CN116299599A - INS-assisted GNSS pseudo-range coarse difference detection method - Google Patents
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Abstract
The invention discloses an INS assisted GNSS pseudo-range coarse difference detection method; fully excavating the effect of INS navigation information on auxiliary robust, and greatly enhancing the robust resistance of the integrated navigation system; firstly, tightly combining a GNSS single-point pseudo-range observation value, a Doppler observation value and an INS, and carrying out sliding window monitoring on real-time estimation of satellite receiver clock error and Zhong Piao; substituting the real-time updated solution position of the INS in the combined system into a satellite observation equation to perform pre-processed adjustment solution, and performing residual error detection on the residual unknowns; and next, setting a relevant threshold value through residual error detection and sliding window monitoring, and circularly eliminating the fault satellite with the largest residual error exceeding the threshold value through a forward search mode. And finally, adopting an M-LS filtering mode, and carrying out GNSS/INS tight combination solution again to obtain a correct positioning result.
Description
Technical Field
The invention belongs to the technical field of navigation and positioning, and particularly relates to an INS-assisted GNSS pseudo-range coarse difference detection method.
Background
With the continuous rapid development of the fields of automatic driving, unmanned aerial vehicles, robots and the like, the method has higher requirements on accuracy and robustness. GNSS (Global Navigation Satellite System, global satellite navigation system) can provide all-weather, continuous, high-precision position, speed and time service information for users, and has the remarkable advantages of low cost, high precision, bounded error and the like, and the multi-constellation multi-frequency-point GNSS positioning mode provides a solution with higher reliability and higher precision. However, GNSS belongs to an active positioning mode, and the environment has a great influence on GNSS signals, such as multipath and non-line-of-sight problems in urban complex environments, and signal interruption problems in tunnel environments all bring challenges to continuous and high-precision positioning of GNSS. INS (InertialNavigationSystem) is a completely independent and autonomous navigation positioning mode, has the advantages of short-time high precision, high frequency, no external interference and the like, but error accumulation can be caused by factors such as zero drift of an inertial device. GNSS and INS have very obvious complementary characteristics, so that GNSS/INS integrated navigation is the most widely used and developed integrated navigation mode at present.
In the practical application of integrated navigation, it is found that the occurrence of the anomaly is mostly caused by the excitation of the observation environment, namely, the quality of the GNSS observation data is seriously disturbed, while the inertial navigation has stronger autonomy, so that the anomaly usually occurs in the measurement model. There is a mature integrity theory in GNSS to evaluate and monitor the failure condition of GNSS, in which receiver autonomous integrity monitoring (Receiver Autonomous Integrity Monitoring, RAIM) is the most widely used inexpensive method for quality control of positioning results by a receiver user side. The method is mainly based on a statistical consistency test of redundant pseudo-range observation values, has better performance on the problem of single system and single fault, has higher omission rate for the problem of multiple systems and multiple faults, and has improved RAIM algorithm for the problem of multiple systems and multiple faults, but the improved algorithm has higher requirements on the distribution of the redundant observation values and the visible satellites. In view of the above problems, an INS-assisted GNSS pseudo range coarse-difference detection method may be introduced to improve positioning accuracy and robustness in complex and large-scale scenarios such as urban canyons, tunnels, and the like. The INS assistance can reduce the requirements of redundant observations and the correlation between observations, and can solve the problem of multiple systems and multiple faults.
Disclosure of Invention
In order to solve the problems, the invention discloses an INS-assisted GNSS pseudo-range coarse-difference detection method for improving the positioning accuracy and robustness in complex and large-scale scenes such as urban canyons and tunnels. The method uses GNSS single-point pseudo-range observation values and Doppler observation values to be tightly combined with INS, and carries out sliding window monitoring on satellite receiver clock errors and real-time estimation of Zhong Piao. And substituting the real-time updated solution position of the INS in the combined system into a satellite observation equation to perform pre-processed adjustment solution, and performing residual error detection on the residual unknowns. And next, setting a relevant threshold value through residual error detection and sliding window monitoring, and circularly eliminating the fault satellite with the largest residual error exceeding the threshold value through a forward search mode. Finally, an M-LS filtering mode is adopted, GNSS/INS tight combination solution is carried out again, and a correct positioning result is obtained, so that the method has high engineering application value.
In order to achieve the above purpose, the technical scheme of the invention is as follows:
an INS assisted GNSS pseudo-range coarse difference detection method comprises the following steps:
(1) GNSS single-point pseudo-range observation value, doppler observation value and INS (inertial navigation system) tight combination
The INS position, velocity and attitude error equations based on the psi-angle (psi) error model are respectively as follows:
in the formula, the superscript n refers to a navigation coordinate system, and the subscripts i, e and b respectively refer to an inertial coordinate system, an earth coordinate system and a carrier coordinate system, and r n Representing a position vector;
representing the transfer rate; v n Representing the carrier velocity; psi represents the stage misalignment angle; f (f) n Representing the specific force under the navigation system; />
Representing the earth rotation rate; />
Representing the gravity of the model calculation; />
Representing a transformation matrix of the carrier system to the navigation system; f (f) b Representing the specific force under the carrier system; />
Indicating the angular velocity of the navigation system relative to the inertial system; />
The angular velocity of the carrier system relative to the inertial system is indicated.
The construction of the tightly-combined filtered state vector is determined by the inertial device error state and the error state of the GNSS:
in the formula, the superscripts n and b respectively represent a navigation coordinate system and a carrier coordinate system. Psi phi type n Representing a three-dimensional platform misalignment angle under a navigation system; δv n Representing a three-dimensional velocity error under a navigation system; δr n Representing a three-dimensional position error under a navigation system; epsilon b Representing three-dimensional gyro drift under a carrier system;
representing a carrier systemZero offset of the lower three-dimensional accelerometer; dt (dt) G Representing a GNSS receiver clock offset; dt (dt) d Indicating GNSS receiver clock drift.
The system error dynamics equation is shown below:
wherein F represents a state transition matrix and is obtainable from formulae [1] to [3 ]; g represents a noise distribution matrix; w represents system noise.
Single point pseudorange observations are used, as well as doppler observations, in close combination with INS, where ionospheric and tropospheric delays of GNSS observations are corrected using Klobuchar and Saastamoinen models, respectively. The measurement model is expressed as follows:
z k ＝H k x k +v k [6]
wherein z is k Representing a measurement vector; subscript k denotes the kth epoch; h k Representing a measurement matrix; x is x k Representing a state vector; v k Representing the measured noise, subject to zero-mean gaussian distribution.
The measurement vector is the GNSS original observation value m GNSS Predicted value with INS
Difference between them. The following is shown:
wherein P is s,f 、
Respectively representing an original pseudo-range observation value and a Doppler observation value; the superscript f denotes frequency; the superscript s denotes a satellite system, including GPS, BDS, galileo; ρ INS 、/>
Respectively representing an INS predicted pseudo-range and a predicted pseudo-range rate; deltatr P 、/>
Representing error correction sums associated with the pseudorange and doppler observations, respectively, from the receiver clock; representing the pseudorange and other error correction sums for the doppler observations, respectively.
The measurement model is expressed as follows:
I＝[1 1 ... 1] T [14]
in the formula e s,f Representing the direction cosine of the receiver to the satellite;
a position error conversion matrix from the navigation coordinate system to the earth coordinate system is represented; />
Representing a velocity error transformation matrix from the navigational coordinate system to the earth coordinate system.
Sliding window detection for real-time estimation of receiver clock error and Zhong Piao consists in calculating the corresponding sample mean and sample mean square error for its real-time estimate within the sliding window as follows:
in the method, in the process of the invention,
representing the mean value of the samples, S representing the mean square error of the samples.
(2) INS assisted GNSS residual error checking
The coordinates of the position parameters calculated by inertial navigation updating under a geocentric and geodetic fixed coordinate system are X= (X, y, z), and the position parameters are substituted into the following pseudo-range observation equation:
wherein, the superscript indicates the ith satellite, and the subscript r indicates the receiver;
representing pseudorange observations; />
Representing the geometrical distance of the toilet; c represents the speed of light; δt r Representing receiver clock skew; δt i Representing satellite clock differences; />
Representing equivalent tropospheric delay; />
Representing an equivalent ionospheric delay; />
Representing an equivalent orbit error; />
Representing random errors. Wherein, error items such as troposphere, ionosphere delay, satellite clock difference and the like are corrected by using corresponding models, only one unknown parameter of the receiver clock difference is remained in the equation, and adjustment solution is carried out on the equation to obtain δt r The residual error corresponding to each equation is as follows:
wherein, the superscript indicates the ith satellite; v i Representing the residual error; l (L) i Representing the ith satellite error;
(3) Forward search loop fault rejection satellite
Because sliding window monitoring is adopted, if the sample mean value and the sample mean square error monitored by the sliding window exceed the set threshold, residual error detection is carried out and forward searching circulation is started to remove the fault satellite.
As previously described, by [18 ]]It can be seen that the residual v of the corresponding observations of each satellite i Will be mainly affected by self errors; if the ith satellite has no gross error, but the jth satellite has gross error, the corresponding residual error v of the jth satellite at the moment j Is affected by
While the ith satellite is affected only by +.>
When the number of satellites is large, there is a great reason to believe that the satellite with the largest residual error and exceeding the threshold value corresponds to the observed value, namely the satellite with the gross error. At this time, the satellite is removed, and the satellite is built again as shown in [17 ]]The observation equation shown but not including the j-th satellite is analogically performed until the residual meets the requirements. When the number of satellites is small, the sample mean value of the sliding window monitoring of the last output epoch is also substituted into [17 ]]And (5) carrying out residual detection, and circularly removing the satellite with the largest residual until the residual meets the requirement.
(4) GNSS/INS tight combination solution based on M-LS filtering
Assuming that the components of the observation vector of the epoch are independent of each other, but may contain abnormal errors and obey the normal distribution of pollution, and the state vector predicted by the dynamics model still obeys the normal distribution, robust M estimation is adopted for the observation vector, and Least Square (LS) estimation is still adopted for the state parameter.
Defining M-LS filter extremum condition by using equivalent weight matrix, thereby obtaining recurrence as follows:
wherein K is MLS Still referred to as a gain matrix, expressed as:
in the method, in the process of the invention,
the equivalent weight matrix representing the observation vector adopts IGGIII weight function:
in the method, in the process of the invention,
for the weight matrix R k The i, j th element, gamma ij The method comprises the following steps:
wherein:
in the method, in the process of the invention,
representing standardized innovation, k 0 、k 1 For the respective threshold value set. Therefore, a more accurate robust positioning result after GNSS gross error elimination can be obtained.
The beneficial effects of the invention are as follows:
according to the INS-assisted GNSS pseudo-range coarse difference detection method, a GNSS single-point pseudo-range observation value, a Doppler observation value and the INS are tightly combined, and sliding window monitoring is carried out on real-time estimation of satellite receiver clock differences and Zhong Piao. And substituting the real-time updated solution position of the INS in the combined system into a satellite observation equation to perform pre-processed adjustment solution, and performing residual error detection on the residual unknowns. And next, setting a relevant threshold value through residual error detection and sliding window monitoring, and circularly eliminating the fault satellite with the largest residual error exceeding the threshold value through a forward search mode. Finally, an M-LS filtering mode is adopted, GNSS/INS tight combination solution is carried out again to obtain a correct positioning result, the function of INS navigation information in auxiliary robust is fully excavated, the robust resistance of the integrated navigation system is greatly enhanced, and the integrated navigation system has high engineering application value.
Drawings
FIG. 1 is a flowchart illustrating an INS assisted GNSS pseudo-range coarse detection method according to an embodiment of the present invention.
FIG. 2 is an experimental verification platform of the present invention.
Fig. 3 to 5 are experimental verification results, namely positioning errors in the E, N, U direction, wherein a broken line and a hollow circle mark represent the positioning errors of the RAIM algorithm, and a solid line represents the positioning errors of the algorithm.
Fig. 6 is a display of an experimental positioning trajectory on a map.
Fig. 7 is a comparison diagram of experimental positioning tracks, dashed lines represent RAIM algorithm positioning tracks, and solid lines represent the algorithm positioning tracks.
Detailed Description
The present invention is further illustrated in the following drawings and detailed description, which are to be understood as being merely illustrative of the invention and not limiting the scope of the invention.
The invention relates to an INS assisted GNSS pseudo-range coarse difference detection method, which comprises the following steps:
(1) GNSS single-point pseudo-range observation value, doppler observation value and INS (inertial navigation system) tight combination
The INS position, velocity and attitude error equations based on the psi-angle (psi) error model are respectively as follows:
in the formula, the superscript n refers to a navigation coordinate system, and the subscripts i, e and b respectively refer to an inertial coordinate system, an earth coordinate system and a carrier coordinate system, and r n Representing a position vector;
representing the transfer rate; v n Representing the carrier velocity; psi represents the stage misalignment angle; f (f) n Representing the specific force under the navigation system; />
Representing the earth rotation rate; />
Representing the gravity of the model calculation; />
Representing a transformation matrix of the carrier system to the navigation system; f (f) b Representing the specific force under the carrier system; />
Indicating the angular velocity of the navigation system relative to the inertial system; />
Representing a carrier systemAngular velocity relative to the inertial frame.
The construction of the tightly-combined filtered state vector is determined by the inertial device error state and the error state of the GNSS:
in the formula, the superscripts n and b respectively represent a navigation coordinate system and a carrier coordinate system. Psi phi type n Representing a three-dimensional platform misalignment angle under a navigation system; δv n Representing a three-dimensional velocity error under a navigation system; δr n Representing a three-dimensional position error under a navigation system; epsilon b Representing three-dimensional gyro drift under a carrier system;
representing zero offset of the three-dimensional accelerometer under the carrier system; dt (dt) G Representing a GNSS receiver clock offset; dt (dt) d Indicating GNSS receiver clock drift.
The system error dynamics equation is shown below:
wherein F represents a state transition matrix and is obtainable from formulae [1] to [3 ]; g represents a noise distribution matrix; w represents system noise.
Single point pseudorange observations are used, as well as doppler observations, in close combination with INS, where ionospheric and tropospheric delays of GNSS observations are corrected using Klobuchar and Saastamoinen models, respectively. The measurement model is expressed as follows:
z k ＝H k x k +v k [6]
wherein z is k Representing a measurement vector; subscript k denotes the kth epoch; h k Representing a measurement matrix; x is x k Representing a state vector; v k Representing the measured noise, subject to zero-mean gaussian distribution.
The measurement vector is the GNSS original observation value m GNSS Predicted value with INS
Difference between them. The following is shown:
wherein P is s,f 、
Respectively representing an original pseudo-range observation value and a Doppler observation value; the superscript f denotes frequency; the superscript s denotes a satellite system, including GPS, BDS, galileo; ρ INS 、/>
Respectively representing an INS predicted pseudo-range and a predicted pseudo-range rate; deltatr P 、/>
Representing error correction sums associated with the pseudorange and doppler observations, respectively, from the receiver clock; representing the pseudorange and other error correction sums for the doppler observations, respectively.
The measurement model is expressed as follows:
I＝[1 1 ... 1] T [14]
in the formula e s,f Representing the direction cosine of the receiver to the satellite;
a position error conversion matrix from the navigation coordinate system to the earth coordinate system is represented; />
Representing a velocity error transformation matrix from the navigational coordinate system to the earth coordinate system.
Sliding window detection for real-time estimation of receiver clock error and Zhong Piao consists in calculating the corresponding sample mean and sample mean square error for its real-time estimate within the sliding window as follows:
in the method, in the process of the invention,
representing the mean value of the samples, S representing the mean square error of the samples.
(2) INS assisted GNSS residual error checking
The coordinates of the position parameters calculated by inertial navigation updating under a geocentric and geodetic fixed coordinate system are X= (X, y, z), and the position parameters are substituted into the following pseudo-range observation equation:
wherein, the superscript indicates the ith satellite, and the subscript r indicates the receiver;
representing pseudorange observations; />
Representing the geometrical distance of the toilet; c represents the speed of light; δt r Representing receiver clock skew; δt i Representing satellite clock differences; />
Representing equivalent tropospheric delay; />
Representing an equivalent ionospheric delay; />
Representing an equivalent orbit error; />
Representing random errors. Wherein, error items such as troposphere, ionosphere delay, satellite clock difference and the like are corrected by using corresponding models, only one unknown parameter of the receiver clock difference is remained in the equation, and adjustment solution is carried out on the equation to obtain δt r The residual error corresponding to each equation is as follows:
wherein, the superscript indicates the ith satellite; v i Representing the residual error; l (L) i Representing the ith satellite error;
(3) Forward search loop fault rejection satellite
Because sliding window monitoring is adopted, if the sample mean value and the sample mean square error monitored by the sliding window exceed the set threshold, residual error detection is carried out and forward searching circulation is started to remove the fault satellite.
As previously described, by the formula [18 ]]It can be seen that the residual v of the corresponding observations of each satellite i Will be mainly affected by self errors; if the ith satellite has no gross error, but the jth satellite has gross error, the corresponding residual error v of the jth satellite at the moment j Is affected by
While the ith satellite is affected only by +.>
When the number of satellites is large, there is a great reason to believe that the satellite with the largest residual error and exceeding the threshold value corresponds to the observed value, namely the satellite with the gross error. At this time, the satellite is removed, and the satellite is built again as shown in [17 ]]The observation equation shown but not including the j-th satellite is analogically performed until the residual meets the requirements. When the number of satellites is small, the sample mean value of the sliding window monitoring of the last output epoch is also substituted into [17 ]]And (5) carrying out residual detection, and circularly removing the satellite with the largest residual until the residual meets the requirement.
(4) GNSS/INS tight combination solution based on M-LS filtering
Assuming that the components of the observation vector of the epoch are independent of each other, but may contain abnormal errors and obey the normal distribution of pollution, and the state vector predicted by the dynamics model still obeys the normal distribution, robust M estimation is adopted for the observation vector, and Least Square (LS) estimation is still adopted for the state parameter.
Defining M-LS filter extremum condition by using equivalent weight matrix, thereby obtaining recurrence as follows:
wherein K is MLS Still referred to as a gain matrix, expressed as:
in the method, in the process of the invention,
the equivalent weight matrix representing the observation vector adopts IGGIII weight function:
in the method, in the process of the invention,
for the weight matrix R k The i, j th element, gamma ij The method comprises the following steps:
wherein:
in the method, in the process of the invention,
representing standardized innovation, k 0 、k 1 For the respective threshold value set. Therefore, a more accurate robust positioning result after GNSS gross error elimination can be obtained.
The technical scheme of the invention is verified to be effective and accurate according to experiments in actual environments, and track accuracy obtained by an algorithm and a conventional algorithm is improved by comparison. The experimental field is a long sand vehicle networking test center, and IE post-calculation is carried out by adopting ADIS16488IMU and UM482GNSS board card collected data, so that the real value evaluation accuracy is obtained. The test results are shown in FIGS. 3-5, table 1.
Table 1RAIM algorithm compared to RMSE (m) in the direction of the present algorithm E, N, U
As can be seen from fig. 3 to fig. 5, in the actual test experiment, on the positioning results of some epochs, the RAIM algorithm still has a large positioning error, and the algorithm has better performance under the condition of coarse and poor pseudo-ranges aiming at the GNSS. As can be seen from Table 1, the RMSE in the E, U direction of the algorithm is significantly improved by about 68.1% and 21.5% compared with the RAIM algorithm. As can be seen through tests, the INS-assisted GNSS pseudo-range coarse-difference detection method provided by the invention has great advantages in the aspects of positioning accuracy, continuity and robustness in an outdoor complex environment which can cause GNSS pseudo-range coarse-difference.
It should be noted that the foregoing merely illustrates the technical idea of the present invention and is not intended to limit the scope of the present invention, and that a person skilled in the art may make several improvements and modifications without departing from the principles of the present invention, which fall within the scope of the claims of the present invention.
Claims (5)
1. An INS assisted GNSS pseudo-range coarse difference detection method is characterized in that: the method comprises the following steps:
(1) GNSS single-point pseudo-range observation value, doppler observation value and INS (inertial navigation system) tight combination
The INS position, velocity and attitude error equations based on the psi-angle (psi) error model are respectively as follows:
in the formula, the superscript n refers to a navigation coordinate system, and the subscripts i, e and b respectively refer to an inertial coordinate system, an earth coordinate system and a carrier coordinate system; r is (r) n Representing a position vector;
representing the transfer rate; v n Representing the carrier velocity; psi represents the stage misalignment angle; f (f) n Representing the specific force under the navigation system; />
Representing the earth rotation rate; />
Representing the gravity of the model calculation; />
Representing a transformation matrix of the carrier system to the navigation system; f (f) b Representing the specific force under the carrier system; />
Indicating the angular velocity of the navigation system relative to the inertial system; />
Representing the angular velocity of the carrier system relative to the inertial system;
the construction of the tightly-combined filtered state vector is determined by the inertial device error state and the error state of the GNSS:
wherein, the superscripts n and b respectively represent a navigation coordinate system and a carrier coordinate system; psi phi type n Representing a three-dimensional platform misalignment angle under a navigation system; δv n Representing a three-dimensional velocity error under a navigation system; δr n Representing a three-dimensional position error under a navigation system; epsilon b Representing three-dimensional gyro drift under a carrier system;
representing zero offset of the three-dimensional accelerometer under the carrier system; dt (dt) G Representing a GNSS receiver clock offset; dt (dt) d Representing a GNSS receiver clock drift;
the system error dynamics equation is shown below:
wherein F represents a state transition matrix and is obtainable from formulae [1] to [3 ]; g represents a noise distribution matrix; w represents system noise;
the single-point pseudo-range observation value and the Doppler observation value are tightly combined with the INS, wherein ionospheric delay and tropospheric delay of the GNSS observation value are corrected by using Klobuchar and Saastamoinen models respectively; the measurement model is expressed as follows:
z k ＝H k x k +v k [6]
wherein z is k Representing a measurement vector; subscript k denotes the kth epoch; h k Representing a measurement matrix; x is x k Representing a state vector; v k Representing measurement noise and obeying zero-mean Gaussian distribution;
the measurement vector is the GNSS original observation value m GNSS Predicted value with INS
A difference between them; the following is shown:
wherein P is s,f 、
Respectively representing an original pseudo-range observation value and a Doppler observation value; the superscript f denotes frequency; the superscript s denotes a satellite system, including GPS, BDS, galileo; ρ INS 、/>
Respectively represent INS prediction pseudoDistance and predicted pseudorange rates; deltatr P 、
Representing error correction sums associated with the pseudorange and doppler observations, respectively, from the receiver clock; representing the pseudo-range and other error correction sums of the Doppler observations, respectively;
the measurement model is expressed as follows:
I＝[11...1] T [14]
in the formula e s,f Representing the direction cosine of the receiver to the satellite;
a position error conversion matrix from the navigation coordinate system to the earth coordinate system is represented; />
A speed error conversion matrix from the navigation coordinate system to the earth coordinate system is represented;
sliding window detection for real-time estimation of receiver clock error and Zhong Piao consists in calculating the corresponding sample mean and sample mean square error for its real-time estimate within the sliding window as follows:
in the method, in the process of the invention,
representing the mean value of the samples, S representing the mean square error of the samples;
(2) INS assisted GNSS residual error checking
The coordinates of the position parameters calculated by inertial navigation updating under a geocentric and geodetic fixed coordinate system are X= (X, y, z), and the position parameters are substituted into the following pseudo-range observation equation:
wherein, the superscript indicates the ith satellite, and the subscript r indicates the receiver;
representing pseudorange observations; />
Representing the geometrical distance of the toilet; c represents the speed of light; δt r Representing receiver clock skew; δt i Representing satellite clock differences; />
Representing equivalent tropospheric delay; />
Representing an equivalent ionospheric delay; />
Representing an equivalent orbit error; />
Representing a random error; wherein, error items such as troposphere, ionosphere delay, satellite clock difference and the like are corrected by using corresponding models, only one unknown parameter of the receiver clock difference is remained in the equation, and adjustment solution is carried out on the equation to obtain δt r The residual error corresponding to each equation is as follows:
wherein, the superscript indicates the ith satellite; v i Representing the residual error; l (L) i Representing the ith satellite error;
(3) Forward search loop fault rejection satellite
Because sliding window monitoring is adopted, if the sample mean value and the sample mean square error monitored by the sliding window exceed the set threshold, residual error detection is carried out and forward searching circulation is started to remove the fault satellite;
as previously described, by the formula [18 ]]It can be seen that the residual v of the corresponding observations of each satellite i Will be mainly affected by self errors; if the ith satellite has no gross error, but the jth satellite has gross error, the corresponding residual error v of the jth satellite at the moment j Is affected by
While the ith satellite is affected only by +.>
When the number of satellites is large, there is a greater reason to believe that the satellite remainsThe satellite with the largest difference and exceeding the threshold value corresponds to the observed value, namely the satellite with the rough difference; at this time, the satellite is removed, and the satellite is built again as shown in [17 ]]The observation equation of the j satellite is shown but not included, and the like is performed until the residual error meets the requirement; when the number of satellites is small, the sample mean value of the sliding window monitoring of the last output epoch is also substituted into [17 ]]Performing residual error detection, and circularly removing the satellite with the largest residual error until the residual error meets the requirement;
(4) GNSS/INS tight combination solution based on M-LS filtering
Assuming that the components of the observation vector of the epoch are independent of each other, but may contain abnormal errors and obey the normal distribution of pollution, and the state vector predicted by the dynamic model still obeys the normal distribution, adopting robust M estimation on the observation vector and adopting Least Square (LS) estimation on the state parameter;
defining M-LS filter extremum condition by using equivalent weight matrix, thereby obtaining recurrence as follows:
wherein K is MLS Still referred to as a gain matrix, expressed as:
in the method, in the process of the invention,
the equivalent weight matrix representing the observation vector adopts IGGIII weight function:
in the method, in the process of the invention,
for the weight matrix R k The i, j th element, gamma ij The method comprises the following steps:
wherein:
in the method, in the process of the invention,
representing standardized innovation, k 0 、k 1 A corresponding threshold value is set; therefore, a more accurate robust positioning result after GNSS gross error elimination is obtained.
2. The INS-aided GNSS pseudo-range coarse-difference detection method of claim 1, wherein in step (1), pseudo-range observations and doppler observations are used for the GNSS/INS tight combination, three systems GPS, BDS, galieo are used to model and estimate the receiver clock difference and receiver Zhong Piao, respectively, and a sliding window monitoring method is used to solve the sample variance and the sample mean square error for the real-time estimation of the receiver clock difference and receiver Zhong Piao.
3. The INS-assisted GNSS pseudo-range coarse-difference detection method according to claim 1, wherein in the INS-assisted GNSS residual error detection in step (2), the carrier position deduced by INS updating is substituted into the GNSS observation equation, the corresponding error term is corrected by a model, and finally, the remaining unknown parameters are subjected to adjustment solution and residual error detection.
4. The INS-assisted GNSS pseudo-range coarse-difference detection method according to claim 1, wherein in the step (3), the faulty satellites are removed by forward circulation, residual error detection is performed on epochs exceeding a sliding window monitoring threshold, and forward search circulation is started to remove the faulty satellites, and when the number of satellites is less than 8, the sample mean value monitored by the sliding window is substituted into the GNSS observation equation, and then forward search circulation is performed to remove the faulty satellites.
5. The INS-aided GNSS pseudo-range coarse-difference detection method of claim 1, wherein the GNSS/INS tight combination solution based on M-LS filtering in step (4) uses robust M estimation for the observation vector and still uses Least Squares (LS) estimation for the state parameters after the failed satellites are removed in step (3); and (3) through setting corresponding threshold values, replacing a noise matrix with an observed quantity equivalent weight matrix to obtain an anti-difference kalman filtering gain, and finally obtaining a more accurate positioning result.
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