CN112578423A

CN112578423A - Integer ambiguity determination method, device and equipment

Info

Publication number: CN112578423A
Application number: CN201910944143.0A
Authority: CN
Inventors: 甘雨; 刘刚; 吴亮; 张硕
Original assignee: Alibaba Group Holding Ltd
Current assignee: Wuzhou Online E Commerce Beijing Co ltd
Priority date: 2019-09-30
Filing date: 2019-09-30
Publication date: 2021-03-30
Also published as: WO2021063209A1

Abstract

The application discloses a method, a device and a system for determining integer ambiguity, a method, a device and a system for positioning mobile equipment, the mobile equipment and a reference station. The integer ambiguity determination method comprises the following steps: a whole-cycle ambiguity determination method. By adopting the processing mode, the ambiguity estimator is constructed based on the inertial navigation position and the carrier phase observation value, and the ambiguity is fixed according to the estimator, so that the mode of assisting RTK fixed ambiguity by INS is realized, on one hand, ambiguity search is not needed, ambiguity fixed solution errors caused by ambiguity search convergence to a local minimum value caused by carrier phase observation value errors can be avoided, on the other hand, pseudo range observation values are not used, and ambiguity fixed solution errors caused by pseudo range influenced by errors such as multipath effect in a severe environment can be avoided; therefore, robustness and efficiency of ambiguity fixing can be effectively improved, and further fast and accurate positioning of the mobile equipment is achieved.

Description

Integer ambiguity determination method, device and equipment

Technical Field

The application relates to the field of mobile equipment positioning, in particular to a method, a device and a system for determining integer ambiguity, a method, a device and a system for positioning mobile equipment, mobile equipment and a reference station.

Background

With the rapid development of satellite positioning technology, people have increasingly strong demands for rapid and high-precision position information. The most widely used high-precision positioning technology at present is RTK (Real-Time Kinematic), which is characterized in that carrier phase observed quantity of GNSS (Global Navigation Satellite System) is used, spatial correlation of observation errors between a reference station and a mobile station is utilized, and most errors in observation data of the mobile station are removed in a differential mode, so that high-precision (decimeter or even centimeter level) positioning is realized.

Accurate fixation of the whole-cycle ambiguity (ambiguities of the whole cycles) is a prerequisite for RTK to obtain reliable high-precision (centimeter-level) positioning results. The integer ambiguity is also called integer unknown, which is the integer unknown corresponding to the first observed value of the phase difference between the carrier phase and the reference phase when the carrier phase is measured in the global positioning system technology. This is also referred to as the integer ambiguity since the integer number of cycles (number of integer cycles) of the carrier in space at this time is an unknown number that cannot be observed. When the integer ambiguity is determined by a certain mathematical method, the distance measurement from the satellite to the user can be accurate to less than one wavelength, and the error magnitude of centimeter or even millimeter is achieved. It can be seen that correctly determining the integer ambiguity is one of the most important and necessary problems in global positioning system carrier phase measurement.

At present, in a single GNSS (Global Navigation Satellite System), an observation equation is generally established by pseudo-range and carrier observation to solve a position parameter and an ambiguity parameter floating solution, and then a lamb da method is used to search for a fixed ambiguity parameter; in a GNSS/INS (Inertial Navigation System) combined System, an INS position is generally used as a virtual observation value, the virtual observation value is combined with a pseudorange and a carrier observation equation to assist ambiguity floating solution, and then a fixed ambiguity parameter is searched by using the LAMBDA method.

However, in the process of implementing the present invention, the inventor finds that the above-mentioned prior art for fixing the integer ambiguity has at least the following problems: 1) due to error interference such as residual atmospheric refraction delay, multipath effect and the like, a GNSS carrier observed value may include large system error and gross error, a floating solution and a covariance matrix thereof are inaccurate when a single GNSS system is used for resolving, and ambiguity searching can be converged to a local minimum value rather than a global minimum value at the moment, so that ambiguity fixing solution errors are caused; 2) the INS position is used as virtual observation in the GNSS/INS combined system, so that the floating solution precision can be improved, but when the error of the INS is large, the INS error is diffused into the floating solution, and the ambiguity fixing accuracy is reduced; 3) in the prior art, pseudo-range observation quantity is needed, the pseudo-range is greatly influenced by errors such as multipath effect and the like, and result deviation can occur in severe environments (such as tunnels, downtown areas, non-open areas of mines and operation of forest vegetation in a wide and flushy coverage area); 4) the ambiguity fixing speed is low because ambiguity search is to be performed. In summary, the prior art has the problems of low robustness of ambiguity fixing caused by weak interference resistance of the whole-cycle ambiguity and low ambiguity fixing efficiency caused by ambiguity searching.

Disclosure of Invention

The application provides an integer ambiguity determination method to solve the problems of low ambiguity fixing robustness and low efficiency in the prior art. The application further provides an integer ambiguity determination device and system, a mobile device positioning method, device and system, a mobile device and a reference station.

The application provides a method for determining integer ambiguity, comprising the following steps:

the mobile equipment collects first carrier phase observation data; receiving second carrier phase observation data sent by the reference station;

determining inertial navigation position data as first position data;

determining an estimator of integer ambiguity of satellite frequency points according to the first position data and the observation data;

and determining the integer ambiguity according to the estimation quantity.

Optionally, the determining an estimator of the integer ambiguity of the satellite frequency points according to the first position data and the observation data includes:

determining a first estimator of integer ambiguity of each frequency point of a first satellite according to the first position data and the observation data; the first satellite comprises a satellite having an altitude angle greater than or equal to an altitude angle threshold;

and determining an integer ambiguity based on the estimate, comprising:

and determining a first integer ambiguity of each frequency point of the first satellite according to the first estimation quantity.

Optionally, the determining an integer ambiguity according to the estimator further includes:

determining second position data of the mobile equipment according to the first integer ambiguity;

determining a second integer ambiguity of each frequency point of a second satellite according to the second position data; the second satellite includes a satellite having an altitude angle less than an altitude angle threshold.

Optionally, the determining a first integer ambiguity of each frequency point of the first satellite according to the first estimator includes:

rounding the first estimate to an integer as the first integer ambiguity.

aiming at each first satellite, constructing at least two wide lane combinations of integer ambiguity of any two frequency points of the first satellite according to the first estimators of the any two frequency points;

determining a second estimator of integer ambiguity for the wide-lane combination;

determining the integer ambiguity of the wide-lane combination according to the second estimator;

and determining the first integer ambiguity according to the integer ambiguity of the wide lane combination.

Optionally, the determining the integer ambiguity of the wide-lane combination according to the second estimator includes:

rounding the second estimator to an integer as the whole-cycle ambiguity for the wide-lane combination.

if the ionospheric error of the wide lane combination is amplified, performing polynomial fitting on the wide lane combination with the amplified ionospheric error to compensate the ionospheric delay error;

and rounding off the second estimator after compensating the ionospheric delay error to obtain an integer as the whole-cycle ambiguity of the wide-lane combination.

Optionally, the determining a third integer ambiguity of the wide-lane combination according to the second estimator further includes:

and if the ionospheric error of the wide-lane combination is reduced, rounding off the second estimator of the wide-lane combination with reduced ionospheric error to obtain an integer as the third integer ambiguity.

The application also provides a method for determining integer ambiguity, comprising:

the reference station acquires second carrier phase observation data;

transmitting the second carrier phase observation data to the mobile device to enable the mobile device to perform the following steps of acquiring first carrier phase observation data by the mobile device; receiving second carrier phase observation data sent by the reference station; determining inertial navigation position data as first position data; determining an estimator of integer ambiguity of satellite frequency points according to the first position data and the observation data; and determining the integer ambiguity according to the estimation quantity.

The present application further provides an integer ambiguity determination apparatus, comprising:

the data acquisition unit is used for acquiring first carrier phase observation data by the mobile equipment;

the data receiving unit is used for receiving second carrier phase observation data sent by the reference station;

a data determination unit for determining inertial navigation position data as first position data;

the estimator determining unit is used for determining the estimator of the integer ambiguity of the satellite frequency points according to the first position data and the observation data;

and the integer ambiguity determining unit is used for determining the integer ambiguity according to the estimation quantity.

the data acquisition unit is used for acquiring second carrier phase observation data by the reference station;

a data sending unit, configured to send the second carrier phase observation data to a mobile device, so that the mobile device performs the following steps that the mobile device collects first carrier phase observation data; receiving second carrier phase observation data sent by the reference station; determining inertial navigation position data as first position data; determining an estimator of integer ambiguity of satellite frequency points according to the first position data and the observation data; and determining the integer ambiguity according to the estimation quantity.

The present application further provides a mobile device, comprising:

a GNSS receiver;

an inertial measurement unit;

a processor; and

a memory for storing a program for implementing the integer ambiguity determination method, the apparatus performing the following steps after being powered on and running the program of the method by the processor: the mobile equipment collects first carrier phase observation data; receiving second carrier phase observation data sent by the reference station; determining inertial navigation position data as first position data; determining an estimator of integer ambiguity of satellite frequency points according to the first position data and the observation data; and determining the integer ambiguity according to the estimation quantity.

The present application further provides a reference station, comprising:

a GNSS receiver;

a processor; and

a memory for storing a program for implementing the integer ambiguity determination method, the apparatus performing the following steps after being powered on and running the program of the method by the processor: the reference station acquires second carrier phase observation data; transmitting the second carrier phase observation data to the mobile device to enable the mobile device to perform the following steps of acquiring first carrier phase observation data by the mobile device; receiving second carrier phase observation data sent by the reference station; determining inertial navigation position data as first position data; determining an estimator of integer ambiguity of satellite frequency points according to the first position data and the observation data; and determining the integer ambiguity according to the estimation quantity.

The present application further provides an integer ambiguity determination system, comprising:

according to the mobile device; and, according to the reference station.

The application also provides a mobile device positioning method, which comprises the following steps:

determining inertial navigation position data as first position data;

determining an integer ambiguity according to the estimator;

and determining the position data of the mobile equipment at least according to the integer ambiguity.

the reference station acquires second carrier phase observation data;

sending the second carrier-phase observation data to the mobile device to cause the mobile device to perform the steps of: the mobile equipment collects first carrier phase observation data; receiving second carrier phase observation data sent by the reference station; determining inertial navigation position data as first position data; determining an estimator of integer ambiguity of satellite frequency points according to the first position data and the observation data; determining an integer ambiguity according to the estimator; and determining the position data of the mobile equipment at least according to the integer ambiguity.

The present application further provides a mobile device positioning apparatus, including:

the integer ambiguity determining unit is used for determining integer ambiguity according to the estimator;

a location determining unit, configured to determine location data of the mobile device at least according to the integer ambiguity.

a data transmitting unit, configured to transmit the second carrier-phase observation data to a mobile device, so that the mobile device performs the following steps: the mobile equipment collects first carrier phase observation data; receiving second carrier phase observation data sent by the reference station; determining inertial navigation position data as first position data; determining an estimator of integer ambiguity of satellite frequency points according to the first position data and the observation data; determining an integer ambiguity according to the estimator; and determining the position data of the mobile equipment at least according to the integer ambiguity.

The present application further provides a mobile device, comprising:

a GNSS receiver;

an inertial measurement unit;

a processor; and

a memory for storing a program for implementing a method for locating a mobile device, the device being powered on and the program for implementing the method being executed by the processor for performing the steps of: the mobile equipment collects first carrier phase observation data; receiving second carrier phase observation data sent by the reference station; determining inertial navigation position data as first position data; determining an estimator of integer ambiguity of satellite frequency points according to the first position data and the observation data; determining an integer ambiguity according to the estimator; and determining the position data of the mobile equipment at least according to the integer ambiguity.

The present application further provides a reference station, comprising:

a GNSS receiver;

a processor; and

a memory for storing a program for implementing a method for locating a mobile device, the device being powered on and the program for implementing the method being executed by the processor for performing the steps of: the reference station acquires second carrier phase observation data; sending the second carrier-phase observation data to the mobile device to cause the mobile device to perform the steps of: the mobile equipment collects first carrier phase observation data; receiving second carrier phase observation data sent by the reference station; determining inertial navigation position data as first position data; determining an estimator of integer ambiguity of satellite frequency points according to the first position data and the observation data; determining an integer ambiguity according to the estimator; and determining the position data of the mobile equipment at least according to the integer ambiguity.

The present application further provides a mobile device positioning system comprising:

according to the mobile device; and, according to the reference station.

The present application also provides a computer-readable storage medium having stored therein instructions, which when run on a computer, cause the computer to perform the various methods described above.

The present application also provides a computer program product comprising instructions which, when run on a computer, cause the computer to perform the various methods described above.

Compared with the prior art, the method has the following advantages:

according to the integer ambiguity determining method provided by the embodiment of the application, first carrier phase observation data are collected through mobile equipment, and second carrier phase observation data sent by a reference station are received; determining inertial navigation position data, determining an estimator of integer ambiguity of satellite frequency points according to the inertial navigation position data and carrier phase observation data, and determining the integer ambiguity according to the estimator; by the aid of the processing mode, the ambiguity estimator is constructed based on the inertial navigation position and the carrier phase observation value, and the ambiguity is fixed according to the estimator, so that an INS assisted RTK ambiguity fixing mode is realized, ambiguity searching is not needed, ambiguity fixing solution errors caused by ambiguity searching convergence to a local minimum value due to carrier phase observation value errors can be avoided, and ambiguity fixing solution errors caused by pseudo range errors under a severe environment and other errors can be avoided due to the fact that the pseudo range is not used; therefore, the error interference resistance of the fixed ambiguity can be effectively improved, the robustness of the fixed ambiguity is improved, the fixed accuracy of the ambiguity is ensured, and the accurate positioning of the mobile equipment is realized. Meanwhile, due to the processing mode, the ambiguity estimators are fixed by direct rounding, and ambiguity search is not needed; therefore, the ambiguity fixing speed can be effectively improved, and the mobile equipment can be quickly positioned.

Drawings

FIG. 1 is a flow chart of an embodiment of a method for integer ambiguity determination provided herein;

FIG. 2 is a detailed flow chart of an embodiment of a method for integer ambiguity determination provided herein;

FIG. 3 is a further detailed flowchart of an embodiment of a method for integer ambiguity determination provided herein;

FIG. 4 is a further detailed flowchart of an embodiment of a method for integer ambiguity determination provided herein;

FIG. 5 is a further detailed flowchart of an embodiment of a method for integer ambiguity determination provided herein;

FIG. 6 is a schematic diagram of an embodiment of an integer ambiguity determination apparatus provided herein;

FIG. 7 is a schematic diagram of an embodiment of a mobile device provided herein;

FIG. 8 is a flow chart of an embodiment of a method for integer ambiguity determination provided herein;

FIG. 9 is a schematic diagram of an embodiment of an integer ambiguity determination apparatus provided herein;

FIG. 10 is a schematic illustration of an embodiment of a reference station provided herein;

FIG. 11 is a schematic diagram of an embodiment of an integer ambiguity determination system provided herein;

FIG. 12 is a schematic view of a scene of an embodiment of an integer ambiguity determination system provided by the present application.

Detailed Description

In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present application. This application is capable of implementation in many different ways than those herein set forth and of similar import by those skilled in the art without departing from the spirit of this application and is therefore not limited to the specific implementations disclosed below.

In the application, an integer ambiguity determination method, device and system, a mobile device positioning method, device and system, a mobile device and a reference station are provided. In the following embodiments, the vehicle will be taken as an example, and each of the various schemes will be described in detail.

First embodiment

Please refer to fig. 1, which is a flowchart illustrating an embodiment of an integer ambiguity determination method according to the present application, wherein the execution subject of the method includes an unmanned vehicle, a robot, and other mobile devices. In this embodiment, the method includes the steps of:

step S101: the mobile equipment collects first carrier phase observation data; and receiving second carrier phase observation data transmitted by the reference station.

RTK is a technique for performing real-time dynamic relative positioning on carrier phase observations. The principle is that satellite data observed by a GNSS receiver (e.g. a GPS receiver) located at a reference station is transmitted in real time via a data communication link (radio station), while a GNSS receiver of a mobile station (mobile device) located nearby receives a station signal from the reference station while observing the satellite, and the received signal is processed in Real Time (RTK) to give a three-dimensional coordinate of the mobile station and estimate its accuracy.

When RTK measurement is used, at least two GNSS receivers are equipped, one GNSS receiver is fixedly arranged on a reference station, and the other GNSS receiver is used as a mobile station for point location measurement. A data communication link is also required between the two receivers to transmit the carrier phase observations at the reference station to the rover station in real time. Real-time processing of data (satellite signals and signals of a reference station) received by a rover station also requires an RTK positioning device which mainly completes solution of double-difference ambiguity (whole-cycle ambiguity), solution of a baseline vector, and transformation of coordinates. When the method provided by this embodiment is used to determine the integer ambiguity, the reference station receiver is required to transmit the second carrier phase observation data and the known data to the rover (mobile device) receiver in real time, and it should be noted that the pseudorange observation value does not need to be transmitted.

Step S103: inertial navigation position data is determined as first position data.

The mobile device may include an inertial measurement unit, IMU. Inertial navigation relies on raw data of inertial devices (gyros, accelerometers, etc.) plus fixed algorithms to output data such as device position (inertial navigation position, INS position), carrier attitude, real-time movement velocity, etc.

Step S105: and determining an estimator of the integer ambiguity of the satellite frequency points according to the first position data and the observation data.

According to the method provided by the embodiment of the application, the INS position and the carrier phase observation value are used for constructing the ambiguity estimator, and the whole-cycle model degree is solved according to the estimator without using the pseudo-range observation value. The estimated integer ambiguity is described in the description of fig. 2.

Step S107: and determining the integer ambiguity according to the estimation quantity.

The integer ambiguity is also called integer unknown, which is the integer unknown corresponding to the first observed value of the phase difference between the carrier phase and the reference phase when the carrier phase is measured in the global positioning system technology.

Please refer to fig. 2, which is a flowchart illustrating the step S105 of an embodiment of the integer ambiguity determination method according to the present application. In this embodiment, step S105 can be implemented as follows: and determining a first estimator of the integer ambiguity of each frequency point of the first satellite according to the first position data and the observation data.

The first satellite includes a satellite having an altitude angle greater than or equal to an altitude angle threshold. The elevation angle may be an angle between a direction line from the mobile device to the observation target satellite and a horizontal plane. The elevation angle is the main observed quantity for calculating the height difference between two points in the triangulation elevation measurement.

The embodiment classifies all the satellites into two types of basic satellites with higher elevation angles and non-basic satellites with lower elevation angles. Taking a satellite with an altitude angle greater than or equal to an altitude angle threshold value as a basic satellite, namely a first satellite; the satellite with the altitude angle smaller than the altitude angle threshold value is taken as a non-basic satellite and is also called a second satellite.

The altitude threshold may be determined according to traffic requirements, for example, set to 25-30 degrees. When determining the altitude angle threshold, it should be ensured that the satellites whose altitude angles are higher than the altitude angle threshold have higher continuity of the observed data, and the error is smaller, otherwise, if the threshold is too small, the data continuity of some satellites is not enough, and the satellites cannot be used as basic satellites.

A satellite typically has multiple frequency points, such as GPS, where each satellite has 3 frequency points, L1 (e.g., 1575.42MHz), L2 (e.g., 1575.42MHz), and L5. In this embodiment, for each basic satellite, the first estimated value of double-difference ambiguity (i.e. integer ambiguity) of a single frequency point of a single satellite can be calculated as follows:

wherein ^ is an inter-satellite difference operator, Δ is an inter-station (between a base station and a rover) difference operator, Δ is a station-satellite double difference (after making a difference between the base station and the rover, making a difference between satellites) operator, [ Δ ρ ^ is ^ Δ ρ_I＝▽ρ_I-▽ρ_iIncluding double-differenced geometric distances calculated from the INS position (i.e., the first position data) and the satellite positions of the mobile device, I represents an INS-related quantity, I represents a reference station-related quantity, Δ Φ is double-differenced ambiguity, λ ^ Δ Φ is the double-differenced ambiguity, and_kthe wavelength of frequency point k.

Taking the GPS L1 and L2 as examples, the first estimate of L1 ambiguity is:

the first estimate of L2 ambiguity is:

accordingly, step S107 may comprise the following sub-steps:

step S1071: and determining a first integer ambiguity of each frequency point of the first satellite according to the first estimation quantity.

In specific implementation, step S1071 may be implemented as follows: rounding the first estimate to an integer value, the integer value being the first integer ambiguity.

Thus, the first integer ambiguity of each frequency point of the basic satellite is determined. In this embodiment, the first integer ambiguity includes: the ambiguity corresponding to the three frequency points L1, L2 and L5 of the basic satellite a, the ambiguity corresponding to the three frequency points L1, L2 and L5 of the basic satellite B, the ambiguity corresponding to the three frequency points L1, L2 and L5 of the basic satellite C, and so on.

Please refer to fig. 3, which is a flowchart illustrating a step S107 of an embodiment of a method for determining integer ambiguity. In this embodiment, step S107 may further include the following sub-steps in addition to determining the first integer ambiguity of each frequency point of the first satellite according to the first estimator:

step S1073: and determining second position data of the mobile equipment according to the first integer ambiguity.

The second position data refers to the position of the mobile equipment determined according to the fixed integer ambiguity of each frequency point of the basic satellite. And estimating the coordinates of the mobile equipment receiver by using the basic satellite with fixed ambiguity of each frequency point, and replacing the INS position with the position, wherein the position is more accurate than the INS position.

Step S1075: and determining a second integer ambiguity of each frequency point of a second satellite according to the second position data.

The second satellite includes a satellite having an altitude angle less than an altitude angle threshold.

After the second position data is determined, the ambiguity parameters of the non-basic satellite can be directly estimated according to the determination formula of the first estimation value, and the ambiguity parameters are directly rounded and fixed. Taking the L1 and L2 of the non-essential satellite E as examples, the first estimate of the L1 ambiguity is:

the first estimate of L2 ambiguity is:

after determining the second estimated value of the integer ambiguity of the non-base satellite, the second estimated value of the integer ambiguity of the non-base satellite can be directly rounded to obtain the second integer ambiguity of the non-base satellite.

And determining the integer ambiguity of each frequency point of all satellites, including the second integer ambiguity of each frequency point of the non-basic satellite. In this embodiment, the second integer ambiguity includes: the integer ambiguity corresponding to the three frequency points L1, L2 and L5 of the non-essential satellite E, the integer ambiguity corresponding to the three frequency points L1, L2 and L5 of the non-essential satellite F, and so on.

Please refer to fig. 4, which is a flowchart illustrating a step S1071 of an embodiment of a method for determining integer ambiguity according to the present application. In one example, step S1051 may include the following sub-steps:

step S10711: and aiming at each first satellite, constructing at least two wide lane combinations of integer ambiguity of any two frequency points of the first satellite according to the first estimators of any two frequency points of the first satellite.

The wide lane combination is a linear combination of the original observed values of the carrier phases, and the wavelength is greater than the wavelength of the original carrier.

Step S10713: determining a second estimator of integer ambiguity for the wide-lane combination.

In this embodiment, two wide lane combinations are selected, and a combined ambiguity statistic is calculated (subscripts 1 and 2 in the following formula represent any two frequency points of the satellite system, and the N-point represents an estimate of the integer ambiguity of the wide lane combination):

(a, b) wide lanes of

(c, d) wide lanes of

Because the wavelength of the wide-lane combination is multiplied by a plurality of times compared with the wavelength of a single frequency point, the tolerance of the statistic (estimation quantity) to the INS error can be increased.

Step S10715: and determining the integer ambiguity of the wide-lane combination according to the second estimator.

For example, wide lane combined ambiguities (including but not limited to):

(1, -1) the wide lane is

(-3,4) wide lane of

(-4,5) wide lane of

(-7,9) wide lane of

Wherein the wavelength of the (1, -1) wide-lane combination is about 4 times that of a single frequency point, and the wavelength of the (-3,4) combination is about 10 times that of a single frequency point. The ambiguity of the whole fixed widelane is obtained by rounding, and the error of the ambiguity of the widelane is required to be within 0.5 week. For the (1, -1) combination, if the INS error is within 0.43m (0.5/1.16), the wide lane estimation error caused by the INS error is within 0.5 week, and the fixed wide lane can be directly rounded (rounded); the tolerance of the (-3,4) combination to INS errors is up to 0.81m, the (-4,5) and (-7,9) being higher. In a vehicle-mounted integrated navigation system (GNSS/INS integrated system), even if the vehicle travels for several minutes in a severe environment such as a tunnel, an INS error under multi-source fusion assistance does not exceed 0.43 m.

In specific implementation, step S10715 may be implemented as follows: rounding the second estimator to an integer as the whole-cycle ambiguity for the wide-lane combination.

Step S10717: and determining the first integer ambiguity according to the integer ambiguity of the wide lane combination.

In the step, the integer ambiguity of each frequency point is inversely calculated by the integer ambiguity of the wide lane combination, and the following formula can be adopted:

taking wide lane combinations (1, -1) and (-3,4) as examples:

▽ΔN₁＝4N_WL11+N_WL34；▽ΔN₂＝3N_WL11+N_WL34。

it should be noted that although the tolerance of the statistics to INS errors can be increased by processing the wide-lane combination, most wide-lane combinations amplify ionospheric errors while increasing the wavelength, such as (-3,4), (-4,5), (-7,9) combinations. It can be seen that the larger the tolerance of the above processing method to INS errors, the larger the ionospheric error is, thereby affecting the accuracy of the integer ambiguity.

In order to solve this problem, the method provided in this embodiment may adopt a polynomial fitting or other manners to fit the systematic errors such as the ionospheric delay and extrapolate the systematic errors to the current epoch, so as to compensate the ionospheric delay errors and weaken the systematic effects such as the ionospheric errors. Please refer to fig. 5, which is a flowchart illustrating an embodiment of the integer ambiguity determination method according to the present application in step S10717. In this embodiment, step S10517 may include the following sub-steps:

step S107171: and if the ionospheric error of the wide-lane combination is amplified, performing polynomial fitting on the wide-lane combination with the amplified ionospheric error to compensate the ionospheric delay error.

Set at k-N to k-m epochs, taking the (a, b) combination as an example, there is (a, b) combination fixed solution sequence [ N [_WLab,k-n,...,N_WLab,k-m]Combining the estimated sequences

An error sequence can be obtained:

wherein, the epoch is a unit for collecting satellite data at intervals. In other words, the epoch is the time at which the satellite signal is received, and k-n and k-m are historical times prior to the current time k. And extrapolating the fitting result to the current epoch k to obtain a current error estimated value:

can estimate the ambiguity

And (3) compensation is carried out:

taking the (-3,4) combination as an example, the solution sequence [ N ] is fixed by the (-3,4) combination_WL34,k-n,...,N_WL34,k-m]Combining the estimated sequences

An error sequence can be obtained:

and extrapolating the fitting result to the current epoch k to obtain a current error estimated value:

can estimate the ambiguity

And (3) compensation is carried out:

step S107173: and rounding off the second estimator after compensating the ionospheric delay error to obtain an integer as the whole-cycle ambiguity of the wide-lane combination.

In specific implementation, step S10517 may further include the following sub-steps:

step S107175: and if the ionospheric error of the wide-lane combination is reduced, rounding off the second estimator of the wide-lane combination with reduced ionospheric error to obtain an integer as the third integer ambiguity.

In specific implementation, the rounding and rounding of the wide lane combination ambiguity can be fixed by adopting the following formula:

wherein, N'_WLabFor the wide lane combination after the ionosphere compensation,

a reduced wide lane combination for ionosphere (no ionosphere compensation required).

Taking the selected wide lanes as (1, -1) and (-3,4) as examples:

as can be seen from the foregoing embodiments, in the integer ambiguity determining method provided in the embodiments of the present application, the mobile device acquires first carrier phase observation data, and receives second carrier phase observation data sent by the reference station; determining inertial navigation position data, determining an estimator of integer ambiguity of satellite frequency points according to the inertial navigation position data and carrier phase observation data, and determining the integer ambiguity according to the estimator; by the aid of the processing mode, the ambiguity estimator is constructed based on the inertial navigation position and the carrier phase observation value, and the ambiguity is fixed according to the estimator, so that an INS assisted RTK ambiguity fixing mode is realized, ambiguity searching is not needed, ambiguity fixing solution errors caused by ambiguity searching convergence to a local minimum value due to carrier phase observation value errors can be avoided, and ambiguity fixing solution errors caused by pseudo range errors under a severe environment and other errors can be avoided due to the fact that the pseudo range is not used; therefore, the error interference resistance of the fixed ambiguity can be effectively improved, the robustness of the fixed ambiguity is improved, the fixed accuracy of the ambiguity is ensured, and the accurate positioning of the mobile equipment is realized. Meanwhile, due to the processing mode, the ambiguity estimators are fixed by direct rounding, and ambiguity search is not needed; therefore, the ambiguity fixing speed can be effectively improved, and the mobile equipment can be quickly positioned.

Second embodiment

Please refer to fig. 6, which is a schematic diagram of an embodiment of an integer ambiguity determination apparatus according to the present application. Since the apparatus embodiments are substantially similar to the method embodiments, they are described in a relatively simple manner, and reference may be made to some of the descriptions of the method embodiments for relevant points. The device embodiments described below are merely illustrative.

An integer ambiguity determination apparatus of this embodiment includes:

a data acquisition unit 601, configured to acquire first carrier phase observation data by a mobile device;

a data receiving unit 603, configured to receive second carrier phase observation data sent by the reference station;

a data determination unit 605 for determining inertial navigation position data as first position data;

an estimator determining unit 607, configured to determine an estimator of integer ambiguity of the satellite frequency points according to the first position data and the observation data;

an integer ambiguity determining unit 609 is configured to determine an integer ambiguity according to the estimator.

Third embodiment

Please refer to fig. 7, which is a diagram illustrating an embodiment of a mobile device according to the present application. Since the apparatus embodiments are substantially similar to the method embodiments, they are described in a relatively simple manner, and reference may be made to some of the descriptions of the method embodiments for relevant points. The device embodiments described below are merely illustrative.

A mobile device of this embodiment, this electronic equipment includes: a GNSS receiver 701, an Inertial Measurement Unit (IMU)702, a processor 703 and memory 704; the memory is used for storing a program for realizing the integer ambiguity determination method, and after the device is powered on and runs the program of the method through the processor, the following steps are executed: the mobile equipment collects first carrier phase observation data; receiving second carrier phase observation data sent by the reference station; determining inertial navigation position data as first position data; determining an estimator of integer ambiguity of satellite frequency points according to the first position data and the observation data; and determining the integer ambiguity according to the estimation quantity.

Fourth embodiment

In the above embodiments, an integer ambiguity determination method is provided, and correspondingly, the present application also provides an integer ambiguity determination method. The method corresponds to the embodiment of the method described above.

Please refer to fig. 8, which is a flowchart illustrating an embodiment of a integer ambiguity determination method according to the present application. Since the method embodiment is basically similar to the method embodiment one, the description is simple, and the relevant points can be referred to the partial description of the method embodiment one. The method embodiments described below are merely illustrative.

The integer ambiguity determining method of the embodiment includes:

step S801: the reference station collects second carrier phase observation data.

Step S803: transmitting the second carrier phase observation data to the mobile device to enable the mobile device to perform the following steps of acquiring first carrier phase observation data by the mobile device; receiving second carrier phase observation data sent by the reference station; determining inertial navigation position data as first position data; determining an estimator of integer ambiguity of satellite frequency points according to the first position data and the observation data; and determining the integer ambiguity according to the estimation quantity.

As can be seen from the above embodiments, in the integer ambiguity determination method provided in the embodiments of the present application, the reference station acquires second carrier phase observation data, and sends the second carrier phase observation data to the mobile device, so that the mobile device performs the following steps of acquiring first carrier phase observation data; receiving second carrier phase observation data sent by the reference station; determining inertial navigation position data as first position data; determining an estimator of integer ambiguity of satellite frequency points according to the first position data and the observation data; determining an integer ambiguity according to the estimator; by the aid of the processing mode, the ambiguity estimator is constructed based on the inertial navigation position and the carrier phase observation value, and the ambiguity is fixed according to the estimator, so that an INS assisted RTK ambiguity fixing mode is realized, ambiguity searching is not needed, ambiguity fixing solution errors caused by ambiguity searching convergence to a local minimum value due to carrier phase observation value errors can be avoided, and ambiguity fixing solution errors caused by pseudo range errors under a severe environment and other errors can be avoided due to the fact that the pseudo range is not used; therefore, the error interference resistance of the fixed ambiguity can be effectively improved, the robustness of the fixed ambiguity is improved, the fixed accuracy of the ambiguity is ensured, and the accurate positioning of the mobile equipment is realized. Meanwhile, due to the processing mode, the ambiguity estimators are fixed by direct rounding, and ambiguity search is not needed; therefore, the ambiguity fixing speed can be effectively improved, and the mobile equipment can be quickly positioned.

Fifth embodiment

Please refer to fig. 9, which is a diagram illustrating an embodiment of a mobile device positioning apparatus according to the present application. Since the apparatus embodiments are substantially similar to the method embodiments, they are described in a relatively simple manner, and reference may be made to some of the descriptions of the method embodiments for relevant points. The device embodiments described below are merely illustrative.

A mobile device positioning apparatus of this embodiment includes:

a data acquisition unit 901, configured to acquire second carrier phase observation data at a reference station;

a data sending unit 903, configured to send the second carrier phase observation data to a mobile device, so that the mobile device performs the following steps that the mobile device collects first carrier phase observation data; receiving second carrier phase observation data sent by the reference station; determining inertial navigation position data as first position data; determining an estimator of integer ambiguity of satellite frequency points according to the first position data and the observation data; and determining the integer ambiguity according to the estimation quantity.

Sixth embodiment

Please refer to fig. 10, which is a diagram illustrating a mobile device according to an embodiment of the present application. Since the apparatus embodiments are substantially similar to the method embodiments, they are described in a relatively simple manner, and reference may be made to some of the descriptions of the method embodiments for relevant points. The device embodiments described below are merely illustrative.

An electronic device of this embodiment, this mobile device includes: GNSS receiver 1001, processor 1002 and memory 1003; the memory is used for storing a program for realizing the positioning method of the mobile equipment, and after the equipment is powered on and runs the program of the method through the processor, the following steps are executed: the mobile equipment collects first carrier phase observation data; receiving second carrier phase observation data sent by the reference station; determining inertial navigation position data as first position data; determining an estimator of integer ambiguity of satellite frequency points according to the first position data and the observation data; and determining the integer ambiguity according to the estimation quantity.

Seventh embodiment

In the above embodiment, an integer ambiguity determination method is provided, and correspondingly, the present application also provides an integer ambiguity determination system. The system corresponds to the embodiment of the method described above.

Please refer to fig. 11, which is a schematic diagram of an embodiment of the integer ambiguity determination system of the present application. Since the system embodiment is basically similar to the method embodiment one, the description is simple, and the relevant points can be referred to the partial description of the method embodiment one. The system embodiments described below are merely illustrative.

An integer ambiguity determination system of this embodiment includes: a reference station and a mobile device. The integer ambiguity determination device according to the second embodiment is deployed in the reference station, and the integer ambiguity determination device according to the fifth embodiment is deployed in the mobile device.

The reference station collects second carrier phase observation data and sends the second carrier phase observation data to the mobile equipment; correspondingly, the mobile equipment collects first carrier phase observation data and receives second carrier phase observation data sent by a reference station; determining inertial navigation position data as first position data; determining an estimator of integer ambiguity of satellite frequency points according to the first position data and the observation data; and determining the integer ambiguity according to the estimation quantity.

Please refer to fig. 12, which is a schematic view illustrating an embodiment of an integer ambiguity determination system according to the present application. As can be seen in fig. 12, the reference station and the mobile device may acquire carrier wave behavior observations for multiple satellites. Satellite data observed by a GNSS receiver located on a reference station is transmitted in real time through a data communication link (radio station), while a GNSS receiver located in the vicinity (mobile device) also receives a station signal from the reference station while observing the satellite, and the mobile station determines the whole-cycle ambiguity of each frequency point of each satellite by performing real-time processing (RTK) on the received signal.

As can be seen from the foregoing embodiments, the integer ambiguity determining system provided in the embodiment of the present application acquires second carrier phase observation data through the reference station, and sends the second carrier phase observation data to the mobile device; correspondingly, the mobile equipment is used for collecting first carrier phase observation data and receiving second carrier phase observation data sent by the reference station; determining inertial navigation position data, determining an estimator of integer ambiguity of satellite frequency points according to the inertial navigation position data and carrier phase observation data, and determining the integer ambiguity according to the estimator; by the aid of the processing mode, the ambiguity estimator is constructed based on the inertial navigation position and the carrier phase observation value, and the ambiguity is fixed according to the estimator, so that an INS assisted RTK ambiguity fixing mode is realized, ambiguity searching is not needed, ambiguity fixing solution errors caused by ambiguity searching convergence to a local minimum value due to carrier phase observation value errors can be avoided, and ambiguity fixing solution errors caused by pseudo range errors under a severe environment and other errors can be avoided due to the fact that the pseudo range is not used; therefore, the error interference resistance of the fixed ambiguity can be effectively improved, the robustness of the fixed ambiguity is improved, the fixed accuracy of the ambiguity is ensured, and the accurate positioning of the mobile equipment is realized. Meanwhile, due to the processing mode, the ambiguity estimators are fixed by direct rounding, and ambiguity search is not needed; therefore, the ambiguity fixing speed can be effectively improved, and the mobile equipment can be quickly positioned.

Eighth embodiment

In the above embodiment, an integer ambiguity determination method is provided, and correspondingly, the present application also provides a mobile device positioning method. The method corresponds to the embodiment of the method described above. Since the method embodiment is basically similar to the method embodiment one, the description is simple, and the relevant points can be referred to the partial description of the method embodiment one. The method embodiments described below are merely illustrative.

A method for positioning a mobile device in this embodiment includes:

step S1301: the mobile equipment collects first carrier phase observation data; receiving second carrier phase observation data sent by the reference station;

step S1303: determining inertial navigation position data as first position data;

step S1305: determining an estimator of integer ambiguity of satellite frequency points according to the first position data and the observation data;

step S1307: determining an integer ambiguity according to the estimator;

step S1309: and determining the position data of the mobile equipment at least according to the integer ambiguity.

Accurate fixed integer ambiguity is a prerequisite for RTK to obtain reliable high-precision (centimeter-level) positioning results, after which high-precision (decimeter or even centimeter-level) positioning of mobile devices can be achieved based on the accurately fixed integer ambiguity.

In specific implementation, step S1309 may adopt a mature prior art, which is not described herein again.

As can be seen from the foregoing embodiments, in the mobile device positioning method provided in the embodiment of the present application, the mobile device acquires the first carrier phase observation data; receiving second carrier phase observation data sent by the reference station; determining inertial navigation position data as first position data; determining an estimator of integer ambiguity of satellite frequency points according to the first position data and the observation data; determining an integer ambiguity according to the estimator; determining location data of the mobile device based at least on the integer ambiguity; the processing mode enables an ambiguity estimator to be constructed based on the inertial navigation position and the carrier phase observation value, and fixes the ambiguity according to the estimator, thereby realizing the mode of assisting RTK fixed ambiguity by INS and further determining the position of the mobile equipment, so that on one hand, ambiguity search is not needed, ambiguity fixed solution errors caused by ambiguity search convergence to a local minimum value caused by carrier phase observation value errors can be avoided, on the other hand, pseudo range observation values are not used, and ambiguity fixed solution errors caused by pseudo range influenced by errors such as multipath effects in a severe environment can be avoided; therefore, the positioning accuracy of the mobile equipment can be effectively improved. Meanwhile, the ambiguity search is not needed due to the processing mode; therefore, the positioning speed of the mobile equipment can be effectively improved.

Ninth embodiment

Since the apparatus embodiments are substantially similar to the method embodiments, they are described in a relatively simple manner, and reference may be made to some of the descriptions of the method embodiments for relevant points. The device embodiments described below are merely illustrative.

A mobile device positioning apparatus of this embodiment includes:

Tenth embodiment

An electronic device of this embodiment, this mobile device includes: a GNSS receiver 1501, an Inertial Measurement Unit (IMU)1502, a processor 1503, and memory 1504; the memory is used for storing a program for realizing the positioning method of the mobile equipment, and after the equipment is powered on and runs the program of the method through the processor, the following steps are executed: the mobile equipment collects first carrier phase observation data; receiving second carrier phase observation data sent by the reference station; determining inertial navigation position data as first position data; determining an estimator of integer ambiguity of satellite frequency points according to the first position data and the observation data; determining an integer ambiguity according to the estimator; and determining the position data of the mobile equipment at least according to the integer ambiguity.

Eleventh embodiment

In the foregoing embodiment, a mobile device positioning method is provided, and correspondingly, the present application also provides a mobile device positioning method. The method corresponds to the embodiment of the method described above.

Since the method embodiment is basically similar to the method embodiment four, the description is simple, and the relevant points can be referred to the part of the description of the method embodiment four. The method embodiments described below are merely illustrative.

A method for positioning a mobile device in this embodiment includes:

step S1601: the reference station collects second carrier phase observation data.

Step S1603: sending the second carrier-phase observation data to the mobile device to cause the mobile device to perform the steps of: the mobile equipment collects first carrier phase observation data; receiving second carrier phase observation data sent by the reference station; determining inertial navigation position data as first position data; determining an estimator of integer ambiguity of satellite frequency points according to the first position data and the observation data; determining an integer ambiguity according to the estimator; and determining the position data of the mobile equipment at least according to the integer ambiguity.

As can be seen from the foregoing embodiments, in the mobile device positioning method provided in the embodiments of the present application, the reference station acquires second carrier phase observation data, and sends the second carrier phase observation data to the mobile device, so that the mobile device performs the following steps: the mobile equipment collects first carrier phase observation data; receiving second carrier phase observation data sent by the reference station; determining inertial navigation position data as first position data; determining an estimator of integer ambiguity of satellite frequency points according to the first position data and the observation data; determining an integer ambiguity according to the estimator; determining location data of the mobile device based at least on the integer ambiguity; the processing mode enables an ambiguity estimator to be constructed based on the inertial navigation position and the carrier phase observation value, and fixes the ambiguity according to the estimator, thereby realizing the mode of assisting RTK fixed ambiguity by INS and further determining the position of the mobile equipment, so that on one hand, ambiguity search is not needed, ambiguity fixed solution errors caused by ambiguity search convergence to a local minimum value caused by carrier phase observation value errors can be avoided, on the other hand, pseudo range observation values are not used, and ambiguity fixed solution errors caused by pseudo range influenced by errors such as multipath effects in a severe environment can be avoided; therefore, the positioning accuracy of the mobile equipment can be effectively improved. Meanwhile, the ambiguity search is not needed due to the processing mode; therefore, the positioning speed of the mobile equipment can be effectively improved.

Twelfth embodiment

A mobile device positioning apparatus of this embodiment includes:

Thirteenth embodiment

An electronic device of this embodiment, this mobile device includes: GNSS receiver 1801, processor 1802, and memory 1803; the memory is used for storing a program for realizing the positioning method of the mobile equipment, and after the equipment is powered on and runs the program of the method through the processor, the following steps are executed: the reference station acquires second carrier phase observation data; sending the second carrier-phase observation data to the mobile device to cause the mobile device to perform the steps of: the mobile equipment collects first carrier phase observation data; receiving second carrier phase observation data sent by the reference station; determining inertial navigation position data as first position data; determining an estimator of integer ambiguity of satellite frequency points according to the first position data and the observation data; determining an integer ambiguity according to the estimator; and determining the position data of the mobile equipment at least according to the integer ambiguity.

Fourteenth embodiment

In the foregoing embodiment, a mobile device positioning method is provided, and correspondingly, the present application also provides a mobile device positioning system. The system corresponds to the embodiment of the method described above. Since the system embodiment is basically similar to the method embodiment one, the description is simple, and the relevant points can be referred to the partial description of the method embodiment one. The system embodiments described below are merely illustrative.

A mobile device positioning system of this embodiment includes: a reference station and a mobile device. The mobile device positioning apparatus according to the ninth embodiment is disposed in the reference station, and the mobile device positioning apparatus according to the twelfth embodiment is disposed in the mobile device.

The reference station and mobile device may collect carrier behavior observations for a plurality of satellites. Satellite data observed by a GNSS receiver located on a reference station is transmitted in real time through a data communication link (radio station), while a GNSS receiver of a mobile station (mobile device) located nearby also receives a station signal from the reference station while observing the satellite, gives a three-dimensional coordinate of the mobile station by performing Real Time Kinematic (RTK) on the received signal, and estimates the accuracy thereof.

As can be seen from the foregoing embodiments, the mobile device positioning system provided in the embodiment of the present application acquires second carrier phase observation data through the reference station, and sends the second carrier phase observation data to the mobile device; correspondingly, the mobile equipment is used for collecting first carrier phase observation data and receiving second carrier phase observation data sent by the reference station; determining inertial navigation position data, determining an estimator of integer ambiguity of satellite frequency points according to the inertial navigation position data and carrier phase observation data, and determining the integer ambiguity according to the estimator; determining location data of the mobile device based at least on the integer ambiguity; the processing mode enables an ambiguity estimator to be constructed based on the inertial navigation position and the carrier phase observation value, and fixes the ambiguity according to the estimator, thereby realizing the mode of assisting RTK fixed ambiguity by INS and further determining the position of the mobile equipment, so that on one hand, ambiguity search is not needed, ambiguity fixed solution errors caused by ambiguity search convergence to a local minimum value caused by carrier phase observation value errors can be avoided, on the other hand, pseudo range observation values are not used, and ambiguity fixed solution errors caused by pseudo range influenced by errors such as multipath effects in a severe environment can be avoided; therefore, the positioning accuracy of the mobile equipment can be effectively improved. Meanwhile, the ambiguity search is not needed due to the processing mode; therefore, the positioning speed of the mobile equipment can be effectively improved.

Fifteenth embodiment

The present embodiments also provide a computer-readable storage medium. Since the storage medium embodiments are substantially similar to the method embodiments, they are described relatively simply, and reference may be made to some descriptions of the method embodiments for relevant points. The storage medium embodiments described below are merely illustrative.

A computer-readable storage medium of the present embodiment has stored therein instructions that, when executed on a computer, cause the computer to perform the various methods described above.

Although the present application has been described with reference to the preferred embodiments, it is not intended to limit the present application, and those skilled in the art can make variations and modifications without departing from the spirit and scope of the present application, therefore, the scope of the present application should be determined by the claims that follow.

In a typical configuration, a computing device includes one or more processors (CPUs), input/output interfaces, network interfaces, and memory.

The memory may include forms of volatile memory in a computer readable medium, Random Access Memory (RAM) and/or non-volatile memory, such as Read Only Memory (ROM) or flash memory (flash RAM). Memory is an example of a computer-readable medium.

1. Computer-readable media, including both non-transitory and non-transitory, removable and non-removable media, may implement information storage by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), Read Only Memory (ROM), Electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), Digital Versatile Discs (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information that can be accessed by a computing device. As defined herein, computer readable media does not include non-transitory computer readable media (transient media), such as modulated data signals and carrier waves.

2. As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.

Claims

1. An integer ambiguity determination method, comprising:

determining inertial navigation position data as first position data;

and determining the integer ambiguity according to the estimation quantity.

2. The method of claim 1,

the determining an estimator of integer ambiguity of satellite frequency points according to the first position data and the observation data comprises:

and determining an integer ambiguity based on the estimate, comprising:

3. The method of claim 2,

the determining an integer ambiguity based on the estimate, further comprising:

4. The method of claim 2,

determining a first integer ambiguity for each frequency point of a first satellite according to the first estimator comprises:

rounding the first estimate to an integer as the first integer ambiguity.

5. The method of claim 2,

6. The method of claim 5,

and determining the integer ambiguity of the wide-lane combination according to the second estimator, including:

7. The method of claim 5,

8. The method of claim 7,

the determining a third integer ambiguity for the wide-lane combination based on the second estimator further comprises:

9. An integer ambiguity determination method, comprising:

the reference station acquires second carrier phase observation data;

10. An integer ambiguity determination apparatus, comprising:

11. An integer ambiguity determination apparatus, comprising:

12. A mobile device, comprising:

a GNSS receiver;

an inertial measurement unit;

a processor; and

13. A reference station, comprising:

a GNSS receiver;

a processor; and

14. An integer ambiguity determination system, comprising:

the mobile device of claim 12; and a reference station according to claim 13 above.

15. A mobile device positioning method, comprising:

determining inertial navigation position data as first position data;

determining an integer ambiguity according to the estimator;

16. A mobile device positioning method, comprising:

the reference station acquires second carrier phase observation data;

17. A mobile device positioning apparatus, comprising:

18. A mobile device positioning apparatus, comprising:

19. A mobile device, comprising:

a GNSS receiver;

an inertial measurement unit;

a processor; and

20. A reference station, comprising:

a GNSS receiver;

a processor; and

21. A mobile device positioning system, comprising:

the mobile device of claim 19; and a reference station according to claim 20 above.

22. A computer-readable storage medium having stored therein instructions which, when executed on a computer, cause the computer to perform the various methods described above.