阅读说明：本技术 一种顾及卫星轨道误差的低轨导航增强实时定位方法 (Low-orbit navigation enhancement real-time positioning method considering satellite orbit error ) 是由 杨轩 谢松 孙一雄 刘晓旭 王刚 韩双林 刘天立 伍蔡伦 易卿武 蔚保国 于 2021-09-07 设计创作，主要内容包括：本发明公开了一种顾及卫星轨道误差的低轨导航增强实时定位方法,属于低轨卫星导航增强定位领域。该方法采用两步法减弱轨道误差的影响,其使用地面接收机接收观测数据与导航电文,计算导航卫星和低轨卫星各自的轨道和钟差；按照常规方式进行定位,待定位收敛后,估计轨道误差参数,通过给定适当的权重,吸收低轨卫星和导航卫星轨道误差,从而达到提高定位精度的作用。本发明利用低轨导航增强PPP收敛速度快的特性,通过快速收敛载波相位模糊度,进而引入轨道误差参数,用以削弱卫星轨道误差对定位的影响,提高低轨导航增强定位的精度。(The invention discloses a low-orbit navigation enhancement real-time positioning method considering satellite orbit errors, and belongs to the field of low-orbit satellite navigation enhancement positioning. The method adopts a two-step method to weaken the influence of orbit errors, and uses a ground receiver to receive observation data and navigation messages and calculate respective orbits and clock errors of a navigation satellite and a low-orbit satellite; positioning is carried out according to a conventional mode, orbit error parameters are estimated after convergence of the position to be positioned, and the orbit errors of the low-orbit satellite and the navigation satellite are absorbed by giving proper weight, so that the effect of improving the positioning precision is achieved. The method utilizes the characteristic that the low-orbit navigation enhances the PPP convergence speed, and introduces the orbit error parameter by rapidly converging the carrier phase ambiguity so as to weaken the influence of the satellite orbit error on the positioning and improve the accuracy of the low-orbit navigation enhanced positioning.)

1. A low-orbit navigation enhancement real-time positioning method considering satellite orbit errors is characterized by comprising the following steps:

step 1, a ground receiver receives observation data from a navigation satellite and a low-orbit navigation enhanced satellite;

step 2, acquiring navigation messages of the navigation satellite and the low-orbit navigation enhanced satellite, calculating broadcast ephemeris and clock error of the navigation satellite and the low-orbit navigation enhanced satellite, acquiring correction information expressed by satellite state space, and correcting the broadcast ephemeris and the clock error to obtain high-precision orbit and clock error;

step 3, preprocessing the observation data obtained in the step 1, and removing gross errors;

step 4, performing traditional single-point positioning calculation;

step 5, performing precise single-point positioning calculation;

step 6, after the precision single-point positioning result is converged, fixing the carrier phase ambiguity, introducing an additional orbit error parameter, and absorbing the influence of a satellite orbit error;

step 7, if the cycle slip and observation lock loss occur in the next epoch, suspending the estimation of the orbit error parameters, re-estimating the ambiguity of the carrier phase, and repeating the step 5; and if the positioning is successful, returning to the step 1 to perform positioning at the next moment.

2. The method as claimed in claim 1, wherein in step 4, the calculation equation of the conventional single-point positioning calculation is:

in the formula (I), the compound is shown in the specification,the pseudo range observation value of the j frequency point received by a satellite s transmitting receiver r is measured in meters;represents the geometric distance between the satellite s and the receiver r; c represents the speed of light in vacuum; dt_rFor receiver clock difference, dt^sIs the satellite clock error;represents a tilted ionospheric delay; m is the tropospheric mapping function, ZWD_rRepresents the zenith tropospheric delay at the receiver r; epsilon_rObservation noise representing pseudo-range observations.

3. The method as claimed in claim 2, wherein in step 5, the calculation equation of the precise point-location calculation is:

in the formula (I), the compound is shown in the specification,the unit of the observed value of the carrier phase of the j frequency point received by a satellite s transmitting receiver r is meter;andpseudorange hardware delays for the receiver and the satellite, respectively;andrepresents the carrier phase hardware delays of the receiver and satellite; n is a radical of^sIs the carrier phase ambiguity; xi_rObservation noise representing a carrier phase observation.

4. The method as claimed in claim 3, wherein in step 6, the positioning equation after introducing the additional orbit error parameter is:

in the formula (I), the compound is shown in the specification,the influence of the orbit error of the low-orbit navigation enhanced satellite and the navigation satellite in the sight direction is shown as follows:

in the formula (X)^s，Y^s，Z^s) Enhance the true position of the satellites for navigation satellites and low-earth navigation,enhancing satellites for computed navigation satellites and low-earth navigationThe position of the star with error; the satellite orbit error presents approximate trigonometric function class characteristics, and the period is consistent with the satellite operation period, so the satellite orbit error can be simply expressed as:

further, the effect of low earth orbit and navigation satellite orbit errors in the look direction can be expressed as:

in the formula, theta represents the included angle between the orbit error of the low-orbit navigation enhanced satellite and the navigation satellite and the sight direction and constantly changes along with the movement of the satellite,not a complete sine or cosine function, but considering that the forecast track is generally shortSimplified as a trigonometric function:

at the moment, the unknown numbers of the equation (4) and the equation (5) are 5+ N, the number of the observation equations is 2N, the redundancy is N-5, N is the number of satellites, and the solution can be carried out only by observing 5 satellites at the same time.

5. The method as claimed in claim 4, wherein the equation of the error in step 6 is:

V＝Hx-L (10)

v is a residual vector of a pseudo range and a carrier phase observation value, H represents a Jacobian matrix of a parameter to be estimated, if deionization layer combination is adopted, the parameter to be estimated comprises receiver position coordinate correction, clock correction, zenith troposphere wet delay and carrier phase ambiguity, and if a non-differential non-combination mode is adopted to establish an observation equation, an inclined ionosphere delay parameter is also included; l represents a vector formed by the difference between the observed quantity and the calculated quantity; the weight of the observed value is determined according to the weighting mode of the satellite altitude:

wherein a and b are empirical constants, and E is the satellite altitude;

the noise variance matrix R of the observations is:

the system noise variance matrix Q is:

wherein the content of the first and second substances,variance matrix representing receiver position, using 10 for dynamic fine single point positioning³White noise of m is variance, and the initial value of the static precise single-point positioning is 10³Estimating a constant of m;

the variance of the receiver clock error is represented and described by white noise:

the variance of the zenith tropospheric wet delay is expressed using a random walk process described:

wherein, tau_kIs white noise;

the variance of the tilted ionospheric delay is expressed, described using a random walk process:

represents the variance of the carrier phase ambiguity with an initial variance of 10⁴m；Representing satellite orbit error parameters, and adopting constant estimation, wherein the initial variance is 2 pi;

the parameter estimation adopts extended Kalman filtering, and the recurrence formula is as follows:

wherein Φ represents a state transition matrix of a parameter to be estimated, K is a gain matrix of kalman filtering, Γ represents a dynamic noise driving matrix, which can be generally regarded as an identity matrix, and I is an identity matrix.

Technical Field

The invention belongs to the technical field of satellite navigation and positioning, and particularly relates to a low-orbit navigation enhanced real-time positioning method considering satellite orbit errors.

Background

With the establishment of the Beidou-III GPS, four global positioning systems including Beidou, GPS, GLONASS and Galileo and regional satellite navigation systems such as Japanese QZSS and India IRNSS are available at present. The basic positioning service precision of the navigation systems is meter level, and the requirements of high-precision positioning such as unmanned driving, unmanned aerial vehicle and robot navigation positioning cannot be met. In order to improve the service precision of the navigation system, a ground-based augmentation system and a satellite-based augmentation system are developed in each country. The foundation enhancement system adopts a differential positioning technology to realize high-precision instantaneous positioning in a certain area range, but because the service range of a single base station is small, a large number of ground base stations need to be arranged, the coverage of remote areas, deserts and ocean areas is difficult to realize, the investment is huge, the construction period is long, and the service range is limited. The satellite-based augmentation system generally depends on GEO satellites, is low in investment and easy to implement, has the investment of WAAS in the United states, SDCM in Russia, EGNOS in Europe, MSAS in Japan and the like, but is constrained by related physical laws and technical levels, has the problems of large link loss, difficulty in miniaturization of ground terminals and the like, and cannot meet the requirements of current users on rapid high-precision navigation services. Although the precision single-point positioning technology can realize the positioning precision of a global centimeter level, the carrier phase ambiguity parameters need to be separated by relatively long convergence time. At present, the convergence time of single-system precise point positioning is 30-40 minutes, and the convergence time of four systems is over 10 minutes, so that the application scene of positioning is seriously influenced.

The low-orbit satellite is close to the ground, the satellite operation speed is high, and the low-orbit satellite can draw a longer track in the sky than a medium-high orbit navigation satellite in the same time interval, so that the change of the observation geometric configuration is relatively severe, the fast separation of the carrier phase ambiguity parameter, the positioning coordinate and the troposphere parameter is facilitated, the bottleneck of the current high-precision positioning service is solved, and the fast convergence of the precise point positioning is realized.

The method realizes the low-orbit navigation enhanced precise point positioning, and firstly needs to obtain the precise orbit and clock error of the low-orbit satellite. In the post-processing, the precise orbit and clock error of the low-orbit satellite with higher precision can be obtained, but the precise orbit and clock error need to be obtained in real time in the low-orbit navigation enhanced precise single-point positioning, and the corresponding ephemeris and clock error can be broadcasted to the ground terminal by adopting the mode of orbit prediction by ground injection and on-satellite real-time clock error calculation. However, the low-orbit ephemeris inevitably has errors, and therefore has a great influence on the positioning of the terrestrial user terminal.

Disclosure of Invention

Aiming at the problems of the existing low-orbit navigation positioning technology, the invention provides a low-orbit navigation enhanced real-time positioning method considering satellite orbit errors, which can absorb the influence of the satellite orbit errors on a positioning result to the greatest extent by constructing a sine function or a cosine function.

In order to achieve the purpose, the technical scheme adopted by the invention is as follows:

a low orbit navigation enhancement real-time positioning method considering satellite orbit errors comprises the following steps:

step 1, a ground receiver receives observation data from a navigation satellite and a low-orbit navigation enhanced satellite;

step 2, acquiring navigation messages of the navigation satellite and the low-orbit navigation enhanced satellite, calculating broadcast ephemeris and clock error of the navigation satellite and the low-orbit navigation enhanced satellite, acquiring correction information expressed by satellite state space, and correcting the broadcast ephemeris and the clock error to obtain high-precision orbit and clock error;

step 3, preprocessing the observation data obtained in the step 1, and removing gross errors;

step 4, performing traditional single-point positioning calculation;

step 5, performing precise single-point positioning calculation;

step 6, after the precision single-point positioning result is converged, fixing the carrier phase ambiguity, introducing an additional orbit error parameter, and absorbing the influence of a satellite orbit error;

step 7, if the cycle slip and observation lock loss occur in the next epoch, suspending the estimation of the orbit error parameters, re-estimating the ambiguity of the carrier phase, and repeating the step 5; and if the positioning is successful, returning to the step 1 to perform positioning at the next moment.

Further, in step 4, the calculation equation of the conventional single-point positioning calculation is as follows:

in the formula (I), the compound is shown in the specification,the pseudo range observation value of the j frequency point received by a satellite s transmitting receiver r is measured in meters;represents the geometric distance between the satellite s and the receiver r; c represents the speed of light in vacuum; dt_rFor receiver clock difference, dt^sIs the satellite clock error;indicating tilted ionospheric delayDelay; tropospheric mapping function, ZWD_rRepresents the zenith tropospheric delay at the receiver r; epsilon_rObservation noise representing pseudo-range observations.

Further, in step 5, the calculation equation of the precise single-point positioning calculation is as follows:

in the formula (I), the compound is shown in the specification,the unit of the observed value of the carrier phase of the j frequency point received by a satellite s transmitting receiver r is meter;andpseudorange hardware delays for the receiver and the satellite, respectively;andrepresents the carrier phase hardware delays of the receiver and satellite; n is a radical of^sIs the carrier phase ambiguity; xi_rObservation noise representing a carrier phase observation.

Further, in step 6, the positioning equation after introducing the additional orbit error parameter is:

in the formula (I), the compound is shown in the specification,the influence of the orbit error of the low-orbit navigation enhanced satellite and the navigation satellite in the sight direction is shown as follows:

in the formula (X)^s，Y^s，Z^s) Enhance the true position of the satellites for navigation satellites and low-earth navigation,error positions of the navigation satellite and the low-orbit navigation enhanced satellite are calculated; the satellite orbit error presents approximate trigonometric function class characteristics, and the period is consistent with the satellite operation period, so the satellite orbit error can be simply expressed as:

further, the effect of low earth orbit and navigation satellite orbit errors in the look direction can be expressed as:

in the formula, theta represents the included angle between the orbit error of the low-orbit navigation enhanced satellite and the navigation satellite and the sight direction and constantly changes along with the movement of the satellite,not a complete sine or cosine function, but considering that the forecast track is generally shortSimplified as a trigonometric function:

at the moment, the unknown numbers of the equation (4) and the equation (5) are 5+ N, the number of the observation equations is 2N, the redundancy is N-5, N is the number of satellites, and the solution can be carried out only by observing 5 satellites at the same time.

Further, the equation of the error in step 6 is:

V＝Hx-L (10)

v is a residual vector of a pseudo range and a carrier phase observation value, H represents a Jacobian matrix of a parameter to be estimated, if deionization layer combination is adopted, the parameter to be estimated comprises receiver position coordinate correction, clock correction, zenith troposphere wet delay and carrier phase ambiguity, and if a non-differential non-combination mode is adopted to establish an observation equation, an inclined ionosphere delay parameter is also included; l represents a vector formed by the difference between the observed quantity and the calculated quantity; the weight of the observed value is determined according to the weighting mode of the satellite altitude:

wherein a and b are empirical constants, and E is the satellite altitude;

the noise variance matrix R of the observations is:

the system noise variance matrix Q is:

wherein the content of the first and second substances,variance matrix representing receiver position, using 10 for dynamic fine single point positioning³White noise of m is variance, and the initial value of the static precise single-point positioning is 10³Estimating a constant of m;

the variance of the receiver clock error is represented and described by white noise:

the variance of the zenith tropospheric wet delay is expressed using a random walk process described:

wherein, tau_{Yao (a)}Is white noise;

the variance of the tilted ionospheric delay is expressed, described using a random walk process:

represents the variance of the carrier phase ambiguity with an initial variance of 10⁴m；Representing satellite orbit error parameters, and adopting constant estimation, wherein the initial variance is 2 pi;

the parameter estimation adopts extended Kalman filtering, and the recurrence formula is as follows:

Q_{yao +1, Yao +1}＝[I-K_k+1，kH_k+1]Q_{Yao +1, Yao} (17)

Wherein Φ represents a state transition matrix of a parameter to be estimated, K is a gain matrix of kalman filtering, Γ represents a dynamic noise driving matrix, which can be generally regarded as an identity matrix, and I is an identity matrix.

Compared with the prior art, the invention has the beneficial effects that:

1. the invention can realize the rapid convergence of precise single-point positioning. By introducing the low-orbit navigation enhancement signal and carrying out combined positioning with the medium and high-orbit navigation satellite signal, the advantages of high running speed and severe geometric transformation of the low-orbit satellite are fully utilized, the convergence speed of global precise single-point positioning is improved, and global high-precision instantaneous positioning service is realized.

2. The method of the invention considers the influence of orbit errors of the current low-orbit satellite and the middle-orbit navigation satellite, can not eliminate and weaken the influence in the current precise single-point positioning method, and achieves the purpose of weakening the orbit errors by introducing the orbit error parameters in the positioning process, thereby improving the positioning precision.

Drawings

Fig. 1 is a flowchart of a low-earth-orbit navigation-enhanced real-time positioning method considering satellite orbit errors in an embodiment of the present invention.

Fig. 2 is a graph of expected achievable positioning accuracy improvement for an embodiment of the present invention.

Detailed Description

The principles and embodiments of the present invention will be described in more detail below with reference to the accompanying drawings, it being understood that the specific embodiments described herein are merely illustrative of the invention and are not limiting.

A low orbit navigation enhancement real-time positioning method considering satellite orbit error, the method utilizes low orbit enhancement signal and navigation satellite signal to carry on the fast accurate positioning to the ground receiver; by utilizing the characteristic of satellite orbit errors and constructing a sine function or a cosine function, the influence of the satellite orbit errors on a positioning result is absorbed to the greatest extent; the method utilizes the characteristics of high running speed and high positioning convergence of a low-orbit satellite and adopts a two-step method to gradually absorb the influence of the satellite orbit error.

The method comprises the following steps:

step 1, a ground receiver receives observation data from a navigation satellite and a low-orbit navigation enhanced satellite;

step 2, acquiring navigation messages of the navigation satellite and the low-orbit navigation enhanced satellite, and calculating a broadcast ephemeris and a clock error of the navigation satellite and the low-orbit navigation enhanced satellite; acquiring correction information expressed by a satellite state space through other modes such as network, satellite communication and the like, and correcting the broadcast ephemeris and clock error to obtain a track and clock error with higher precision;

step 3, preprocessing the obtained observation data, and removing gross errors by using a method including MW combination;

step 4, performing traditional single-point positioning calculation;

step 5, performing precise single-point positioning calculation;

step 6, after the precision single-point positioning result is converged, fixing the carrier phase ambiguity, introducing an additional orbit error parameter into a precision single-point positioning equation, and absorbing the influence of a satellite orbit error;

step 7, if the cycle slip and observation lock loss occur in the next epoch, suspending the estimation of the orbit error parameters, re-estimating the ambiguity of the carrier phase, and repeating the step 5; and if the positioning is successful, returning to the step 1 to perform positioning at the next moment.

Linearizing the positioning observation equation, and absorbing the code and carrier phase deviation into the receiver clock error and ionospheric delay parameters to obtain the following formula:

in the formula (I), the compound is shown in the specification,representing the unit vector transmitted by satellite s to receiver r,indicating a receiver clock error that absorbs code and carrier phase deviations,represents the tilted ionospheric delay absorbing code and carrier phase deviations; tropospheric mapping function, ZWD_rRepresenting the zenith tropospheric delay at the receiver,to absorb ambiguity of carrier phase deviation;representing the influence of orbit errors of low-orbit satellites and navigation satellites in a sight direction; epsilon_rAnd xi_rObservation noise, multipath effects, and other effects that represent pseudorange and carrier phase observations.

The low earth satellite and navigation satellite orbital errors can be expressed as:

in the formula (X)^s，Y^s，Z^s) For navigation satellites and low earth orbit satellites true position,erroneous positions are taken for the calculated navigation satellites and low orbit satellites. The orbit broadcast by the navigation satellite and the low orbit satellite is obtained by orbit prediction after the former precision orbit determination, the orbit error of the satellite presents approximate trigonometric function characteristics, and the period is consistent with the satellite operation period, so the orbit error of the satellite can be simply expressed as:

further, the effect of low earth orbit and navigation satellite orbit errors in the look direction can be expressed as:

in the formula, theta represents the included angle between the orbit error of the low orbit satellite and the navigation satellite and the sight direction and constantly changes along with the movement of the satellite,not a complete sine or cosine function, but considering that the forecast track is generally shortSimplified as a trigonometric function:

from the observation equation, an error equation can be listed:

V＝Hx-L (24)

v is a residual vector of a pseudo range and a carrier phase observation value, H represents a Jacobian matrix of a parameter to be estimated, if deionization layer combination is adopted, the parameter to be estimated comprises receiver position coordinate correction, clock correction, zenith troposphere wet delay, carrier phase ambiguity and the like, and if an observation equation is established in a non-differential non-combination mode, an inclined ionosphere delay parameter is also included; l represents a vector consisting of the difference between the observed and calculated quantities. The weight of the observed value is determined according to the weighting mode of the satellite altitude:

wherein a and b are empirical constants, and E is the satellite altitude, a noise variance matrix R of the observed value can be formed:

the system noise variance matrix Q may be expressed as:

wherein the content of the first and second substances,variance matrix representing receiver position, using 10 for dynamic fine single point positioning³White noise of m is variance, and the initial value of the static precise single-point positioning is 10³And (5) estimating the constant of m.The variance of the receiver clock error is represented and described by white noise: the variance of the zenith tropospheric wet delay is expressed using a random walk process described:wherein tau is_{Yao (a)}Is white noise.The variance of the tilted ionospheric delays is also described using a random walk process: represents the variance of the carrier phase ambiguity with an initial variance of 10⁴m。Representing satellite orbit error parameters, using constant estimation, the estimated parameters being of formula (23)The initial variance is 2 pi, wherein B is set according to the actual track precision and is generally 0.1-3 m.

The parameter estimation adopts the extended kalman filtering, and can be described by the following equation:

X_{yao +1}＝Φ_{Yao +1, Yao}X_{Yao (a)}+Γ_{Yao +1, k}W_{Yao (a)}

L_{Yao +1}＝H_k+1X_{Yao +1}-V_{Yao +1}

The recurrence formula is:

Q_{yao +1, Yao +1}＝[I-K_k+1，kH_k+1]Q_{Yao +1, Yao}(31) Wherein Φ represents a state transition matrix of a parameter to be estimated, K is a gain matrix of kalman filtering, Γ represents a dynamic noise driving matrix, which can be generally regarded as an identity matrix, and I is an identity matrix.

At the initial positioning moment, carrier phase ambiguity exists, so that orbit errors of a low orbit satellite and a navigation satellite are ignored firstly, and single-point positioning and precise single-point positioning are respectively carried out by adopting a traditional method. Because the low-orbit satellite has high running speed and drastic change of the geometric configuration, the low-orbit navigation enhanced precise single-point positioning convergence speed is high, and the carrier phase ambiguity is converged after the positioning convergence.

After the first positioning convergence, fixing the carrier phase ambiguity parameters, and introducing the orbit error parameters of the low-orbit satellite and the navigation satelliteSetting upInIs 0, the initial variance is 2 pi, and the system noise variance matrix Q is reconstructed. According to the nominal precision of the low-earth orbit satellite and the orbit of the navigation satellite, giving a corresponding initial value B for an orbit error parameter equation, and estimating a parameter to be estimated according to a corresponding satellite operation period TWith the parameter to be estimatedAnd the positioning accuracy can be further improved after the fixing is successfully carried out. If cycle slip occurs in subsequent observations, carrier phase ambiguities and parameters need to be reconvergedIts initial value and initial variance will also be reset.

The following is a more specific example:

as shown in fig. 1, the method for enhancing real-time positioning of low-orbit navigation considering satellite orbit errors is based on extended kalman filtering, and can be used as a real-time positioning algorithm and a post-processing algorithm, and the application range includes static positioning, dynamic positioning and the like. The method is used in real-time positioning, and the specific steps are described as follows:

1) the ground receiver receives observation data from a navigation satellite and a low-orbit navigation enhancement satellite;

2) the receiver analyzes the navigation messages of the navigation satellite and the low-orbit navigation enhanced satellite, calculates the broadcast ephemeris and clock error of the navigation satellite and the low-orbit navigation enhanced satellite, and can also acquire the correction information expressed by the satellite state space through other modes such as network, satellite communication and the like to correct the broadcast ephemeris and clock error, wherein the correction method comprises the following steps:

the broadcast ephemeris is located in a geocentric earth-fixed coordinate system, and the coordinate system where the orbit correction number is located is a satellite-fixed coordinate system, so that the orbit correction number is converted into the correction number under the geocentric earth-fixed coordinate system, and then the satellite orbit is corrected, wherein the formula is as follows:

X_orbit＝X_broadcast-δX (32)

in the formula, X_orbitRepresenting the satellite orbit corrected by low-orbit enhancement information, X_broadcastThe method is characterized in that the method represents the satellite position calculated by the broadcast ephemeris, and δ X is the orbit correction number under the geocentric earth fixation system calculated by the low-orbit enhancement information, and the method comprises the following steps:

e_n＝e_t×r_r (35)

δX＝[e_re_te_n]δ O (36) wherein r ═ X_broadcastA satellite position vector representing the broadcast ephemeris calculation, represents the satellite velocity vector of the broadcast ephemeris calculation and δ O represents the orbit correction vector.

The satellite clock error correction parameters are generally expressed by using a quadratic polynomial coefficient, and firstly, the clock error correction parameters corresponding to the current time need to be recovered:

Δt＝C₀+C₁(t-t₀)+C₂(t-t₀)²(37) the satellite clock error can be recovered according to the following formula:

wherein, t_broadcastRepresenting the satellite clock error parameter, t, calculated from the broadcast ephemeris_sFor the corrected satellite precision clock error parameter, c represents the speed of light.

3) Preprocessing the obtained observation data, and removing gross errors by using a method including MW combination;

4) the positioning observation equation considering the satellite orbit error provided by the invention is linearized, and the code and carrier phase deviation is absorbed into the receiver clock error and the ionosphere delay parameter, so that the following formula can be obtained:

in the formula (I), the compound is shown in the specification,representing the unit vector transmitted by satellite s to receiver r,indicating a receiver clock error that absorbs code and carrier phase deviations,represents the tilted ionospheric delay absorbing code and carrier phase deviations; tropospheric mapping function, ZWD_rRepresenting the zenith tropospheric delay at the receiver,to absorb ambiguity of carrier phase deviation;representing the influence of orbit errors of low-orbit satellites and navigation satellites in a sight direction; epsilon_rAnd xi_rObservation noise, multipath effects, and other effects that represent pseudorange and carrier phase observations.

And performing traditional single-point positioning calculation by using a least square method according to the calculated broadcast ephemeris clock error or the precise ephemeris and clock error and the linearized positioning observation equation. If the number of the satellites exceeds 4, continuously using the GF and MW combination to carry out cycle slip detection;

5) and (4) not considering the track error, and performing precise single-point positioning. From the observation equation, an error equation can be listed:

V＝Hx-L (41)

v is a residual vector of a pseudo range and a carrier phase observation value, H represents a Jacobian matrix of a parameter to be estimated, if deionization layer combination is adopted, the parameter to be estimated comprises receiver position coordinate correction, clock correction, zenith troposphere wet delay, carrier phase ambiguity and the like, and if an observation equation is established in a non-differential non-combination mode, an inclined ionosphere delay parameter is also included; l represents a vector consisting of the difference between the observed and calculated quantities. The weight of the observed value is determined according to the weighting mode of the satellite altitude:

wherein a and b are empirical constants, and E is the satellite altitude, a noise variance matrix of the observed values can be formed:

the system noise variance matrix Q may be expressed as:

wherein the content of the first and second substances,variance matrix representing receiver position, using 10 for dynamic fine single point positioning³White noise of m is variance, and the initial value of the static precise single-point positioning is 10³And (5) estimating the constant of m.The variance of the receiver clock error is represented and described by white noise: the variance of the zenith tropospheric wet delay is expressed using a random walk process described:wherein tau is_{Yao (a)}Is white noise.The variance of the tilted ionospheric delays is also described using a random walk process: represents the variance of the carrier phase ambiguity with an initial variance of 10⁴m。

The parameter estimation adopts extended Kalman filtering:

X_{yao +1}＝Φ_{Yao +1, Yao}X_{Yao (a)}+Γ_{Yao +1, k}W_{Yao (a)} (45)

L_{Yao +1}＝H_k+1X_{Yao +1}-V_{Yao +1}(46) The recurrence formula is:

Q_{yao +1, Yao +1}＝[I-K_k+1，kH_k+1]Q_{Yao +1, Yao}(50) Wherein Φ represents a state transition matrix of a parameter to be estimated, K is a gain matrix of kalman filtering, Γ represents a dynamic noise driving matrix, which can be generally regarded as an identity matrix, and I is an identity matrix.

Sequentially carrying out parameter estimation on the observed value of each epoch, if the precision single-point positioning result is not converged, storing the variance covariance matrix of the parameter to be estimated at the moment, and continuing to calculate the next epoch; if the precise single-point positioning result is converged at the moment, the carrier phase ambiguity is fixed, an additional orbit error parameter is introduced into a positioning equation, and an orbit error parameter is introduced into a system noise variance matrix Q:

wherein the content of the first and second substances,and representing satellite orbit error parameters, and adopting constant estimation, wherein the initial variance is 2 pi. And performing precise point positioning calculation by using the extended Kalman filtering again.

6) If the conditions of unrepairable cycle slip, observation lock losing and the like occur, suspending the estimation of the track error parameters and returning to the step 4; and if the cycle slip does not exist, returning to the step 1 to perform next epoch positioning.

The expected accuracy enhancement effect of the method is shown in fig. 2. In the diagram, at the initial positioning moment, carrier phase ambiguity exists, so that the positioning has a first convergence process, and because the low-orbit satellite has high running speed and severe change of geometric configuration, the positioning convergence speed is higher than that of the traditional precise single-point positioning, and the carrier phase ambiguity is converged after the positioning convergence. After the first positioning convergence, fixing the carrier phase ambiguity parameters, and introducing the orbit error parameters of the low-orbit satellite and the navigation satelliteThe improvement in accuracy can be represented by the staircase shape in fig. 2.

The invention adopts a two-step method to weaken the influence of orbit errors, and a ground receiver is used for receiving observation data and navigation messages and calculating the orbit and clock error of a navigation satellite and a low-orbit satellite respectively; positioning is carried out according to a conventional mode, orbit error parameters are estimated after convergence of the position to be positioned, and the orbit errors of the low-orbit satellite and the navigation satellite are absorbed by giving proper weight, so that the effect of improving the positioning precision is achieved. The method utilizes the characteristic that the low-orbit navigation enhances the PPP convergence speed, and introduces the orbit error parameter by rapidly converging the carrier phase ambiguity so as to weaken the influence of the satellite orbit error on the positioning and improve the accuracy of the low-orbit navigation enhanced positioning.

In a word, the method fully considers the characteristic of the satellite orbit error, and the influence of the satellite orbit error on the precision positioning precision is absorbed by adding the orbit error parameter in the observation equation. The invention can provide high-quality positioning service for users with high requirement on positioning accuracy, has certain delay for first positioning, and can provide uninterrupted high-quality positioning result after positioning convergence.