ .\\ .\\ .\\ L_B^n\left(t_1\right)\end{array}\right]$

Reference station coordinates is precise known values, if reference station coordinates is (X _b, Y _b, Z _b), for t ₁moment coordinate is (X ⁱ(t ₁), Y ⁱ(t ₁), Z ⁱ(t ₁)) i-th satellite:

$l_B^i\left(t_1\right)=\frac{X_B-X^i\left(t_1\right)}{{\mathrm{\ρ}}_B^i\left(t_1\right)},m_B^i\left(t_1\right)=\frac{Y_B-Y^i\left(t_1\right)}{{\mathrm{\ρ}}_B^i\left(t_1\right)},n_B^i\left(t_1\right)=\frac{Z_B-Z^i\left(t_1\right)}{{\mathrm{\ρ}}_B^i\left(t_1\right)}$

$L_B^i\left(t_1\right)=P_B^i\left(t_1\right)-{\mathrm{\ρ}}_B^i\left(t_1\right)+c\·\mathrm{\δ}{t}^i\left(t_1\right)$

Wherein, for t ₁moment reference station is to the geometric distance of i satellite; Use least-squares estimation criterion to described t ₁the moment error equation of reference station One-Point Location model solves, and can obtain:

${\hat{X}}_B\left(t_1\right)={\left(B_B^T\left(t_1\right)P_B\left(t_1\right)B_B\left(t_1\right)\right)}^{-1}{B}_B^T\left(t_1\right)P_B\left(t_1\right)L_B\left(t_1\right)---\left(3\right)$

Wherein, Quan Zhen P _b(t ₁) be:

Wherein, (δ x _b(t ₁), δ y _b(t ₁), δ z _b(t ₁)) be reference station One-Point Location coordinate corrective value, its valuation is δ t _b(t ₁) be t ₁moment terminal receiver clock correction, its valuation is for t ₁moment satellite i is relative to the elevation angle of reference station B;

(3) according to t ₁the reference station observation data in moment, inverting obtains t ₁the reference station low frequency aberration in moment described low frequency aberration comprise the tropospheric delay of satellite ionosphere delay the orbit error of satellite satellite clock mistake difference dt ⁱ(t ₁) and other errors wherein:

$\begin{array}{c}{\mathrm{dL}}_B^i\left(t\right)=-c\·{\mathrm{dt}}^i\left(t_1\right)+{\mathrm{\δ}}_{\mathrm{trop}}^i\left(t_1\right)+{\mathrm{\δ}}_{\mathrm{ion}}^i\left(t_1\right)+{\mathrm{\δ}}_{\mathrm{others}}^i\left(t_1\right)\\ =P_B^i\left(t_1\right)-{\mathrm{\ρ}}_B^i\left(t_1\right)-c\·d{\hat{t}}_B\left(t_1\right)+c\·\mathrm{\δ}{t}^i\left(t_1\right)\end{array}---\left(4\right)$

By t ₁the reference station low frequency aberration in moment terminal user is sent to as forecast information, described in as terminal user at the low frequency aberration calculated value dL of t to i satellite observation ⁱ _b(t);

(4) One-Point Location of terminal user:

Because reference station is arranged on the extraordinary position of observation condition, and employ comparatively high-end receiver; Suppose that user receives m satellite, and n >=m, i.e. the satellite that receives of terminal user, reference station also can ensure to receive;

(41) terminal user's One-Point Location model, is constructed: the pseudorange observation equation of t terminal user to i satellite is:

$P_r^i\left(t\right)={\mathrm{\ρ}}_r^i\left(t\right)+c\·\mathrm{\δ}{t}_r\left(t\right)-c\·\mathrm{\δ}{t}^i\left(t\right)-c\·{\mathrm{dt}}^i\left(t\right)+{\mathrm{\δ}}_{\mathrm{trop}}^i\left(t\right)+{\mathrm{\δ}}_{\mathrm{ion}}^i\left(t\right)+{\mathrm{\δ}}_{\mathrm{orbit}}^i\left(t\right)+{\mathrm{\δ}}_{\mathrm{others}}^i\left(t\right)$

Wherein: for t terminal user is to the Pseudo-range Observations of i satellite; for t terminal user is to the geometric distance of i satellite; δ t _rt () is t terminal user receiver clock-offsets; for the satellite clock correction of t i satellite; Dt ⁱt satellite clock mistake that () is t i satellite is poor; for the tropospheric delay of t i satellite; for the ionosphere delay of t i satellite; for the orbit error of t i satellite; for other errors of t; C is the light velocity;

(42), obtain the pseudorange observation equation of t terminal user to a described m satellite according to described step (41), the error equation of structure t terminal user One-Point Location model is:

V _r(t)＝B _r(t)X _r(t)-L _r(t) (5)

Wherein:

$V_r\left(t\right)=\left[\begin{array}{c}{V}_r^1\left(t\right)\\ V_r^2\left(t\right)\\ .\\ .\\ .\\ V_r^m\left(t\right)\end{array}\right]B_r\left(t\right)=\left[\begin{array}{cccc}{l}_r^1\left(t\right)& m_r^1\left(t\right)& n_r^1\left(t\right)& -1\\ l_r^2\left(t\right)& m_r^2\left(t\right)& n_r^2\left(t\right)& -1\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ l_r^m\left(t\right)& m_r^m\left(t\right)& n_r^m\left(t\right)& -1\end{array}\right]$

$X_r\left(t\right)=\left[\begin{array}{c}\mathrm{\δ}{x}_r\left(t\right)\\ \mathrm{\δ}{y}_r\left(t\right)\\ \mathrm{\δ}{z}_r\left(t\right)\\ \mathrm{\δ}{t}_r\left(t\right)\end{array}\right]L_r\left(t\right)=\left[\begin{array}{c}{L}_r^1\left(t\right)\\ L_r^2\left(t\right)\\ .\\ .\\ .\\ L_r^m\left(t\right)\end{array}\right]$

If the initial coordinate of terminal user is (X _r0(t), Y _r0(t), Z _r0(t)), be (X for t coordinate ⁱ(t), Y ⁱ(t), Z ⁱ(t)) i-th satellite:

$l_r^i\left(t\right)=\frac{X_{r0}\left(t\right)-X^i\left(t\right)}{{\mathrm{\ρ}}_r^i\left(t\right)},m_r^i\left(t\right)=\frac{Y_{r0}\left(t\right)-Y^i\left(t\right)}{{\mathrm{\ρ}}_r^i\left(t\right)},n_r^i\left(t\right)=\frac{Z_{r0}\left(t\right)-Z^i\left(t\right)}{{\mathrm{\ρ}}_r^i\left(t\right)}$

Can obtain according to the forecast information received from reference station:

$\begin{array}{c}{L}_r^i\left(t\right)=P_r^i\left(t\right)-{\mathrm{\ρ}}_r^i\left(t\right)+c\·\mathrm{\δ}{t}^i\left(t\right)-{\mathrm{dL}}_B^i\left(t\right)\\ =P_r^i\left(t\right)-{\mathrm{\ρ}}_r^i\left(t\right)+c\·\mathrm{\δ}{t}^i\left(t\right)+P_B^i\left(t_1\right)-{\mathrm{\ρ}}_B^i\left(t_1\right)-c\·{\hat{t}}_B\left(t_1\right)+c\·\mathrm{\δ}{t}^i\left(t_1\right)\end{array}---\left(6\right)$

Wherein, for t i satellite is to the geometric distance of terminal user;

(43), use the error equation of least-squares estimation criterion to described t terminal user One-Point Location model to solve, can obtain:

${\hat{X}}_r\left(t\right)={\left(B_r^T\left(t\right)P_r\left(t\right)B_r\left(t\right)\right)}^{-1}{B}_r^T\left(t\right)P_r\left(t\right)L_r\left(t\right)---\left(7\right)$

Wherein weigh battle array P _r(t) be:

Wherein, (δ x _r(t), δ y _r(t), δ z _r(t)) be t terminal user One-Point Location coordinate corrective value, its valuation is δ t _rt () is t terminal receiver clock correction, its valuation is for t ₁moment satellite i is relative to the elevation angle of terminal user r;

(5) described in basis computing terminal user coordinates (X _r(t), Y _r(t), Z _r(t)):

$\left[\begin{array}{c}{X}_r\left(t\right)\\ Y_r\left(t\right)\\ Z_r\left(t\right)\end{array}\right]=\left[\begin{array}{c}{X}_{r0}\left(t\right)\\ Y_{r0}\left(t\right)\\ Z_{r0}\left(t\right)\end{array}\right]+\left[\begin{array}{c}\mathrm{\δ}{\hat{x}}_r\left(t\right)\\ \mathrm{\δ}{\hat{y}}_r\left(t\right)\\ \mathrm{\δ}{\hat{z}}_r\left(t\right)\end{array}\right]---\left(8\right).$

When using the method in multisystem fusion location, for different navigational system, when carrying out reference station One-Point Location, in each epoch of observation, corresponding each navigational system all needs by solving receiver clock-offsets, thus obtains the forecast information of each navigational system.

The present embodiment adopts two groups of data to verify, wherein one group is a hour data, and sampling rate is 1 second, the spacing 19KM of reference station and terminal, do not changing the calculation result in satellite situation for verifying, when these data calculate, reference station uses the data prediction low frequency aberration part of first 10 seconds; Other one group is a day data, and sampling rate is 30 seconds, and the distance between reference station and terminal is 10KM, and for verifying the stability that whole day calculates, when these data calculate, reference station uses the data prediction low frequency aberration part of first 30 seconds.

One, a hour data checking

1. first carry out data prediction, gps system selects satellite to be G02, G04, G05 and G10; BDS Systematic selection C01, C02, C03, C04, C06 and C08; Concrete stellar map as shown in Figure 3;

2. use C1 observed reading, utilize standard One-Point Location model to carry out standard One-Point Location, use formula (3) to calculate the reference station receiver clock-offsets part of high frequency, as shown in Figure 4, owing to there being GPS and BDS two navigational system, so there are 2 receiver clock-offsets each epoch;

3. use formula (4) to be finally inversed by the troposphere ionospheric error of every satellite, satellite clock mistake difference and the low frequency aberration part such as satellite orbital error, as shown in Figure 5 and Figure 6, in this case display is clear, gps system only shows G02 and G10 satellite, and BDS system only shows C04 and C05 satellite;

(4) terminal receives the low frequency aberration part of reference station prediction in first 10 seconds, formula (5) is used to carry out One-Point Location, formula (8) is utilized to obtain terminal user's coordinate, and compare with the pseudo range difference positioning result of standard, result as shown in Figure 7 and Figure 8, concrete average and medial error more as shown in table 1, as can be seen from Table 1, two kinds of methods can ensure that on N and E direction average is less, and have the error of more than 1 meter in the u-direction, the reason producing this phenomenon is the spacing 19KM of reference station and terminal, the impact of its troposphere and ionospheric error belongs to systematic error (low frequency aberration), be mainly reflected on elevation direction, as can be seen from medial error, the scheme medial error that this patent proposes can meet sub-meter grade and require (medial error <1m) in N and E direction, and the method that this patent proposes is higher than the pseudo range difference positioning precision of standard, reason is that the pseudo range difference of standard uses two differential mode type, amplify larger to noise, and the method that this patent proposes is to carrying out difference between satellite, belong to a kind of form of the single differential mode type in border, station,

Table 1 two kinds of Pattern localization error contrasts

Two, a day data checking

Above-mentioned in order to carry out comparatively detailed description to each step result, unify the satellite of reference station and terminal participation calculating, and in actual conditions, reference station is with terminal and the identical satellite of non-usage, in order to prove the versatility of this patent, use the data of a day to verify this patent, result as shown in Figure 9 and Figure 10, as seen from the figure, use this patent method stability better.

The above is only the preferred embodiment of the present invention; it should be pointed out that for those skilled in the art, under the premise without departing from the principles of the invention; can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.

Claims (2)

1. low-and high-frequency error shunting prediction without a time delay sub-meter grade Differential positioning method, it is characterized in that, comprise the steps:

First, use standard One-Point Location model, isolate reference station receiver clock-offsets, and according to reference station accurate coordinate inverting low frequency aberration, it is poor that described low frequency aberration comprises tropospheric delay, ionosphere delay, the orbit error of satellite and satellite clock mistake;

Then, the low frequency aberration separated is sent to terminal user as forecast information;

Finally, when terminal user carries out the calculation of One-Point Location solution to model, the forecast information received from reference station is used for eliminating the low frequency aberration terminal user's location model.

2. a kind of low-and high-frequency error shunting prediction according to claim 1 without time delay sub-meter grade Differential positioning method, it is characterized in that, comprise following concrete steps:

Step (1), single reference station continuous acquisition Satellite Observations, and carry out real time data pre-service; Wherein said Satellite Observations comprises satellite L1, L2 carrier phase observation data and C1, P2 Pseudo-range Observations;

Step (2), uses standard One-Point Location model, computing reference station receiver clock-offsets:

(21), if current time is t, t is made ₁=t-t ₀, t ₀get the arbitrary value between 10 ~ 100 seconds, then t ₁the pseudorange observation equation of moment reference station to i satellite is:

$P_B^i\left(t_1\right)={\mathrm{\&rho;}}_B^i\left(t_1\right)+c\&CenterDot;\mathrm{\&delta;}{t}_B\left(t_1\right)-c\&CenterDot;\mathrm{\&delta;}{t}^i\left(t_1\right)-c\&CenterDot;{\mathrm{dt}}^i\left(t_1\right)+{\mathrm{\&delta;}}_{\mathrm{trop}}^i\left(t_1\right)+{\mathrm{\&delta;}}_{\mathrm{ion}}^i\left(t_1\right)+{\mathrm{\&delta;}}_{\mathrm{orbit}}^i\left(t_1\right)+{\mathrm{\&delta;}}_{\mathrm{others}}^i\left(t_1\right)---\left(1\right)$

Wherein: for t ₁moment reference station is to the Pseudo-range Observations of i satellite; for t ₁moment reference station is to the geometric distance of i satellite; δ t _b(t ₁) be t ₁moment reference station receiver clock-offsets; δ t ⁱ(t ₁) be t ₁the satellite clock correction of moment i satellite; Dt ⁱ(t ₁) be t ₁the satellite clock mistake of moment i satellite is poor; for t ₁the tropospheric delay of moment i satellite; for t ₁the ionosphere delay of moment i satellite; for t ₁the orbit error of moment i satellite; for t ₁other errors in moment; C is the light velocity;

(22), hypothetical reference station receives n satellite, then obtain the pseudorange observation equation of described reference station to n satellite, then construct t ₁the error equation of moment reference station One-Point Location model:

V _B(t ₁)＝B _B(t ₁)X _B(t ₁)-L _B(t ₁) (2)

Wherein:

$V_B\left(t_1\right)=\left[\begin{array}{c}{V}_B^1\left(t_1\right)\\ V_B^2\left(t_1\right)\\ .\\ .\\ .\\ V_B^n\left(t_1\right)\end{array}\right]$ $B_B\left(t_1\right)=\left[\begin{array}{cccc}{l}_B^1\left(t_1\right)& m_B^1\left(t_1\right)& n_B^1\left(t_1\right)& -1\\ l_B^2\left(t_1\right)& m_B^2\left(t_1\right)& n_B^2\left(t_1\right)& -1\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ l_B^n\left(t_1\right)& m_B^n\left(t_1\right)& n_B^n\left(t_1\right)& -1\end{array}\right]$

$X_B\left(t_1\right)=\left[\begin{array}{c}\mathrm{\&delta;}{x}_B\left(t_1\right)\\ \mathrm{\&delta;}{y}_B\left(t_1\right)\\ \mathrm{\&delta;}{z}_B\left(t_1\right)\\ \mathrm{\&delta;}{t}_B\left(t_1\right)\end{array}\right]$ $L_B\left(t_1\right)=\left[\begin{array}{c}{L}_B^1\left(t_1\right)\\ L_B^2\left(t_1\right)\\ .\\ .\\ .\\ L_B^n\left(t_1\right)\end{array}\right]$

If reference station coordinates is (X _b, Y _b, Z _b), for t ₁moment coordinate is (X ⁱ(t ₁), Y ⁱ(t ₁), Z ⁱ(t ₁)) i-th satellite:

$l_B^i\left(t_1\right)=\frac{X_B-X^i\left(t_1\right)}{{\mathrm{\&rho;}}_B^i\left(t_1\right)}$ $m_B^i\left(t_1\right)=\frac{Y_B-Y^i\left(t_1\right)}{{\mathrm{\&rho;}}_B^i\left(t_1\right)}$ $n_B^i\left(t_1\right)=\frac{Z_B-Z^i\left(t_1\right)}{{\mathrm{\&rho;}}_B^i\left(t_1\right)}$

$L_B^i\left(t_1\right)=P_B^i\left(t_1\right)-{\mathrm{\&rho;}}_B^i\left(t_1\right)+c\&CenterDot;\mathrm{\&delta;}{t}^i\left(t_1\right)$

Wherein, for t ₁moment reference station is to the geometric distance of i satellite; Use least-squares estimation criterion to described t ₁the moment error equation of reference station One-Point Location model solves, and can obtain:

${\hat{X}}_B\left(t_1\right)={\left(B_B^T\left(t_1\right)P_B\left(t_1\right)B_B\left(t_1\right)\right)}^{-1}{B}_B^T\left(t_1\right)P_B\left(t_1\right)L_B\left(t_1\right)---\left(3\right)$

Wherein, Quan Zhen P _b(t ₁) be:

Wherein, (δ x _b(t ₁), δ y _b(t ₁), δ z _b(t ₁)) be reference station One-Point Location coordinate corrective value, its valuation is δ t _b(t ₁) be t ₁moment terminal receiver clock correction, its valuation is (i=1,2 ..., n) be t ₁moment satellite i is relative to the elevation angle of reference station B;

(3) according to t ₁the reference station observation data in moment, inverting obtains t ₁the reference station low frequency aberration in moment described low frequency aberration comprise the tropospheric delay of satellite ionosphere delay the orbit error of satellite satellite clock mistake difference dt ⁱ(t ₁) and other errors wherein:

$\begin{array}{c}{\mathrm{dL}}_B^i\left(t\right)=-c\&CenterDot;{\mathrm{dt}}^i\left(t_1\right)+{\mathrm{\&delta;}}_{\mathrm{trop}}^i\left(t_1\right)+{\mathrm{\&delta;}}_{\mathrm{ion}}^i\left(t_1\right)+{\mathrm{\&delta;}}_{\mathrm{orbit}}^i\left(t_1\right)+{\mathrm{\&delta;}}_{\mathrm{others}}^i\left(t_1\right)\\ =P_B^i\left(t_1\right)-{\mathrm{\&rho;}}_B^i\left(t_1\right)-c\&CenterDot;d{\hat{t}}_B\left(t_1\right)+c\&CenterDot;\mathrm{\&delta;}{t}^i\left(t_1\right)\end{array}---\left(4\right)$

By t ₁the reference station low frequency aberration in moment terminal user is sent to as forecast information, described in as terminal user at the low frequency aberration calculated value of t to i satellite observation

(4) One-Point Location of terminal user:

Suppose that user receives m satellite, and n >=m, i.e. the satellite that receives of terminal user, reference station also can ensure to receive;

(41) terminal user's One-Point Location model, is constructed: the pseudorange observation equation of t terminal user to i satellite is:

$P_r^i\left(t\right)={\mathrm{\&rho;}}_r^i\left(t\right)+c\&CenterDot;\mathrm{\&delta;}{t}_r\left(t\right)-c\&CenterDot;\mathrm{\&delta;}{t}^i\left(t\right)-c\&CenterDot;{\mathrm{dt}}^i\left(t\right)+{\mathrm{\&delta;}}_{\mathrm{trop}}^i\left(t\right)+{\mathrm{\&delta;}}_{\mathrm{ion}}^i\left(t\right)+{\mathrm{\&delta;}}_{\mathrm{orbit}}^i\left(t\right)+{\mathrm{\&delta;}}_{\mathrm{others}}^i\left(t\right)$

Wherein: for t terminal user is to the Pseudo-range Observations of i satellite; for t terminal user is to the geometric distance of i satellite; δ t _rt () is t terminal user receiver clock-offsets; δ t ⁱt satellite clock correction that () is t i satellite; Dt ⁱt satellite clock mistake that () is t i satellite is poor; for the tropospheric delay of t i satellite; for the ionosphere delay of t i satellite; for the orbit error of t i satellite; for other errors of t; C is the light velocity;

(42), obtain the pseudorange observation equation of t terminal user to a described m satellite according to described step (41), the error equation of structure t terminal user One-Point Location model is:

V _r(t)＝B _r(t)X _r(t)-L _r(t) (5)

Wherein:

$V_r\left(t\right)=\left[\begin{array}{c}{V}_r^1\left(t\right)\\ V_r^2\left(t\right)\\ .\\ .\\ .\\ V_r^m\left(t\right)\end{array}\right]$ $B_r\left(t\right)=\left[\begin{array}{cccc}{l}_r^1\left(t\right)& m_r^1\left(t\right)& n_r^1\left(t\right)& -1\\ l_r^2\left(t\right)& m_r^2\left(t\right)& n_r^2\left(t\right)& -1\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ l_r^m\left(t\right)& m_r^m\left(t\right)& n_r^m\left(t\right)& -1\end{array}\right]$

$X_r\left(t\right)=\left[\begin{array}{c}\mathrm{\&delta;}{x}_r\left(t\right)\\ \mathrm{\&delta;}{y}_r\left(t\right)\\ \mathrm{\&delta;}{z}_r\left(t\right)\\ \mathrm{\&delta;}{t}_r\left(t\right)\end{array}\right]$ $L_r\left(t\right)=\left[\begin{array}{c}{L}_r^1\left(t\right)\\ L_r^2\left(t\right)\\ .\\ .\\ .\\ L_r^m\left(t\right)\end{array}\right]$

If the initial coordinate of terminal user is (X _r0(t), Y _r0(t), Z _r0(t)), be (X for t coordinate ⁱ(t), Y ⁱ(t), Z ⁱ(t)) i-th satellite:

$l_r^i\left(t\right)=\frac{X_{r0}\left(t\right)-X^i\left(t\right)}{{\mathrm{\&rho;}}_r^i\left(t\right)},$ $m_r^i\left(t\right)=\frac{Y_{r0}\left(t\right)-Y^i\left(t\right)}{{\mathrm{\&rho;}}_r^i\left(t\right)},$ $n_r^i\left(t\right)=\frac{Z_{r0}\left(t\right)-Z^i\left(t\right)}{{\mathrm{\&rho;}}_r^i\left(t\right)}$

Can obtain according to the forecast information received from reference station:

$\begin{array}{c}{L}_r^i\left(t\right)=P_r^i\left(t\right)-{\mathrm{\&rho;}}_r^i\left(t\right)+c\&CenterDot;\mathrm{\&delta;}{t}^i\left(t\right)-d{L}_B^i\left(t\right)\\ =P_r^i\left(t\right)-{\mathrm{\&rho;}}_r^i\left(t\right)+c\&CenterDot;\mathrm{\&delta;}{t}^i\left(t\right)+P_B^i\left(t_1\right)-{\mathrm{\&rho;}}_B^i\left(t_1\right)-c\&CenterDot;\mathrm{\&delta;}{\hat{t}}_B\left(t_1\right)+c\&CenterDot;\mathrm{\&delta;}{t}^i\left(t_1\right)\end{array}---\left(6\right)$

Wherein, for t i satellite is to the geometric distance of terminal user;

(43), use the error equation of least-squares estimation criterion to described t terminal user One-Point Location model to solve, can obtain:

${\hat{X}}_r\left(t\right)={\left(B_r^T\left(t\right)P_r\left(t\right)B_r\left(t\right)\right)}^{-1}{B}_r^T\left(t\right)P_r\left(t\right)L_r\left(t\right)---\left(7\right)$

Wherein weigh battle array P _r(t) be:

Wherein, (δ x _r(t), δ y _r(t), δ z _r(t)) be t terminal user One-Point Location coordinate corrective value, its valuation is δ t _rt () is t terminal receiver clock correction, its valuation is (i=1,2 ..., m) be t ₁moment satellite i is relative to the elevation angle of terminal user r;

(5) described in basis computing terminal user coordinates (X _r(t), Y _r(t), Z _r(t)):

$\left[\begin{array}{c}{X}_r\left(t\right)\\ Y_r\left(t\right)\\ Z_r\left(t\right)\end{array}\right]=\left[\begin{array}{c}{X}_{r0}\left(t\right)\\ Y_{r0}\left(t\right)\\ Z_{r0}\left(t\right)\end{array}\right]+\left[\begin{array}{c}\mathrm{\&delta;}{\hat{x}}_r\left(t\right)\\ \mathrm{\&delta;}{\hat{y}}_r\left(t\right)\\ \mathrm{\&delta;}{\hat{z}}_r\left(t\right)\end{array}\right]---\left(8\right).$