CN116819585B - GNSS single-point positioning method and navigation method based on nonlinear optimization - Google Patents
GNSS single-point positioning method and navigation method based on nonlinear optimization Download PDFInfo
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Abstract
The invention discloses a GNSS single-point positioning method based on nonlinear optimization, which comprises the steps of obtaining an original observed quantity of a GNSS system; calculating to obtain a speed value of the GNSS system at each moment; calculating to obtain a position value of each moment of the GNSS system; and completing single-point positioning of the GNSS system according to the position value. The invention also discloses a navigation method comprising the GNSS single-point positioning method based on nonlinear optimization. The invention builds a system speed optimizer based on Doppler observed quantity and a kinematic model to optimize the speed of the system at each moment; meanwhile, the invention constructs a position optimizer based on pseudo-range observance, epoch carrier phase observance, optimized speed and receiver frequency drift, optimizes the position of the system at each moment, and obtains a navigation positioning result with high reliability and good accuracy; therefore, the invention has high reliability, good accuracy and good persistence.
Description
Technical Field
The invention belongs to the technical field of positioning and navigation, and particularly relates to a GNSS single-point positioning method and a navigation method based on nonlinear optimization.
Background
Along with the development of economic technology and the improvement of living standard of people, the positioning and navigation technology is widely applied to the production and living of people, and brings endless convenience to the production and living of people. Therefore, ensuring the accuracy and reliability of the positioning and navigation process becomes one of the most important tasks in the positioning and navigation process.
At present, in the navigation positioning process, the traditional positioning technology generally adopts a Kalman filtering estimation-based scheme to estimate a real-time positioning result. In this kalman filter based solution, it is necessary to accurately determine the variance of the GNSS (Global Navigation Satellite System ) observations. However, in real urban complex environments, the uncertainty of the observables of GNSS is very large; moreover, in single point positioning scenarios, it is difficult for the system to determine the variance of the GNSS observables. Thus, these practical problems will directly lead to a reduction in the accuracy of state prediction during positioning and navigation, resulting in a larger positioning jump. Moreover, if the positioning or navigation terminal is continuously in a complex environment, the state quantity and the prediction accuracy of the Kalman filtering in the system are continuously reduced, and finally the divergence of the system filter is caused, so that the positioning process is not available, and the positioning and navigation functions cannot be provided.
Disclosure of Invention
The invention aims to provide a GNSS single-point positioning method based on nonlinear optimization, which has high reliability, good accuracy and good persistence.
The second objective of the present invention is to provide a navigation method including the non-linear optimization-based GNSS single point positioning method.
The GNSS single-point positioning method based on nonlinear optimization provided by the invention comprises the following steps:
s1, acquiring an original observed quantity of a GNSS system;
s2, calculating a speed value of each moment of the GNSS system based on the kinematic model and acceleration constraint between two adjacent moments according to the original observed quantity obtained in the step S1;
s3, calculating a position value of each moment of the GNSS system based on the pseudo-range and epoch carrier phase observed quantity according to the speed value calculated in the step S2;
s4, according to the position value obtained by calculation in the step S3, single-point positioning of the GNSS system is completed.
The step S2 specifically comprises the following steps:
calculating to obtain Doppler residual values according to the acquired original observed quantity of the GNSS system and the data of the receiver;
calculating to obtain a first kinematic residual value according to the kinematic model and acceleration constraint between two adjacent moments;
and calculating the speed value of the GNSS system at each moment according to the Doppler residual value and the first kinematic residual value.
The step S2 specifically comprises the following steps:
is calculated by the following formulaiDoppler difference value of time：In->Is thatiSatellite observation vectors at the moment; />Is thatiA velocity value of the satellite at the moment; />Is thatiA receiver speed value at a time; />Is thatiA satellite Zhong Piao at time; />Is thatiTime-of-day receiver frequency drift; />Is thatiTime Doppler observation; />Is wavelength;
is calculated by the following formulaiFirst kinematic residual value of time instant：/>In->Is thatiA receiver speed value at a time; />Is thati-a receiver speed value at time-1; />Is thatiTime of moment;is thati-time of moment-1; />Is thatiAcceleration values of the time of day receiver;
the following formula is adopted as a speed nonlinear optimization model:in the middle ofXTo be treatedOptimized first parameter values comprisingiVelocity value sum of receiver at time instantiTime-of-day receiver frequency drift; />The minimum value is calculated;nthe number of Doppler observables; />Is the mahalanobis norm;
solving the constructed speed nonlinear optimization model to obtain a GNSS systemiA speed value at time.
The step S3 specifically comprises the following steps:
calculating to obtain a pseudo-range residual value according to the obtained pseudo-range observed quantity and the data of the receiver;
calculating to obtain an epoch carrier phase difference residual value according to the epoch carrier phase observed quantity and the epoch carrier phase difference constraint;
calculating a second kinematic residual value according to the kinematic model and the speed constraint between two adjacent moments;
calculating to obtain a receiver frequency drift residual value according to the receiver clock error and the receiver frequency drift;
and calculating to obtain a receiver position value of the GNSS system at each moment according to the obtained pseudo-range residual value, the epoch carrier phase difference residual value, the second kinematic residual value and the receiver frequency drift residual value.
The step S3 specifically comprises the following steps:
is calculated by the following formulajPseudo-range residual value of time：
In the middle ofIs thatjTime of dayIs a satellite position of (2); />Is thatjA receiver position at time; />Is thatjReceiver clock difference at time; />Is thatjSatellite clock difference at moment; />Is thatjIonospheric delay at time; />Is thatjTime delay of troposphere at moment; />Is thatjPseudo-range observations of time; />Is the mahalanobis norm;
judging whether cycle slip occurs in the carrier phase:
if cycle slip occurs, epoch carrier phase differential constraint is not used;
if no cycle slip occurs, adding epoch carrier phase difference constraint, and calculating according to epoch carrier phase observed quantity by adopting the following formulajEpoch carrier-phase differential residual for time of day：In->Is thatjSatellite observation vectors at the moment; />Is thatjA receiver position at time; />Is thatj-receiver position at time-1; />Is thatjTime-of-day receiver frequency drift; />Is wavelength; />Is thatjTime of dayj-carrier phase difference score at time-1; />Is thatjSatellite position at time;is thatj-satellite observation vector at time 1; />Is thatj-satellite position at time 1; />Is thatjTime of dayj-receiver clock differential value at time-1; />Is thatjTime of dayj-tropospheric delay difference values at time-1; />Is thatjTime of dayjIonospheric delay difference score at time-1;
is calculated by the following formulajSecond kinematic residual value of time instant：/>In->Is thatjTime of moment; />Is thatj-time of moment-1; />Is thatjReceiver speed at time;
is calculated by the following formulajTime-of-day receiver frequency drift residual value：In->Is thatjReceiver clock difference at time; />Is thatj-receiver clock difference at time 1; />Is thatjTime-of-day receiver frequency drift;
the following formula is adopted as a position nonlinear optimization model:in the middle ofXXFor the second parameter value to be optimized, includejPosition value sum of receiver at timejClock skew of the receiver at the moment;nnthe number of observed quantities for the pseudo range;mmthe number of epoch carrier phase differences;
solving the constructed nonlinear optimization model to obtain a GNSS systemjA position value of the moment.
The invention also discloses a navigation method comprising the GNSS single-point positioning method based on nonlinear optimization, which further comprises the following steps:
s5, performing real-time navigation according to the single-point positioning result of the GNSS system obtained in the step S4.
The GNSS single-point positioning method and the navigation method based on nonlinear optimization, provided by the invention, are used for constructing a system speed optimizer based on Doppler observed quantity and a kinematic model, so as to optimize the speed of the system at each moment; meanwhile, the invention constructs a position optimizer based on pseudo-range observance, epoch carrier phase observance, optimized speed and receiver frequency drift, optimizes the position of the system at each moment, and obtains a navigation positioning result with high reliability and good accuracy; therefore, the invention has high reliability, good accuracy and good persistence.
Drawings
FIG. 1 is a flow chart of a positioning method according to the present invention.
Fig. 2 is a statistical diagram of east error in an embodiment of the positioning method of the present invention.
FIG. 3 is a diagram illustrating the north error statistics of an embodiment of the positioning method of the present invention.
Fig. 4 is a schematic diagram of an embodiment of an error statistic of the positioning method according to the present invention.
FIG. 5 is a flow chart of a navigation method according to the present invention.
Detailed Description
Fig. 1 is a schematic flow chart of a positioning method according to the present invention: the GNSS single-point positioning method based on nonlinear optimization provided by the invention comprises the following steps:
s1, acquiring an original observed quantity of a GNSS system;
s2, calculating a speed value of each moment of the GNSS system based on the kinematic model and acceleration constraint between two adjacent moments according to the original observed quantity obtained in the step S1; the method specifically comprises the following steps:
calculating to obtain Doppler residual values according to the acquired original observed quantity of the GNSS system and the data of the receiver;
calculating to obtain a first kinematic residual value according to the kinematic model and acceleration constraint between two adjacent moments;
calculating to obtain a speed value of the GNSS system at each moment according to the Doppler residual value and the first kinematic residual value;
the method specifically comprises the following steps:
is calculated by the following formulaiDoppler difference value of time：In->Is thatiSatellite observation vectors at the moment; />Is thatiA velocity value of the satellite at the moment; />Is thatiA receiver speed value at a time; />Is thatiA satellite Zhong Piao at time; />Is thatiTime-of-day receiver frequency drift; />Is thatiTime Doppler observation; />Is wavelength;
is calculated by the following formulaiFirst kinematic residual value of time instant：/>In->Is thatiTime of dayA velocity value of a receiver of (a); />Is thati-a receiver speed value at time-1; />Is thatiTime of moment;is thati-time of moment-1; />Is thatiAcceleration values of the time of day receiver;
the following formula is adopted as a speed nonlinear optimization model:in the middle ofXFor the first parameter value to be optimized, includeiVelocity value sum of receiver at time instantiThe receiver frequency drift of time of day, wherein,ithe speed value of the receiver at the moment of time comprisesiTime of dayxSpeed in axial direction>，iTime of dayySpeed in axial direction>Anditime of dayzSpeed in axial direction>，iThe receiver frequency drift of the moment is then denoted +.>；/>The minimum value is calculated;nthe number of Doppler observables; />Is the mahalanobis norm;
solving the constructed speed nonlinear optimization model to obtain a GNSS systemiA speed value at a time;
s3, calculating a position value of each moment of the GNSS system based on the pseudo-range and epoch carrier phase observed quantity according to the speed value calculated in the step S2; the method specifically comprises the following steps:
calculating to obtain a pseudo-range residual value according to the obtained pseudo-range observed quantity and the data of the receiver;
calculating to obtain an epoch carrier phase difference residual value according to the epoch carrier phase observed quantity and the epoch carrier phase difference constraint;
calculating a second kinematic residual value according to the kinematic model and the speed constraint between two adjacent moments;
calculating to obtain a receiver frequency drift residual value according to the receiver clock error and the receiver frequency drift;
calculating to obtain a receiver position value of the GNSS system at each moment according to the obtained pseudo-range residual value, epoch carrier phase difference residual value, second kinematic residual value and receiver frequency drift residual value;
the specific implementation method comprises the following steps:
is calculated by the following formulajPseudo-range residual value of time：In->Is thatjSatellite position at time; />Is thatjA receiver position at time; />Is thatjReceiver clock difference at time; />Is thatjSatellite clock difference at moment; />Is thatjIonospheric delay at time; />Is thatjTime delay of troposphere at moment; />Is thatjPseudo-range observations of time; />Is the mahalanobis norm;
judging whether cycle slip occurs in the carrier phase:
if cycle slip occurs, epoch carrier phase differential constraint is not used;
if no cycle slip occurs, adding epoch carrier phase difference constraint, and calculating according to epoch carrier phase observed quantity by adopting the following formulajEpoch carrier-phase differential residual for time of day：In->Is thatjSatellite observation vectors at the moment; />Is thatjA receiver position at time; />Is thatj-receiver position at time-1; />Is thatjTime-of-day receiver frequency drift; />Is wavelength; />Is thatjTime of dayj-carrier phase difference score at time-1; />Is thatjSatellite position at time;is thatj-satellite observation vector at time 1; />Is thatj-satellite position at time 1; />Is thatjTime of dayj-receiver clock differential value at time-1; />Is thatjTime of dayj-tropospheric delay difference values at time-1; />Is thatjTime of dayjIonospheric delay difference score at time-1;
is calculated by the following formulajSecond kinematic residual value of time instant：/>In->Is thatjTime of moment; />Is thatj-time of moment-1; />Is thatjTime of day receiverA speed;
is calculated by the following formulajTime-of-day receiver frequency drift residual value：In->Is thatjReceiver clock difference at time; />Is thatj-receiver clock difference at time 1; />Is thatjTime-of-day receiver frequency drift;
the following formula is adopted as a position nonlinear optimization model:in the middle ofXXFor the second parameter value to be optimized, includejPosition value sum of receiver at timejThe clock difference of the receiver at the moment in time, wherein,jthe position value of the receiver at the moment of time comprisesjTime of dayxPosition in axial direction->、jTime of dayyPosition in axial direction->Andjtime of dayzPosition in axial direction->，jThe clock difference of the receiver at the moment is then indicated as +.>；nnThe number of observed quantities for the pseudo range;mmthe number of epoch carrier phase differences;
nonlinear optimization of constructed positionSolving the model to obtain the GNSS systemjA position value of the moment;
s4, according to the position value obtained by calculation in the step S3, single-point positioning of the GNSS system is completed.
The positioning method of the present invention is further described below with reference to a specific embodiment:
the method is based on the existing baseband chip board, a GNSS external antenna is connected to the board, a program corresponding to the positioning method is burnt on the board, and a positioning resolving result is output in a GGA protocol mode in real time based on a serial port mode. Specifically, two board cards, GNSS receivers, antennae and the like are installed on a vehicle for verification test, the vehicle is tested around the foot valley area of the foot area of a long-sand city, one board card burns the program of the positioning method, the other board card burns the program of the positioning method based on Kalman filtering, high-precision RTK is used as a true value for precision statistics comparison, error statistics in the east, north and sky directions are shown in the following figures, and compared with the positioning method based on Kalman filtering, the errors in the east, north and sky directions are smaller, and the precision is higher, as can be seen from figures 2, 3 and 4.
Respectively calculating the RMS index, CEP95 precision index and maximum value index of the positioning method and the positioning method based on Kalman filtering, as shown in the following table 1;
TABLE 1 precision index schematic table based on nonlinear optimization and based on Kalman filtering method
As can be seen from the table, compared with the Kalman filtering method, the positioning method has remarkable improvement on the positioning accuracy in the horizontal and elevation directions.
Fig. 5 is a flow chart of the navigation method according to the present invention: the navigation method comprising the GNSS single-point positioning method based on nonlinear optimization provided by the invention comprises the following steps:
s1, acquiring an original observed quantity of a GNSS system;
s2, calculating a speed value of each moment of the GNSS system based on the kinematic model and acceleration constraint between two adjacent moments according to the original observed quantity obtained in the step S1;
s3, calculating a position value of each moment of the GNSS system based on the pseudo-range and epoch carrier phase observed quantity according to the speed value calculated in the step S2;
s4, completing single-point positioning of the GNSS system according to the position value obtained by calculation in the step S3;
s5, performing real-time navigation according to the single-point positioning result of the GNSS system obtained in the step S4.
Claims (4)
1. The GNSS single-point positioning method based on nonlinear optimization is characterized by comprising the following steps:
s1, acquiring an original observed quantity of a GNSS system;
s2, calculating a speed value of each moment of the GNSS system based on the kinematic model and acceleration constraint between two adjacent moments according to the original observed quantity obtained in the step S1; the method specifically comprises the following steps:
calculating to obtain Doppler residual values according to the acquired original observed quantity of the GNSS system and the data of the receiver;
calculating to obtain a first kinematic residual value according to the kinematic model and acceleration constraint between two adjacent moments;
calculating to obtain a speed value of the GNSS system at each moment according to the Doppler residual value and the first kinematic residual value;
the specific implementation method comprises the following steps:
is calculated by the following formulaiDoppler difference value of time：In->Is thatiSatellite observation vectors at the moment; />Is thatiA velocity value of the satellite at the moment; />Is thatiA receiver speed value at a time; />Is thatiA satellite Zhong Piao at time; />Is thatiTime-of-day receiver frequency drift; />Is thatiTime Doppler observation; />Is wavelength;
is calculated by the following formulaiFirst kinematic residual value of time instant：/>In->Is thatiA receiver speed value at a time; />Is thati-a receiver speed value at time-1; />Is thatiTime of moment;/>is thati-time of moment-1; />Is thatiAcceleration values of the time of day receiver;
the following formula is adopted as a speed nonlinear optimization model:in the middle ofXFor the first parameter value to be optimized, includeiVelocity value sum of receiver at time instantiTime-of-day receiver frequency drift; />The minimum value is calculated;nthe number of Doppler observables; />Is the mahalanobis norm;
solving the constructed speed nonlinear optimization model to obtain a GNSS systemiA speed value at a time;
s3, calculating a position value of each moment of the GNSS system based on the pseudo-range and epoch carrier phase observed quantity according to the speed value calculated in the step S2;
s4, according to the position value obtained by calculation in the step S3, single-point positioning of the GNSS system is completed.
2. The method for positioning a GNSS single point based on nonlinear optimization according to claim 1, wherein the step S3 specifically includes the following steps:
calculating to obtain a pseudo-range residual value according to the obtained pseudo-range observed quantity and the data of the receiver;
calculating to obtain an epoch carrier phase difference residual value according to the epoch carrier phase observed quantity and the epoch carrier phase difference constraint;
calculating a second kinematic residual value according to the kinematic model and the speed constraint between two adjacent moments;
calculating to obtain a receiver frequency drift residual value according to the receiver clock error and the receiver frequency drift;
and calculating to obtain a receiver position value of the GNSS system at each moment according to the obtained pseudo-range residual value, the epoch carrier phase difference residual value, the second kinematic residual value and the receiver frequency drift residual value.
3. The method for positioning a GNSS single point based on nonlinear optimization according to claim 2, wherein said step S3 comprises the steps of:
is calculated by the following formulajPseudo-range residual value of time：In->Is thatjSatellite position at time; />Is thatjA receiver position at time; />Is thatjReceiver clock difference at time; />Is thatjSatellite clock difference at moment; />Is thatjIonospheric delay at time; />Is thatjTime delay of troposphere at moment; />Is thatjPseudo-range observations of time; />Is the mahalanobis norm;
judging whether cycle slip occurs in the carrier phase:
if cycle slip occurs, epoch carrier phase differential constraint is not used;
if no cycle slip occurs, adding epoch carrier phase difference constraint, and calculating according to epoch carrier phase observed quantity by adopting the following formulajEpoch carrier-phase differential residual for time of day：In->Is thatjSatellite observation vectors at the moment; />Is thatjA receiver position at time; />Is thatj-receiver position at time-1; />Is thatjTime-of-day receiver frequency drift; />Is wavelength; />Is thatjTime of dayj-carrier phase difference score at time-1; />Is thatjSatellite position at time;is thatj-satellite observation vector at time 1; />Is thatj-satellite position at time 1; />Is thatjTime of dayj-receiver clock differential value at time-1; />Is thatjTime of dayj-tropospheric delay difference values at time-1; />Is thatjTime of dayjIonospheric delay difference score at time-1;
is calculated by the following formulajSecond kinematic residual value of time instant：/>In the middle ofIs thatjTime of moment; />Is thatj-time of moment-1; />Is thatjReceiver speed at time;
is calculated by the following formulajTime-of-day receiver frequency drift residual value：/>In->Is thatjReceiver clock difference at time; />Is thatj-receiver clock difference at time 1; />Is thatjTime-of-day receiver frequency drift;
the following formula is adopted as a position nonlinear optimization model:in the middle ofXXFor the second parameter value to be optimized, includejPosition value sum of receiver at timejClock skew of the receiver at the moment;nnthe number of observed quantities for the pseudo range;mmthe number of epoch carrier phase differences;
solving the constructed nonlinear optimization model to obtain a GNSS systemjA position value of the moment.
4. A navigation method comprising the non-linear optimization-based GNSS single point positioning method of any of claims 1 to 3, further comprising the steps of:
s5, performing real-time navigation according to the single-point positioning result of the GNSS system obtained in the step S4.
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