A BDS3 single-receiver ambiguity fixation method with additional prior constraints

Abstract

A BDS3 single-receiver ambiguity fixation method with additional prior constraints belongs to the field of spacecraft engineering technology and solves the problem of how to achieve single-receiver ambiguity fixation in satellite-borne BDS3 kinematic precision orbit determination. The present invention constructs pseudorange and carrier phase observation equations and pseudorange and carrier phase observation equations, constructs corrected pseudorange and carrier phase observation equations, and constructs the spacecraft's kinematic orbit determination equations by superimposing the pseudorange and carrier phase observation equations epoch by epoch. Absolute constraints are added to corresponding undifferenced ambiguities in the kinematic orbit determination equations, single-differenced ambiguities are constructed, single-differenced wide-lane ambiguities are constructed, and single-differenced wide-lane ambiguity fixed solutions are obtained by rounding. Single-differenced narrow-lane ambiguities are calculated and rounded to obtain single-differenced narrow-lane ambiguity fixed solutions. Relative constraints are added to the undifferenced ambiguities in the kinematic orbit determination equations to complete single-receiver ambiguity fixation. The present invention improves the accuracy level of satellite-borne BDS3 kinematic precision orbit.

Description

Technical Field

[0001] The invention belongs to the technical field of spacecraft engineering and relates to a BDS3 single-receiver ambiguity fixing method with additional prior constraints. Background Art

[0002] Traditional global navigation satellite system (GNSS)-based kinematic precision orbit determination for low-orbit satellites mostly estimates carrier phase ambiguities as floating-point numbers, failing to exploit their integer nature. Experimental results based on GPS data tracked by low-orbit satellites such as Swarm, Sentinel-6A, and TH2 demonstrate that fixing the carrier phase ambiguities significantly enhances the observation geometry of low-orbit satellites. This approach improves the orbit accuracy of fixed solutions for GPS kinematic ambiguities by 30% to 50% compared to floating-point solutions.

[0003] The key to fixing the carrier phase ambiguity is to eliminate the navigation satellite and onboard receiver hardware delays in the ambiguity. The existing method is to use the satellite bias products released by the GNSS analysis center to eliminate the satellite hardware delay, and to eliminate the receiver hardware delay based on the single-receiver ambiguity fixation method of inter-satellite single difference. As various GNSS analysis centers have successively released satellite bias products of the Beidou Global Satellite Navigation System (BDS3), it has become possible to fix the single-receiver ambiguity in the onboard BDS3 kinematic precise orbit determination. However, due to the limitations of the accuracy of the BDS3 precise ephemeris and clock error products, the current accuracy of the onboard BDS3 kinematic precise orbit is still a certain distance away from that of the onboard GPS, which makes it difficult to fix the ambiguity to an integer in the onboard BDS3 kinematic precise orbit determination.

[0004] Therefore, how to restore the integer characteristics of carrier phase ambiguity and fix the single-receiver ambiguity in the onboard BDS3 kinematic precise orbit determination is a technical problem that needs to be solved urgently at this stage. Summary of the Invention

[0005] The technical solution of the present invention is used to solve the problem of how to achieve single-receiver ambiguity fixation in the onboard BDS3 kinematic precise orbit determination.

[0006] The present invention solves the above technical problems through the following technical solutions:

[0007] A BDS3 single-receiver ambiguity fixing method with additional prior constraints comprises the following steps:

[0008] Step 1: construct pseudorange and carrier phase observation equations for the pseudorange and carrier phase observation data of all visible satellites at each moment, and further construct pseudorange and carrier phase ionospheric elimination combined observation equations based on the pseudorange and carrier phase observation data of two frequencies;

[0009] Step 2: Based on the BDS3 satellite signal bias products released by the GNSS Analysis Center, correct the pseudorange and carrier phase observation data tracked by the onboard BDS3 receiver, deduct the navigation satellite signal bias from the data, and construct the corrected pseudorange and carrier phase ionospheric-free combined observation equations;

[0010] Step 3: Based on the corrected pseudorange and carrier phase ionospheric elimination observation equation, the observation equation is linearly expanded near the approximate state of the spacecraft. The kinematic orbit determination equation of the spacecraft is constructed by superimposing the pseudorange and carrier phase ionospheric elimination observation equation epoch by epoch.

[0011] Step 4: According to the a priori fixed solution of the non-differenced ionospheric combined ambiguity estimated by the simplified dynamics precise orbit determination, an absolute constraint is added to the corresponding non-differenced ionospheric combined ambiguity in the kinematic orbit determination equation;

[0012] Step 5: Differencing the non-differenced ionospheric elimination combined ambiguity to construct the single-differenced ionospheric elimination combined ambiguity;

[0013] Step 6: Construct undifferenced wide-lane ambiguities based on the corrected pseudorange and carrier phase observation data, perform subtraction on the undifferenced wide-lane ambiguities, construct single-differenced wide-lane ambiguities, and round them to obtain the fixed solution of the single-differenced wide-lane ambiguities.

[0014] Step 7: Calculate the single-difference narrow-lane ambiguity based on the single-difference ionospheric elimination combined ambiguity and the single-difference wide-lane ambiguity fixed solution, and round it to obtain the single-difference narrow-lane ambiguity fixed solution;

[0015] Step 8. Calculate the single-differenced ionospheric-eliminator combined ambiguity fixed solution based on the single-differenced wide-lane ambiguity fixed solution and the single-differenced narrow-lane ambiguity fixed solution. Add relative constraints to the non-differenced ionospheric-eliminator combined ambiguity in the kinematic orbit determination equation to complete the single-receiver ambiguity fixation.

[0016] Furthermore, the method for constructing pseudorange and carrier phase observation equations for the pseudorange and carrier phase observation data of all visible satellites at each moment described in step 1 is as follows:

[0017] The pseudorange and carrier phase observation data tracked by the onboard BDS3 receiver at time t are recorded as and The pseudorange and carrier phase observation equations at this moment are expressed as:

[0018]

[0019] Among them, f i and λ i Respectively represent the frequency and wavelength of the carrier, and the number of the frequency point i = 1, 2, represents the first-order ionospheric delay, is the geometric distance from the location of the BDS3 satellite to the location of the low-orbit satellite, x s 、y s 、z s They represent the coordinate values ​​of the BDS3 satellite's location, x r 、y r 、z r They represent the coordinate values ​​of the low-orbit satellite’s location, dt r and dt s are the clock differences between the receiver and the BDS3 satellite, B r；i and are the pseudorange hardware delays at the receiver and BDS3 satellite, respectively, and b r；i and are the carrier phase hardware delays at the receiver and BDS3 satellite, respectively, and N i is the carrier phase ambiguity, ε P and ε L They represent the random errors of pseudorange and carrier phase respectively, and c represents the speed of light.

[0020] Furthermore, the ionospheric-free combined observation equations of pseudorange and carrier phase are constructed based on the pseudorange and carrier phase observation data of two frequencies described in step 1 as follows:

[0021]

[0022] in, is the pseudorange observation data of the first frequency point and the pseudorange observation data of the second frequency point The deionospheric combination, is the carrier phase observation data of the first frequency point and the carrier phase observation data of the second frequency point The deionospheric combination, A IF is the deionospheric combination of λ1N1 and λ2N2, B r；IF is the pseudorange hardware delay B of the first and second frequency points at the receiver end r；1 and B r；2 The deionospheric combination, It is the pseudo-range hardware delay of the 1st and 2nd frequency points on the satellite side and The deionospheric combination, b r；IF is the carrier phase hardware delay b of the first and second frequency points at the receiver end r；1 and b r；2 The deionospheric combination, It is the carrier phase hardware delay of the 1st and 2nd frequency points on the satellite side and The deionospheric combination, It is the ionospheric elimination combination of the pseudorange observation data of the 1st and 2nd frequency points The random error, It is the ionospheric-free combination of carrier phase observation data at the 1st and 2nd frequency points random error.

[0023] Furthermore, the method described in step 2 for correcting the pseudorange and carrier phase observation data tracked by the onboard BDS3 receiver based on the BDS3 satellite signal bias product released by the GNSS Analysis Center is as follows:

[0024] The deviation product of the two frequency pseudoranges and carrier phase signals of the BDS3 satellite released by the GNSS analysis center at time t is recorded as and use and Correct the pseudorange and carrier phase observation data to obtain the corrected pseudorange and carrier phase observation data as follows:

[0025]

[0026] in, It is a product that corrects the deviation of the pseudo-range signal at the first frequency point The pseudo-range observation data of the first frequency point obtained after It is a product that corrects the deviation of the pseudo-range signal at the second frequency point The pseudo-range observation data of the second frequency point obtained after It is a product that corrects the carrier phase signal deviation of the first frequency point The carrier phase observation data of the first frequency point obtained after It is a product that corrects the deviation of the carrier phase signal at the second frequency point The carrier phase observation data of the second frequency point obtained after

[0027] The pseudorange and carrier phase ionospheric elimination combined observation equation after constructing the corrected satellite signal bias is as follows:

[0028]

[0029] in, yes and The pseudorange-ionospheric elimination combination, yes and The carrier phase ionospheric elimination combination.

[0030] Furthermore, the observation equation described in step 3 is linearly expanded around the approximate state of the spacecraft as follows:

[0031]

[0032] in, is the spacecraft position x in the X direction of the Earth-centered Earth-fixed coordinate system r Approximate position of the spacecraft in this direction The difference, is the spacecraft position y in the Y direction of the Earth-centered Earth-fixed coordinate system r Approximate position of the spacecraft in this direction The difference, is the spacecraft position z in the Earth-centered Earth-fixed coordinate system in the Z direction r Approximate position of the spacecraft in this direction The difference, is the difference between the receiver clock error and the receiver approximate clock error, is the difference between the ionospheric-free combined ambiguity and the approximate value of the ionospheric-free combined ambiguity, Indicates the pseudorange observation data The linearized residual of Indicates the carrier phase observation data The linearized residual of

[0033] The method for constructing the kinematic orbit determination equations for a spacecraft by superimposing pseudorange and carrier phase ionospheric elimination combined observation equations epoch by epoch is specifically as follows:

[0034] The pseudorange and carrier phase observation data at time t (t = 1, 2, ..., M) are uniformly recorded as y t , the pseudorange and carrier phase approximate values ​​are uniformly recorded as The components of the spacecraft position at all times in the Earth-centered Earth-fixed coordinate system along the X, Y, and Z axes are denoted by x and r =(x1,x2,…,x M ) T 、y r =(y1,y2,…,y M ) T 、z r =(z1,z2,…,z M ) T , the receiver clock error at all times is recorded as dt r =(dt1,dt2,…,dt M ) T The vector of all ambiguities is denoted as A, and the pseudorange and carrier phase are about the vector (x r ,y r ,z r ,dt r , the partial derivative of A) is uniformly recorded as h t (x r ,yr ,z r ,dt r ,A), then the linearized observation equation is expressed as: where Δx r =(Δx1, Δx2,…, Δx M ) T , Δy r =(Δy1, Δy2,…, Δy M ) T , Δz r =(Δz1,Δz2,…,Δz M ) T is the component of the spacecraft position improvement at all times in the Earth-centered Earth-fixed coordinate system X, Y, and Z axes, Δdt r =(Δdt1, Δdt2,…, Δdt M ) T is the receiver clock error improvement at all times, and ΔA is the vector of all ambiguity improvements. By superimposing the pseudorange and carrier phase ionospheric elimination combined observation equations on an epoch-by-epoch basis, the kinematic orbit determination equation for the spacecraft is constructed as follows:

[0035]

[0036] in, W represents the weight of the observation data.

[0037] Furthermore, the method for fixing the a priori solution of the non-differenced ionospheric combined ambiguity estimated by the simplified dynamics precise orbit determination in step 4 and adding absolute constraints to the corresponding non-differenced ionospheric combined ambiguity in the kinematic orbit determination equation is as follows:

[0038] The fixed prior solution of the undifferenced ionospheric combined ambiguity of the simplified dynamical precise orbit determination estimation is denoted as A IF；prior , add the following absolute constraints to the corresponding undifferenced ionospheric combined ambiguity in the spacecraft's kinematic orbit determination equations:

[0039] E.W.E. T ·δA=E·W·E T ΔA

[0040] Where E = (0,…,0,1,0,…,0) T ,δA=(0,…,0,A IF；prior -A IF ,0,…,0) T , the non-zero position in E and A IF The positions in the ambiguity vector A are consistent.

[0041] Furthermore, the method of subtracting the non-differenced ionospheric elimination combined ambiguity in step 5 to construct the single-differenced ionospheric elimination combined ambiguity is as follows:

[0042] The difference of the ionospheric-free combined ambiguity corresponding to any two BDS3 satellites J and K tracked simultaneously by the receiver is obtained:

[0043]

[0044] in, represents the ionospheric-free combined ambiguity corresponding to BDS3 satellite J, It represents the ionospheric-free combined ambiguity corresponding to BDS3 satellite K.

[0045] Furthermore, the method described in step 6 for constructing undifferenced widelane ambiguities based on the corrected pseudorange and carrier phase observation data, subtracting the undifferenced widelane ambiguities, constructing single-differenced widelane ambiguities, and rounding to obtain a fixed solution for the single-differenced widelane ambiguities is as follows:

[0046] The MW combination is constructed using the corrected pseudorange and carrier phase observation data to estimate the wide-lane ambiguity, and then the wide-lane ambiguity corresponding to any two BDS3 satellites H and K tracked simultaneously by the receiver is subtracted;

[0047] The described construction MW combination is as follows:

[0048]

[0049] Among them, N wl = N1-N2 is the wide lane ambiguity, λ wl =c / (f1-f2) is the wide-lane wavelength, MW(b r；1 ,b r；2 ,B r；1 ,B r；2 ) is the MW combination of pseudorange and carrier phase delay at the receiver;

[0050] To eliminate The hardware delay of the receiver is taken into account, and the satellite bias-free MW combination of any two BDS3 satellites J and K tracked simultaneously by the receiver is calculated using the inter-satellite single difference method. and Do the difference and get the single-difference MW combined ambiguity:

[0051]

[0052] After eliminating the hardware delay term, directly round The fixed solution of the single-difference wide-lane ambiguity is obtained as follows:

[0053]

[0054] in, For Perform rounding operation, For Perform rounding operation.

[0055] Furthermore, the method described in step 7 for calculating the single-difference narrow-lane ambiguity based on the single-difference ionospheric-free combined ambiguity and the single-difference wide-lane ambiguity fixed solution and rounding to obtain the single-difference narrow-lane ambiguity fixed solution is as follows:

[0056] The ionospheric-free combined ambiguity corresponding to any two BDS3 satellites J and K tracked simultaneously by the receiver is and difference Expressed as single-difference wide-lane ambiguity and single-difference narrow lane ambiguity The combination is as follows:

[0057]

[0058] in, λ nl =c / (f1+f2) is the narrow lane wavelength;

[0059] The single-difference wide-lane ambiguity is fixed Substitution Rounding Get the fixed solution of single-difference narrow lane ambiguity:

[0060]

[0061] in, For Perform rounding operation, For Perform rounding operation.

[0062] Furthermore, the single-differenced wide-lane ambiguity fixed solution and the single-differenced narrow-lane ambiguity fixed solution described in step 8 are used to calculate the single-differenced ionospheric-eliminate combined ambiguity fixed solution. A relative constraint is added to the non-differenced ionospheric-eliminate combined ambiguity in the kinematic orbit determination equation to complete the single-receiver ambiguity fixation method as follows:

[0063] Using single-difference wide-lane ambiguity fixed solution and single-difference narrow lane ambiguity fixed solution Compute single-difference ionospheric combined ambiguity fixed solution as follows:

[0064]

[0065] Then, relative constraints are added to the undifferenced ionospheric combined ambiguity in the kinematic orbit determination equations to complete the single-receiver ambiguity fixation as follows:

[0066] D.W.D. T ·ηA=D·W·D T ΔA

[0067] Where D = (0,…,0,1,0,…,0,-1,0…,0) T ,

[0068] The advantages of the present invention are:

[0069] The present invention constructs the pseudorange and carrier phase ionospheric elimination combined observation equations after correcting the BDS3 satellite signal bias by using the constructed pseudorange and carrier phase observation equations and the BDS3 satellite signal bias products released by the GNSS Analysis Center. By superimposing the pseudorange and carrier phase observation equations epoch by epoch, the kinematic orbit determination equations of the spacecraft are constructed. Absolute constraints are added to the corresponding undifferenced ambiguities in the kinematic orbit determination equations. Single-differenced ionospheric elimination combined ambiguities are constructed. Single-differenced wide-lane ambiguities are constructed, and rounding is performed to obtain a single-differenced wide-lane ambiguity fixed solution. Single-differenced narrow-lane ambiguities are calculated and rounded to obtain a single-differenced narrow-lane ambiguity fixed solution. Relative constraints are added to the undifferenced ambiguities in the kinematic orbit determination equations to complete the single-receiver ambiguity fixation. The present invention enhances the observation geometry strength and improves the accuracy level of the onboard BDS3 kinematic precision orbit. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 Flowchart of a BDS3 single-receiver ambiguity fixing method with additional a priori constraints according to Embodiment 1 of the present invention;

[0071] Figure 2 This is the BDS3 single-difference ambiguity residual distribution diagram obtained by the traditional single-receiver ambiguity fixation method based on inter-satellite single difference;

[0072] Figure 3 : is a BDS3 single-difference ambiguity residual distribution diagram obtained by the BDS3 single-receiver ambiguity fixing method with additional prior constraints in Example 1 of the present invention;

[0073] Figure 4 3 is a comparison diagram of the differences between the onboard BDS3 kinematic orbit and the reference orbit obtained by using the traditional single-receiver ambiguity fixation method based on inter-satellite single difference and the BDS3 single-receiver ambiguity fixation method with additional prior constraints according to the first embodiment of the present invention. DETAILED DESCRIPTION

[0074] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0075] The technical solution of the present invention is further described below with reference to the accompanying drawings and specific embodiments:

[0076] Example 1

[0077] like Figure 1 As shown, a BDS3 single-receiver ambiguity fixing method with additional prior constraints according to an embodiment of the present invention includes the following steps:

[0078] Step 1: Construct pseudorange and carrier phase observation equations for the pseudorange and carrier phase observation data of all visible satellites at each moment, and further construct pseudorange and carrier phase ionospheric elimination combined observation equations based on the pseudorange and carrier phase observation data of two frequencies.

[0079] Specifically, the pseudorange and carrier phase observation data tracked by the onboard BDS3 receiver at time t are recorded as and The pseudorange and carrier phase observation equations at this moment are expressed as:

[0080]

[0081] Among them, f i and λ i Respectively represent the frequency and wavelength of the carrier, and the number of the frequency point i = 1, 2, represents the first-order ionospheric delay, is the geometric distance from the location of the BDS3 satellite to the location of the low-orbit satellite, x s 、y s 、z s They represent the coordinate values ​​of the BDS3 satellite's location, x r 、y r 、z r They represent the coordinate values ​​of the low-orbit satellite’s location, dt r and dt s are the clock differences between the receiver and the BDS3 satellite, B r；i and are the pseudorange hardware delays at the receiver and BDS3 satellite, respectively, and b r；i and are the carrier phase hardware delays at the receiver and BDS3 satellite, respectively, and N iis the carrier phase ambiguity, ε P and ε L They represent the random errors of pseudorange and carrier phase respectively, and c represents the speed of light.

[0082] Furthermore, the ionosphere-free (IF) combined observation equation of pseudorange and carrier phase is constructed based on the pseudorange and carrier phase observation data of the two frequencies as follows:

[0083]

[0084] in, is the pseudorange observation data of the first frequency point and the pseudorange observation data of the second frequency point The deionospheric combination, is the carrier phase observation data of the first frequency point and the carrier phase observation data of the second frequency point The deionospheric combination, A IF is the deionospheric combination of λ1N1 and λ2N2, B r；IF is the pseudorange hardware delay B of the first and second frequency points at the receiver end r；1 and B r；2 The deionospheric combination, It is the pseudo-range hardware delay of the 1st and 2nd frequency points on the satellite side and The deionospheric combination, b r；IF is the carrier phase hardware delay b of the first and second frequency points at the receiver end r；1 and b r；2 The deionospheric combination, It is the carrier phase hardware delay of the 1st and 2nd frequency points on the satellite side and The deionospheric combination, It is the ionospheric-free combination of pseudorange observation data at the 1st and 2nd frequency points The random error, It is the ionospheric-free combination of carrier phase observation data at the 1st and 2nd frequency points random error.

[0085] Step 2: Based on the BDS3 satellite signal bias product released by the GNSS Analysis Center, correct the pseudorange and carrier phase observation data tracked by the onboard BDS3 receiver, deduct the navigation satellite signal bias in the data, and construct the pseudorange and carrier phase ionospheric combined observation equation after correcting the satellite signal bias.

[0086] The BDS3 satellite signal deviation product contains the pseudorange and carrier phase signal deviations of all BDS3 navigation satellites and can be obtained from the websites of various GNSS analysis centers.

[0087] Specifically, the deviation product of the two frequency pseudoranges and carrier phase signals of the BDS3 satellite released by the GNSS analysis center at time t is recorded as and use and Correct the pseudorange and carrier phase observation data to obtain the corrected pseudorange and carrier phase observation data as follows:

[0088]

[0089]

[0090] in, It is a product that corrects the deviation of the pseudo-range signal at the first frequency point The pseudo-range observation data of the first frequency point obtained after It is a product that corrects the deviation of the pseudo-range signal at the second frequency point The pseudo-range observation data of the second frequency point obtained after It is a product that corrects the carrier phase signal deviation of the first frequency point The carrier phase observation data of the first frequency point obtained after It is a product that corrects the deviation of the carrier phase signal at the second frequency point The carrier phase observation data of the second frequency point is obtained.

[0091] The pseudorange and carrier phase ionospheric combined observation equation after correcting the satellite signal bias is constructed as follows:

[0092]

[0093] in, yes and The pseudorange-ionospheric elimination combination, yes and The carrier phase ionospheric elimination combination.

[0094] Step 3: Based on the pseudorange and carrier phase ionospheric elimination observation equation after correcting the satellite signal bias, the observation equation is linearly expanded near the approximate state of the spacecraft. By superimposing the pseudorange and carrier phase ionospheric elimination observation equation epoch by epoch, the kinematic orbit determination equation of the spacecraft is constructed.

[0095] Specifically, the BDS3 satellite position, BDS3 satellite clock error and approximate state of the spacecraft are obtained from the BDS3 satellite product, and the pseudorange and carrier phase ionospheric combined observation equation after the correction of satellite signal deviation is introduced to obtain the approximate values ​​of the pseudorange and carrier phase observations. and The approximate state of the spacecraft includes: the approximate position of the spacecraft in the X direction of the Earth-centered Earth-fixed coordinate system Approximate position of the spacecraft in the Y direction Approximate position of the spacecraft in the Z direction Receiver approximate clock error and ambiguity approximation in and The approximate value of ambiguity can be directly obtained by single point positioning calculation Can be achieved through and Directly perform the difference to obtain; then linearly expand the observation equation near the approximate state of the spacecraft, expressed as follows:

[0096]

[0097] in, is the spacecraft position x in the X direction of the Earth-centered Earth-fixed coordinate system t Approximate position of the spacecraft in this direction The difference is also called the improvement of the spacecraft position in the X direction of the Earth-centered Earth-fixed coordinate system; is the spacecraft position y in the Y direction of the Earth-centered Earth-fixed coordinate system t Approximate position of the spacecraft in this direction The difference is also called the improvement of the spacecraft position in the Y direction of the Earth-centered Earth-fixed coordinate system; is the spacecraft position z in the Earth-centered Earth-fixed coordinate system in the Z direction t Approximate position of the spacecraft in this direction The difference is also called the spacecraft position improvement in the Z direction of the Earth-centered Earth-fixed coordinate system. It is the difference between the receiver clock error and the receiver approximate clock error, also known as the receiver clock error improvement. is the difference between the ionospheric-free combined ambiguity and the approximate value of the ionospheric-free combined ambiguity, also known as the ambiguity improvement amount. Indicates the pseudorange observation data The linearized residual of Indicates the carrier phase observation data The linearized residual.

[0098] The method for constructing the kinematic orbit determination equations for a spacecraft by superimposing pseudorange and carrier phase ionospheric elimination combined observation equations epoch by epoch is specifically as follows:

[0099] The pseudorange and carrier phase observation data at time t (t = 1, 2, ..., M) are uniformly recorded as y t , the pseudorange and carrier phase approximate values ​​are uniformly recorded as The components of the spacecraft position at all times in the Earth-centered Earth-fixed coordinate system along the X, Y, and Z axes are denoted by x and r =(x1,x2,…,x M ) T 、y r =(y1,y2,…,y M ) T 、z r =(z1,z2,…,z M ) T , the receiver clock error at all times is recorded as dt r =(dt1,dt2,…,dt M ) T The vector of all ambiguities is denoted as A, and the pseudorange and carrier phase are about the vector (x r ,y r ,z r ,dt r , the partial derivative of A) is uniformly recorded as h t (x r ,y r ,z r ,dt r ,A), then the linearized observation equation is expressed as: where Δx r =(Δx1, Δx2,…, Δx M ) T , Δy r =(Δy1, Δy2,…, Δy M ) T , Δz r =(Δz1, Δz2,…, Δz M ) T is the component of the spacecraft position improvement at all times in the Earth-centered Earth-fixed coordinate system X, Y, and Z axes, Δdt r =(Δdt1, Δdt2,…, Δdt M ) T is the receiver clock error improvement at all times, and ΔA is the vector of all ambiguity improvements. By superimposing the pseudorange and carrier phase ionospheric elimination combined observation equations on an epoch-by-epoch basis, the kinematic orbit determination equation for the spacecraft is constructed as follows:

[0100]

[0101] in, W represents the weight of the observation data.

[0102] Step 4: According to the a priori fixed solution of the non-differenced ionospheric combined ambiguity estimated by simplified dynamics precise orbit determination, add absolute constraints to the corresponding non-differenced ionospheric combined ambiguity in the kinematic orbit determination equations.

[0103] The non-differenced ionospheric combined ambiguity prior fixed solution estimated by the simplified dynamical precise orbit determination is the non-differenced ionospheric combined ambiguity fixed solution obtained by the traditional inter-satellite single-difference ambiguity fixation method in the BDS3 simplified dynamical precise orbit determination; the added absolute constraint is to constrain the non-differenced ionospheric combined ambiguity estimated in the kinematic orbit determination to the non-differenced ionospheric combined ambiguity prior fixed solution by adding a pseudo-observation equation.

[0104] Specifically, the undifferenced ionospheric combined ambiguity prior fixed solution of the simplified dynamical precise orbit determination estimation is denoted as A IF；prior , add the following absolute constraints to the corresponding undifferenced ionospheric combined ambiguity in the spacecraft's kinematic orbit determination equations:

[0105] E.W.E. T ·δA=E·W·E T ΔA

[0106] Where E = (0,…,0,1,0,…,0) T ,δA=(0,…,0,A IF；prior -A IF ,0,…,0) T , the non-zero position in E and A IF The positions in the ambiguity vector A are consistent.

[0107] Step 5: Differ the non-differenced ionospheric elimination combined ambiguity to construct the single-differenced ionospheric elimination combined ambiguity

[0108] The constructed single-difference ionospheric-free combined ambiguity is the difference obtained by directly subtracting the different undifferenced ambiguities tracked simultaneously by the receiver.

[0109] Specifically, the ionospheric-free combined ambiguity corresponding to any two BDS3 satellites J and K tracked simultaneously by the receiver is subtracted to obtain:

[0110]

[0111] in, represents the ionospheric-free combined ambiguity corresponding to BDS3 satellite J, It represents the ionospheric-free combined ambiguity corresponding to BDS3 satellite K.

[0112] Step 6: Construct the undifferenced wide lane ambiguity based on the corrected pseudorange and carrier phase observation data, make a difference on the undifferenced wide lane ambiguity, construct the single-differenced wide lane ambiguity, and round it to get the fixed solution of the single-differenced wide lane ambiguity.

[0113] The constructed single-difference widelane ambiguity is the difference obtained by directly subtracting the different widelane ambiguities tracked simultaneously by the receiver.

[0114] Specifically, the MW combination is constructed using the corrected pseudorange and carrier phase observation data to estimate the wide-lane ambiguity, and then the wide-lane ambiguity corresponding to any two BDS3 satellites J and K tracked simultaneously by the receiver is subtracted;

[0115] The described construction MW combination is as follows:

[0116]

[0117] Among them, N wl = N1-N2 is the wide lane ambiguity, λ wl =c / (f1-f2) is the wide-lane wavelength, MW(b r；1 ,b r；2 ,B r；1 ,B r；2 ) is the MW combination of pseudorange and carrier phase delay at the receiver.

[0118] To eliminate The hardware delay of the receiver is taken into account, and the satellite bias-free MW combination of any two BDS3 satellites J and K tracked simultaneously by the receiver is calculated using the inter-satellite single difference method. and Do the difference and get the single-difference MW combined ambiguity:

[0119]

[0120] After eliminating the hardware delay term, directly round The fixed solution of the single-difference wide-lane ambiguity is obtained as follows:

[0121]

[0122] in, For Perform rounding operation, For Perform rounding operation.

[0123] Step 7: Calculate the single-difference narrow-lane ambiguity based on the single-difference ionospheric elimination combined ambiguity and the single-difference wide-lane ambiguity fixed solution, and round it to obtain the single-difference narrow-lane ambiguity fixed solution.

[0124] Specifically, the ionospheric-free combined ambiguity corresponding to any two BDS3 satellites J and K tracked simultaneously by the receiver is: and difference Expressed as single-difference wide-lane ambiguity and single-difference narrow lane ambiguity The combination is as follows:

[0125]

[0126] in, λ nl =c / (f1+f2) is the narrow lane wavelength;

[0127] The single-difference wide-lane ambiguity is fixed Substitution Rounding Get the fixed solution of single-difference narrow lane ambiguity:

[0128]

[0129] in, For Perform rounding operation, For Perform rounding operation.

[0130] Step 8: Calculate the single-differenced ionospheric elimination combined ambiguity fixed solution based on the single-differenced wide-lane ambiguity fixed solution and the single-differenced narrow-lane ambiguity fixed solution. Add relative constraints to the non-differenced ionospheric elimination combined ambiguity in the kinematic orbit determination equation to complete the single-receiver ambiguity fixed solution.

[0131] The relative constraints for the non-differenced ionospheric combination ambiguities in the kinematic orbit determination equations are added by adding pseudo-observation equations, which constrain the differences between all non-differenced ionospheric combination ambiguities to the corresponding single-differenced ionospheric combination ambiguity fixed solutions.

[0132] Specifically, the single-difference wide-lane ambiguity fixed solution is adopted and single-difference narrow lane ambiguity fixed solution Compute single-difference ionospheric combined ambiguity fixed solution as follows:

[0133]

[0134] Then, relative constraints are added to the undifferenced ionospheric combined ambiguity in the kinematic orbit determination equations to complete the single-receiver ambiguity fixation as follows:

[0135] D.W.D. T ·ηA=D·W·D T ΔA

[0136] Where D = (0,…,0,1,0,…,0,-1,0…,0)T ,

[0137] Experimental verification

[0138] For example, a domestic satellite equipped with a BDS3 receiver can simultaneously track pseudorange and carrier phase observations from both BDS3 B1I and B3I. Single-receiver ambiguity fixation is performed in the BDS3 kinematic precise orbit determination for this satellite.

[0139] like Figure 2 As shown in the figure, the single-difference wide-lane and single-difference narrow-lane ambiguity residuals are obtained by the traditional single-receiver ambiguity fixation method based on inter-satellite single difference, where the ambiguity residual is the difference between the single-difference wide-lane and single-difference narrow-lane ambiguities and their rounded integer values. It can be found that the single-difference narrow-lane ambiguity fractional residual cannot be concentrated near 0, indicating that the single-difference narrow-lane ambiguity is not an integer. The traditional single-receiver ambiguity fixation method based on inter-satellite single difference fails to restore the integer characteristics of the single-difference narrow-lane ambiguity.

[0140] like Figure 3 As shown in the figure, the distribution of the single-difference ambiguity fractional residuals of satellite BDS3 obtained by the method of the present invention shows that more than 80% of the single-difference narrow-lane ambiguity fractional residuals are distributed between [-0.05, 0.05] weeks, indicating that the method of the present invention can effectively restore the integer characteristics of the single-difference narrow-lane ambiguity, which is conducive to achieving ambiguity fixation.

[0141] like Figure 4 As shown in the figure, the differences between the onboard BDS3 kinematic orbits and the reference orbits obtained by the traditional inter-satellite single-difference method and the single-receiver ambiguity fixation method with additional prior constraints, respectively, can be found that the satellite BDS3 kinematic orbits obtained by the single-receiver ambiguity fixation method with additional prior constraints are better than those of the traditional inter-satellite single-difference method in the radial, tangential and normal directions of the orbit, and the orbit error is reduced from 8.9 cm to 3.0 cm. The method of the present invention significantly improves the kinematic orbit accuracy of the onboard BDS3.

[0142] Example 2

[0143] An electronic device includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the BDS3 single-receiver ambiguity fixation method with additional prior constraints in embodiment 1, and the processor is configured to execute the program stored in the memory.

[0144] Example 3

[0145] A storage medium stores a computer program, which, when executed by a processor, performs the steps of the BDS3 single-receiver ambiguity fixing method with additional prior constraints in embodiment 1.

[0146] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A BDS3 single-receiver ambiguity fixation method with additional prior constraints, characterized by: The following steps are involved: Step 1: construct pseudorange and carrier phase observation equations for the pseudorange and carrier phase observation data of all visible satellites at each moment, and further construct pseudorange and carrier phase ionospheric elimination combined observation equations based on the pseudorange and carrier phase observation data of two frequencies; Step 2: Based on the BDS3 satellite signal bias products released by the GNSS Analysis Center, correct the pseudorange and carrier phase observation data tracked by the onboard BDS3 receiver, deduct the navigation satellite signal bias from the data, and construct the corrected pseudorange and carrier phase ionospheric-free combined observation equations; Step 3: Based on the corrected pseudorange and carrier phase ionospheric elimination observation equation, the observation equation is linearly expanded near the approximate state of the spacecraft. The kinematic orbit determination equation of the spacecraft is constructed by superimposing the pseudorange and carrier phase ionospheric elimination observation equation epoch by epoch. Step 4: According to the a priori fixed solution of the non-differenced ionospheric combined ambiguity estimated by the simplified dynamics precise orbit determination, an absolute constraint is added to the corresponding non-differenced ionospheric combined ambiguity in the kinematic orbit determination equation; Step 5: Differencing the non-differenced ionospheric elimination combined ambiguity to construct the single-differenced ionospheric elimination combined ambiguity; Step 6: Construct undifferenced wide-lane ambiguities based on the corrected pseudorange and carrier phase observation data, perform subtraction on the undifferenced wide-lane ambiguities, construct single-differenced wide-lane ambiguities, and round them to obtain the fixed solution of the single-differenced wide-lane ambiguities. Step 7: Calculate the single-difference narrow-lane ambiguity based on the single-difference ionospheric elimination combined ambiguity and the single-difference wide-lane ambiguity fixed solution, and round it to obtain the single-difference narrow-lane ambiguity fixed solution; Step 8. Calculate the single-differenced ionospheric-eliminator combined ambiguity fixed solution based on the single-differenced wide-lane ambiguity fixed solution and the single-differenced narrow-lane ambiguity fixed solution. Add relative constraints to the non-differenced ionospheric-eliminator combined ambiguity in the kinematic orbit determination equation to complete the single-receiver ambiguity fixation.

2. The BDS3 single-receiver ambiguity fixing method with additional prior constraints according to claim 1, characterized in that: The method described in step 1 to construct pseudorange and carrier phase observation equations for the pseudorange and carrier phase observation data of all visible satellites at each moment is as follows: The pseudorange and carrier phase observation data tracked by the onboard BDS3 receiver at time t are recorded as and The pseudorange and carrier phase observation equations at this moment are expressed as: Among them, f i and λ i Respectively represent the frequency and wavelength of the carrier, and the number of the frequency point i = 1, 2, represents the first-order ionospheric delay, is the geometric distance from the location of the BDS3 satellite to the location of the low-orbit satellite, x s 、y s 、z s They represent the coordinate values ​​of the BDS3 satellite's location, x r 、y r 、z r They represent the coordinate values ​​of the low-orbit satellite’s location, dt r and dt s are the clock differences between the receiver and the BDS3 satellite, B r；i and are the pseudorange hardware delays at the receiver and BDS3 satellite, respectively, and b r；i and are the carrier phase hardware delays at the receiver and BDS3 satellite, respectively, and N i is the carrier phase ambiguity, ε P and ε L They represent the random errors of pseudorange and carrier phase respectively, and c represents the speed of light.

3. The BDS3 single-receiver ambiguity fixing method with additional prior constraints according to claim 2, characterized in that: The ionospheric-free combined observation equations for pseudorange and carrier phase are constructed based on the pseudorange and carrier phase observation data of two frequencies described in step 1 as follows: in, is the pseudorange observation data of the first frequency point and the pseudorange observation data of the second frequency point The deionospheric combination, is the carrier phase observation data of the first frequency point and the carrier phase observation data of the second frequency point The deionospheric combination, A IF is the deionospheric combination of λ1N1 and λ2N2, B r；IF is the pseudorange hardware delay B of the first and second frequency points at the receiver end r；1 and B r；2 The deionospheric combination, It is the pseudo-range hardware delay of the 1st and 2nd frequency points on the satellite side and The deionospheric combination, b r；IF is the carrier phase hardware delay b of the first and second frequency points at the receiver end r；1 and b r；2 The deionospheric combination, It is the carrier phase hardware delay of the 1st and 2nd frequency points on the satellite side and The deionospheric combination, It is the ionospheric-free combination of pseudorange observation data at the 1st and 2nd frequency points The random error, It is the ionospheric-free combination of carrier phase observation data at the 1st and 2nd frequency points random error.

4. The BDS3 single-receiver ambiguity fixing method with additional prior constraints according to claim 3, characterized in that: The method described in step 2 to correct the pseudorange and carrier phase observation data tracked by the onboard BDS3 receiver based on the BDS3 satellite signal bias products released by the GNSS Analysis Center is as follows: The deviation product of the two frequency pseudoranges and carrier phase signals of the BDS3 satellite released by the GNSS analysis center at time t is recorded as and use and Correct the pseudorange and carrier phase observation data to obtain the corrected pseudorange and carrier phase observation data as follows: in, It is a product that corrects the deviation of the pseudo-range signal at the first frequency point The pseudo-range observation data of the first frequency point obtained after It is a product that corrects the deviation of the pseudo-range signal at the second frequency point The pseudo-range observation data of the second frequency point obtained after It is a product that corrects the carrier phase signal deviation of the first frequency point The carrier phase observation data of the first frequency point obtained after It is a product that corrects the deviation of the carrier phase signal at the second frequency point The carrier phase observation data of the second frequency point obtained after The pseudorange and carrier phase ionospheric elimination combined observation equation after constructing the corrected satellite signal bias is as follows: in, yes and The pseudorange-ionospheric elimination combination, yes and The carrier phase ionospheric elimination combination.

5. The BDS3 single-receiver ambiguity fixing method with additional prior constraints according to claim 4, characterized in that: The observation equation described in step 3 is linearly expanded around the approximate state of the spacecraft as follows: in, is the spacecraft position x in the X direction of the Earth-centered Earth-fixed coordinate system r Approximate position of the spacecraft in this direction The difference, is the spacecraft position y in the Y direction of the Earth-centered Earth-fixed coordinate system r Approximate position of the spacecraft in this direction The difference, is the spacecraft position z in the Earth-centered Earth-fixed coordinate system in the Z direction r Approximate position of the spacecraft in this direction The difference, is the difference between the receiver clock error and the receiver approximate clock error, is the difference between the ionospheric-free combined ambiguity and the approximate value of the ionospheric-free combined ambiguity, Indicates the pseudorange observation data The linearized residual of Indicates the carrier phase observation data The linearized residual of The method for constructing the kinematic orbit determination equations for a spacecraft by superimposing pseudorange and carrier phase ionospheric elimination combined observation equations epoch by epoch is specifically as follows: The pseudorange and carrier phase observation data at time t (t = 1, 2, ..., M) are uniformly recorded as y t , the pseudorange and carrier phase approximate values ​​are uniformly recorded as The components of the spacecraft position at all times in the Earth-centered Earth-fixed coordinate system along the X, Y, and Z axes are denoted by x and r =(x1,x2,…,x M ) T 、y r =(y1,y2,…,y M ) T 、z r =(z1,z2,…,z M ) T , the receiver clock error at all times is recorded as dt r =(dt1,dt2,…,dt M ) T The vector of all ambiguities is denoted as A, and the pseudorange and carrier phase are about the vector (x r ,y r ,z r ,dt r , the partial derivative of A) is uniformly recorded as h t (x r ,y r ,z r ,dt r ,A), then the linearized observation equation is expressed as: where Δx r =(Δx1, Δx2,…, Δx M ) T , Δy r =(Δy1, Δy2,…, Δy M ) T , Δz r =(Δz1,Δz2,…,Δz M ) T is the component of the spacecraft position improvement at all times in the Earth-centered Earth-fixed coordinate system X, Y, and Z axes, Δdt r =(Δdt1, Δdt2,…, Δdt M ) T is the receiver clock error improvement at all times, and ΔA is the vector of all ambiguity improvements. By superimposing the pseudorange and carrier phase ionospheric elimination combined observation equations on an epoch-by-epoch basis, the kinematic orbit determination equation for the spacecraft is constructed as follows: in, W represents the weight of the observation data.

6. The BDS3 single-receiver ambiguity fixing method with additional prior constraints according to claim 5, characterized in that: The method for fixing the a priori solution of the non-differenced ionospheric combined ambiguity estimated by the simplified dynamics precise orbit determination in step 4 and adding absolute constraints to the corresponding non-differenced ionospheric combined ambiguity in the kinematic orbit determination equation is as follows: The fixed prior solution of the undifferenced ionospheric combined ambiguity of the simplified dynamical precise orbit determination estimation is denoted as A IF；prior , add the following absolute constraints to the corresponding undifferenced ionospheric combined ambiguity in the spacecraft's kinematic orbit determination equations: EWE T ·δA0E·W·E T ·ΔA Where E = (0,…,0,1,0,…,0) T ,δA=(0,…,0,A IF；prior -A IF ,0,…,0) T , the non-zero position in E and A IF The positions in the ambiguity vector A are consistent.

7. The BDS3 single-receiver ambiguity fixing method with additional prior constraints according to claim 6, characterized in that: The method for constructing the single-differenced ionospheric-eliminated ambiguity by subtracting the non-differenced ionospheric-eliminated combined ambiguity described in step 5 is as follows: The difference of the ionospheric-free combined ambiguity corresponding to any two BDS3 satellites J and K tracked simultaneously by the receiver is obtained: in, represents the ionospheric-free combined ambiguity corresponding to BDS3 satellite J, It represents the ionospheric-free combined ambiguity corresponding to BDS3 satellite K.

8. The BDS3 single-receiver ambiguity fixing method with additional prior constraints according to claim 7, characterized in that: The method described in step 6 for constructing undifferenced widelane ambiguities based on the corrected pseudorange and carrier phase observation data, subtracting the undifferenced widelane ambiguities, constructing single-differenced widelane ambiguities, and rounding to obtain a fixed solution for the single-differenced widelane ambiguities is as follows: The MW combination is constructed using the corrected pseudorange and carrier phase observation data to estimate the wide-lane ambiguity, and then the wide-lane ambiguity corresponding to any two BDS3 satellites J and K tracked simultaneously by the receiver is subtracted; The described construction MW combination is as follows: Among them, N wl = N1-N2 is the wide lane ambiguity, λ wl =c / (f1-f2) is the wide-lane wavelength, MW(b r；1 ,b r；2 ,B r；1 ,B r；2 ) is the MW combination of pseudorange and carrier phase delay at the receiver; To eliminate The hardware delay of the receiver is taken into account, and the satellite bias-free MW combination of any two BDS3 satellites J and K tracked simultaneously by the receiver is calculated using the inter-satellite single difference method. and Do the difference and get the single-difference MW combined ambiguity: After eliminating the hardware delay term, directly round The fixed solution of the single-difference wide-lane ambiguity is obtained as follows: in, For Perform rounding operation, For Perform rounding operation.

9. The BDS3 single-receiver ambiguity fixing method with additional prior constraints according to claim 8, characterized in that: The method described in step 7 for calculating the single-difference narrow-lane ambiguity based on the single-difference ionospheric-free combined ambiguity and the single-difference wide-lane ambiguity fixed solution and rounding to obtain the single-difference narrow-lane ambiguity fixed solution is as follows: The ionospheric-free combined ambiguity corresponding to any two BDS3 satellites J and K tracked simultaneously by the receiver is and difference Expressed as single-difference wide-lane ambiguity and single-difference narrow lane ambiguity The combination is as follows: in, λ nl =c / (f1+f2) is the narrow lane wavelength; The single-difference wide-lane ambiguity is fixed Substitution Rounding Get the fixed solution of single-difference narrow lane ambiguity: in, For Perform rounding operation, For Perform rounding operation.

10. The BDS3 single-receiver ambiguity fixing method with additional prior constraints according to claim 9, characterized in that: The method described in step 8 is to calculate the single-differenced ionospheric-eliminated combined ambiguity fixed solution based on the single-differenced wide-lane ambiguity fixed solution and the single-differenced narrow-lane ambiguity fixed solution, and to add relative constraints to the non-differenced ionospheric-eliminated combined ambiguity in the kinematic orbit determination equation to complete the single-receiver ambiguity fixation as follows: Using single-difference wide-lane ambiguity fixed solution and single-difference narrow lane ambiguity fixed solution Compute single-difference ionospheric combined ambiguity fixed solution as follows: Then, relative constraints are added to the undifferenced ionospheric combined ambiguity in the kinematic orbit determination equations to complete the single-receiver ambiguity fixation as follows: D·W·D T ·ηA=D·W·D T ·ΔA Where D = (0,…,0,1,0,…,0,-1,0…,0) T ,

Images