CN111896987A - Method and device for GNSS/INS integrated navigation under low-orbit navigation enhancement - Google Patents
Method and device for GNSS/INS integrated navigation under low-orbit navigation enhancement Download PDFInfo
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- G01C21/165—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments
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Abstract
The invention relates to a method and a device for GNSS/INS combined navigation under low-orbit navigation enhancement, which make up the defect of accumulation of errors of an inertial navigation system along with time through the combination of satellite navigation and inertial navigation, make up the defect of signal lock loss of the satellite navigation system easily affected by the environment, improve the output rate of the system by dozens to hundreds of times and greatly enhance the dynamic adaptability of the system. In addition, the satellite navigation system adopts the low-orbit navigation enhancement signal, and utilizes the high low-orbit motion speed and the real-time GNSS precision correction information to realize the real-time wide-area high-precision positioning and get rid of the dependence of the traditional real-time high-precision positioning on the RTK reference station. By utilizing the method, the ground receiver adopts the inertial navigation combination positioning result to initialize the combined real-time non-differential precise single-point positioning module when in short-time lock losing recapture, thereby shortening the time of high-precision positioning convergence.
Description
Technical Field
The invention relates to the technical field of ground real-time high-precision positioning, in particular to a method and a device for GNSS/INS integrated Navigation under Low earth orbit Navigation enhancement (LEO-NA).
Background
The satellite navigation system and the inertial navigation system are currently widely used navigation systems, and the currently established global satellite navigation system includes: the American GPS system, the Russian GLONASS system, the European Union Galileo system and the China Beidou system.
The satellite navigation system is not autonomous positioning, and is prone to signal interruption and other problems due to building obstruction and the like. In addition, because of various errors such as ionosphere errors and troposphere errors, the current traditional GNSS (global navigation satellite system) can only provide 5-10 m positioning accuracy for users.
The inertial navigation system can continuously provide navigation parameters such as position, speed, attitude, course and the like through measurement equipment such as an accelerometer, a gyroscope and the like, has high short-time precision and continuous output, but has the inherent defects: positioning errors accumulate over time, and long-time independent work is difficult, so other navigation means are needed for assistance.
Currently, a ground-based augmentation system carries out positioning accuracy augmentation on GNSS users, and through building a ground reference station, the users adopt a differential RTK technology to realize real-time centimeter-level service, but the single station coverage of the ground reference station is limited, and the users need to carry out information interaction with the reference station through a UHF/VHF radio station or a mobile cellular network, so that the use of the users is limited.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, provides a method and a device for GNSS/INS integrated navigation based on low-earth-orbit navigation enhancement, integrates the advantages of a satellite navigation system and an inertial navigation system, realizes real-time centimeter-level high-precision positioning of satellite navigation by using low-earth-orbit satellite enhancement, and solves the problems in the prior art.
The purpose of the invention can be realized by the following technical scheme:
a method for performing GNSS/INS combined navigation under low-orbit navigation enhancement can comprise the following steps:
the method comprises the following steps: receiving GNSS signals, realizing coarse positioning, and performing initialization setting according to a coarse positioning result;
step two: receiving an LEO enhanced signal, and performing combined real-time non-differential precise single-point positioning;
step three: obtaining an optimal estimation result and feedback correction according to a high-precision positioning result of a satellite navigation system and a result of an inertial navigation system;
step four: when the satellite navigation signal is unlocked, the inertial navigation independent positioning mode is entered;
step five: when the satellite navigation signal is locked again, the current positioning precision is calculated through the lock losing time and the precision of the inertial navigation system equipment;
step six: judging whether the current positioning precision is smaller than the system coarse positioning precision or not, and when the judgment result is smaller than the system coarse positioning precision, using the current positioning result to reinitialize the combined non-poor precision single-point positioning module;
step seven: and judging whether the current positioning precision is smaller than the system coarse positioning precision or not, and when the judgment result is larger than the system coarse positioning precision, using the coarse positioning result to reinitialize the combined non-poor precision single point positioning module.
Further, the first step comprises:
step 101: the method comprises the steps of obtaining a pseudo-range measurement value and a carrier phase measurement value by receiving and processing GNSS signals, analyzing broadcast messages in the GNSS signals, and calculating to obtain the corresponding GNSS satellite position;
step 102: and performing positioning calculation according to the pseudo-range measurement value and the GNSS satellite position to obtain a user coarse positioning result including position speed, and then performing initialization assignment on the inertial navigation system according to the position speed.
Further, the second step comprises:
step 201: performing data preprocessing on the received pseudo-range carrier phase observation value of the GNSS and the received pseudo-range carrier phase observation value of the LEO-NA;
step 202: analyzing an enhanced message in the LEO-NA signal, and acquiring GNSS satellite precision orbit data, GNSS satellite precision clock error data, GNSS code deviation correction, earth rotation parameters, ionosphere correction and low-orbit satellite precision orbit and clock error;
step 203: according to the enhanced correction information, carrying out error correction on the observation data;
step 204: according to a joint observation equation, parameter estimation and integer ambiguity fixing processing are carried out through kalman filtering, and a precise single-point positioning high-precision positioning result is obtained;
further, the third step comprises:
step 301: obtaining a position velocity difference value according to a high-precision positioning result of the satellite navigation system and a result of the inertial navigation system, wherein the processing mode can be a difference between the two;
step 302: establishing a combined navigation Kalman filtering state equation;
step 303: establishing a measurement equation of the integrated navigation system;
step 304: and performing Kalman filtering recursion.
Further, the sixth step comprises:
step 601: if the result is less than the predetermined threshold, setting an initial value of the filter of the joint non-differential precision single-point positioning module by using the current positioning result, that is, setting the initial value of the filter in step 204;
step 602: and performing joint non-differential precise single-point positioning again, and performing combined navigation filtering to obtain optimal estimation.
Further, the seventh step includes:
step 701: if the result is not less than the predetermined value, setting an initial value of the filter of the joint non-differential precision single-point positioning module by using the coarse positioning result, that is, setting the initial value of the filter in step 204;
step 702: and performing joint non-differential precise single-point positioning again, and performing combined navigation filtering to obtain optimal estimation.
According to another aspect of the present application, there is also provided a device for performing GNSS/INS integrated navigation under low-orbit navigation augmentation, which includes a satellite navigation system, an inertial navigation system and an integrated navigation kalman filter module, and may perform the aforementioned method for performing GNSS/INS integrated navigation under low-orbit navigation augmentation.
According to another aspect of the present application, a device for performing GNSS/INS integrated navigation under low-earth-orbit navigation augmentation is provided, which includes a satellite navigation system, an inertial navigation system, and an integrated navigation kalman filter module, wherein the satellite navigation system receives and processes a GNSS signal and an LEO augmentation signal through a GNSS reception processing module and an LEO augmentation signal reception processing module respectively to obtain a GNSS observation data coarse positioning result, LEO observation data, and an augmentation signal, and then outputs the GNSS observation data coarse positioning result, the LEO observation data, and the augmentation signal to a joint non-differential precise single-point positioning module for processing to obtain a final satellite navigation system output position and speed; the inertial navigation system carries out initialization assignment, carries out integral operation according to the initial position, the accelerometer and the gyro measurement data and outputs the current position and speed result; and the integrated navigation Kalman filtering module performs integrated operation according to the positioning result of the satellite navigation system and the positioning result of the inertial navigation system to obtain an optimal estimation result.
Compared with the prior art, the technical scheme of the application has the following advantages:
(1) the combination of satellite navigation and inertial navigation makes up the defects of both parties, the high precision of the satellite navigation system makes up the defect of the accumulation of the error of the inertial navigation system along with the time, the stability of the inertial navigation system makes up the defect of the easy signal lock loss of the satellite navigation system under the influence of the environment, the output rate of the system is improved by dozens to hundreds of times, and the dynamic adaptive capacity of the system is greatly enhanced.
(2) The satellite navigation system adopts the low-orbit navigation enhancement signal, utilizes the high low-orbit motion speed and the real-time GNSS precision correction information to realize the real-time wide-area high-precision positioning, has higher positioning precision than the prior GNSS/INS combined navigation system, and gets rid of the dependence of the traditional real-time high-precision positioning on the RTK reference station.
(3) And when the short-time lock losing is recaptured, the inertial navigation combined positioning result is adopted to initialize the combined real-time non-differential precise single-point positioning module, so that the time of high-precision positioning convergence can be shortened.
Drawings
FIG. 1 is a schematic diagram of a GNSS/INS integrated navigation system under low-earth-orbit navigation augmentation according to the present invention;
FIG. 2 is a schematic diagram illustrating a process flow of GNSS/INS integrated navigation under low-earth-orbit navigation augmentation in accordance with the present invention;
FIG. 3 is a flow chart illustrating data preprocessing in GNSS/INS integrated navigation under low-earth-orbit navigation augmentation according to the present invention.
In the figure, 11-inertial navigation system, 12-satellite navigation system, 13-integrated navigation Kalman filter module.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, shall fall within the scope of protection of the present invention.
In this description, the dynamic vehicle is a vehicle carrying the GNSS module and the inertial navigation module, however, in other implementation processes, the dynamic vehicle may also be other moving carriers, such as an unmanned aerial vehicle and a human. In addition, Low earth orbit-Navigation augmentation (LEO-NA) refers to enhancement of Navigation performance by using Low-orbit satellites. INS refers to an inertial navigation system. LEO refers to low orbit satellites.
As shown in fig. 1, an apparatus for performing GNSS/INS combined navigation under low-orbit navigation augmentation is shown, which includes: a satellite navigation system 11, an inertial navigation system 12 and an integrated navigation kalman filter module 13. The inertial navigation system can comprise an accelerometer and a gyro module. The satellite navigation system can comprise a GNSS receiving and processing module, a LEO enhanced signal receiving and processing module and a combined non-differential precise single-point positioning module.
The satellite navigation system receives and processes the GNSS signal and the LEO enhanced signal respectively through the GNSS receiving and processing module and the LEO enhanced signal receiving and processing module, so that a GNSS observation data coarse positioning result, LEO observation data and an enhanced signal are obtained and are output to the combined non-differential precise single-point positioning module for processing, finally the satellite navigation system outputs the position and the speed, the inertial navigation system performs initialization assignment, and performs integral operation according to the initial position, the accelerometer and gyroscope measurement data to output a current position and speed result; and the integrated navigation Kalman filtering module performs integrated operation according to the positioning result of the satellite navigation system and the positioning result of the inertial navigation system to obtain an optimal estimation result.
As shown in fig. 2, correspondingly, a method for performing GNSS/INS combined navigation under low-orbit navigation augmentation is shown, which includes steps one to seven (S1 to S7):
the method comprises the following steps: the equipment is powered on and started, receives GNSS signals, realizes coarse positioning, and assigns an initial position to the inertial navigation system according to the coarse positioning result. The device may be, for example, an in-vehicle GNSS system. The reception of GNSS signals, and the implementation of coarse positioning, may be performed by a satellite navigation system. The coarse positioning result corresponds to the coarse positioning precision.
Step two: and receiving the LEO enhanced signal, and enabling the satellite navigation system to enter a high-precision positioning mode. In this mode, the satellite navigation system performs joint real-time non-differential precise single-point positioning through the joint non-differential precise single-point positioning module.
Step three: and performing combined operation by subtracting the high-precision positioning result of the satellite navigation system and the positioning result of the inertial navigation system to obtain an optimal estimation result and feedback correction.
Step four: and when the satellite navigation signal is unlocked, the inertial navigation independent positioning mode is entered. The reason for the loss of lock of the satellite navigation signal is various, for example, the device enters a tunnel, etc. The inertial navigation standalone positioning mode refers to a mode in which the device described herein is positioned by an inertial navigation system only.
Step five: when the satellite navigation signal is locked again, the current positioning precision is calculated according to the lock losing time and the precision of each part of the inertial navigation system. The satellite navigation signal relocking means that the tracking acquisition of the navigation signal is realized again. The out-of-lock time refers to the time that the satellite navigation signal is found out-of-lock until re-locked. The inertial navigation system component accuracy may include, for example, accelerometer null, gyro drift rate, and the like.
Step six: and judging whether the current positioning precision is smaller than the system coarse positioning precision or not, and when the judgment result is smaller than the system coarse positioning precision, re-initializing the combined non-poor precision single-point positioning module by using the current positioning result.
Step seven: and judging whether the current positioning precision is smaller than the system coarse positioning precision or not, and when the judgment result is not smaller than the system coarse positioning precision, using the coarse positioning result to reinitialize the combined non-poor precision single point positioning module.
Specifically, the first step may include the following steps:
step 101: the method comprises the steps of obtaining a pseudo-range measured value and a carrier phase measured value by receiving and processing a GNSS signal, analyzing broadcast messages in the GNSS signal, and calculating according to the broadcast messages to obtain the corresponding GNSS satellite position.
Step 102: and performing positioning calculation according to the pseudo-range measurement value and the GNSS satellite position to obtain a user coarse positioning result including position speed, and then performing initialization assignment on the inertial navigation system according to the position speed.
The second step may include the following steps:
step 201: and performing data preprocessing on the received pseudo-range carrier phase observed value of the GNSS and the received pseudo-range carrier phase observed value of the LEO-NA.
The combined precise single-point positioning is to perform positioning by using a non-differential observation value, and errors cannot be eliminated by a differential method, so that data preprocessing (including cycle slip detection and restoration, gross error wild value elimination, initial integer ambiguity determination, phase smoothing pseudo codes and the like) in a non-differential positioning mode is very important work, and is an important guarantee for obtaining high-precision positioning later. The specific technical process is shown in figure 3. And detecting double cycle slip gross errors of GNSS observation data by a MW combination method and an ionosphere residual error method, calculating cycle slip of the observation value with cycle slip, and repairing the original observation value.
The GNSS receiving and processing module acquires four types of observation values corresponding to the following four observation equations:
L1＝c·φ1/f1＝R-I/f1 2+λ1·N1+L1
L2＝c·φ2/f2＝R-I/f2 2+λ2·N2+L2
P1＝R+I/f1 2+P1
P2＝R+I/f2 2+P2
wherein c is the speed of light, phi1,φ2、f1,f2、λ1＝c/f1,λ2＝c/f2、N1,N2Phase observations, frequency, wavelength, and integer ambiguity for L1, L2, respectively; p1、P2Is a code observation value corresponding to the L1 and L2 frequency bands; i is ionospheric influence; r is a pseudo-range observed value part comprising a geometric distance rho and a satellite clock error delta tsClock difference of receiver Δ tRTropospheric delay deltatropEtc., can be expressed as follows:
R～ρ+c·ΔtR+c·Δts+Δtrop
firstly, detecting cycle slip gross error by a Melbourne-Wubbena combined observation method, wherein the formula is as follows:
in the formula
φw＝φ1-φ2。
In cycle slip detection, the time difference is directly made by using the ambiguity mutual difference Nw. Mean error of carrier phase observed value in assumed observation processLThe error in the precise pseudorange positioning is +/-0.01 cyclesp± 20cm, according to the law of error propagation:
taking the error in the 4-fold as the tolerance, if the error is not in the value range, the gross error or cycle slip is indicated to occur.
If yes, the cycle slip is considered to exist between the epochs i-1 and i, and a new arc section is divided from the i epoch data;
if yes, the epoch i is considered as gross error, and the i epoch observed value is removed.
Then, detecting cycle slip by utilizing the change rate of the ionized layer; in a short time, the ionospheric change rate can be considered as a constant, and the ionospheric TEC calculation formula for epoch k-1 is:
wherein γ ═ f1 2/f2 2，f1And f2For the corresponding carrier frequency, biAnd BpThe signal inter-frequency offset, respectively at the receiver side and at the satellite side, can be considered constant over a period of time. Thus, the calculation of the ionospheric TEC rate of change TECR for epoch k is
Because the change of the ionosphere TECR is smooth in a short time, the difference between the TECR calculated value of the current epoch and the TECR predicted value is small when the cycle slip does not occur theoretically, when the difference exceeds a threshold value, the cycle slip is considered to occur, the observation data threshold value of the medium orbit GNSS satellite is 0.15TECU/s, and the observation data threshold value of the low orbit navigation enhanced satellite is 0.2 TECU/s. Namely:
the corresponding cycle slip is:
calculating the corresponding cycle skip value and counting the original observation numberThe repair is performed accordingly. Assuming that the cycle slip value obtained by the M-W combined detection is a, the cycle slip value lambda obtained by the TECR detection1ΔN1(k)-λ2ΔN2(k) B, the cycle slip of the original observed value can be calculated according to the following formula
Wherein a is an integer and b is a real number. The real value Δ N obtained by the above formula1、ΔN2Rounding to obtain L1Frequency sum L2And restoring the observed value by the whole cycle slip value on the frequency.
Step 202: and analyzing an enhanced message in the LEO-NA signal to acquire GNSS satellite precision orbit data, GNSS satellite precision clock error data, GNSS code deviation correction, earth rotation parameters, ionosphere correction and low-orbit satellite precision orbit and clock error.
Step 203: and according to the information in the LEO-NA enhanced message, carrying out error correction on the pseudo-range measurement value and the carrier phase measurement value.
1) GNSS satellite orbit error, GNSS satellite clock error correction
Based on real-time non-differential precise single-point positioning under low-orbit navigation enhancement, real-time GNSS precise track products with the interval of 1min and real-time GNSS precise clock-error products with the interval of 10s are adopted. Different from the Lagrange interpolation of a precise product by a post-precision single-point positioning algorithm, the algorithm needs to extrapolate according to the precise track of the previous time point and the clock error product, and the extrapolation accuracy of the trigonometric function polynomial interpolation is higher than that of the Lagrange interpolation, so the method adopts the ten-order trigonometric function polynomial interpolation extrapolation. The trigonometric polynomial interpolation function is:
y＝a0+a1sin(ωt)+a2cos(ωt)+a3sin(2ωt)+a4cos(2ωt)+....+a10cos(5ωt)
wherein y is the corresponding precise orbital coordinate value or the precise clock error, a0,a1,....a10For the coefficients to be found, ω is 2 pi/T, and T is the period of satellite operation.
2) Antenna phase center correction
The method comprises phase center correction of three aspects of GNSS/LEO satellite antenna phase center deviation (PCO), satellite antenna phase center change (PCV) and ground receiver antenna phase center deviation (PCO).
The satellite antenna phase center deviation correction method is that coordinates (dx, dy, dz) of the satellite antenna phase center deviation (PCO) under a satellite-fixed system are known, and the coordinates under the earth-fixed system are as follows:
wherein
The unit vector of the star-solid system under the earth-solid system is calculated by the following method:
satellite in underground position
The sun is located at the lower position of the earth fixed system
Through the calculation of the solar ephemeris, the position of the satellite after the correction of the antenna phase center PCO is as follows:
the method for correcting the antenna phase center deviation (PCO) of the ground receiver comprises the following steps: knowing that the phase center deviation of the receiver antenna is in three components (North, East, Up) of a horizon coordinate system, then performing coordinate conversion, converting to a ground fixed system (x yz), and then obtaining the true position of a reference point of the receiver antenna as follows:
the antenna Phase Center Variation (PCV) is divided into a terrestrial receiver antenna phase center variation and a satellite antenna phase center variation. Firstly, calculating the zenith distance of the current receiver, the azimuth angle of a receiver signal and the zenith angle of a satellite according to the position of the current receiver and the position of the satellite, and then obtaining a corresponding correction value through table lookup. Then, the satellite-ground distance is corrected as follows:
geometric distance between satellite and ground-PCV
3) Ionospheric delay correction
And for a dual-frequency receiver user, ionosphere delay error correction is carried out by adopting dual-frequency observation value deionization layer combination.
And for a single-frequency receiver user, carrying out ionospheric error elimination by adopting grid point ionospheric correction information. The grid point ionospheric correction information is broadcast by the low-orbit enhancement signal.
Firstly, calculating the corresponding longitude and latitude of an ionosphere puncture point of a received signal by a trigonometric function according to the satellite position and the receiver position by a single-frequency user, wherein the ionosphere reference height is 400km, and the earth radius is 6378 km;
then, four grid points around the puncture point are found from the received global grid point ionosphere correction information according to the longitude and latitude of the puncture point;
and finally, calculating the ionospheric delay of the puncture point by adopting bilinear interpolation, wherein the calculation formula is as follows:
ω1＝(1-xp)(1-yp)，ω2＝xp(1-yp)，ω3＝xpyp，ω2＝(1-xp)yp
in the formula (phi)p，λp) The four grid points around the puncture point are located as phi for the longitude and latitude of the puncture pointi，λiAnd i is 1-4), and VTECi is the vertical ionospheric delay corresponding to the grid point.
4) Tropospheric delay correction
Because the troposphere is composed of a dry and wet component, troposphere delay is often expressed in terms of zenith direction dry delay, wet delay, and corresponding mapping functions:
ΔDtrop＝ddryMdry(E)+dwetMwet(E)
in the formula ddryA zenith direction dry delay, dwetFor zenith direction wet retardation, Mdry(E) As a function of the dry-delayed projection, Mwet(E) E is the satellite elevation angle for the wet delay projection function.
The dry delay was corrected by the Sastamonine (Saastamoinen) model plus the NMF projection model. The wet delay is post-corrected by parameter estimation.
The correction formula of the dry error of the troposphere of the Sas Tamournin model is as follows:
P＝1013.25·(1.0-0.022557H)5.2568
in the formula, the pressure of a P measuring station,
the survey station latitude (in radians) and H the survey station altitude (in km). The calculated result is the tropospheric delay in the zenith direction of the survey station, and the tropospheric delay is mapped by a mapping functionI.e. it can be scaled to the tropospheric delay on the signal propagation path.
The NMF dry delay projection function is:
in the formula, aht＝2.53×10-5，bht＝5.49×10-3，cht＝1.14×10-3H is positive height, e is satellite altitude. a ish、bh、chThe dry delay projection coefficient is calculated by a periodic term correction formula:
aaverage、aamplitudeDOY is given in Table 1 below as the cumulative year, DOY028 for the reference year.
TABLE 1 corresponding table of relation between NMF dry delay projection function correction coefficient and latitude
5) Hardware delay error correction
Time deviations between different frequencies at the same time or different pseudo-code observations at the same frequency due to hardware delays. Correction is performed using the GNSS differential code bias correction.
When using the observation data of the frequency band corresponding to the reference point of the system clock error time, the correction of the code deviation is needed, for example, the GPS system uses the combined electronic phase center of the L1 and L2 frequency points as the reference, and when using the P1 code alone for positioning, the corresponding hardware delay is:
similarly, when the C/a code is used alone, the corresponding hardware delay is:
wherein f1 and f2 are GPS L1 and L2 carrier center frequencies, DCBp1p2And DCBp1c1To enhance the correction of code deviations broadcast in a text.
The BD system uses the antenna electronic phase center of B3 frequency point as the reference point of satellite clock error, so when the user uses the B1c and B2a signals, the corresponding dual-frequency ionosphere-free combination observed value is:
wherein f1 and f2 are the center frequencies of B1c and B2a carriers of BD, DCBB1cAnd DCBB2aTo enhance the correction of code deviations broadcast in a text.
Step 204: and according to a joint observation equation, performing parameter estimation and integer ambiguity fixing processing through Kalman filtering to obtain a precise single-point positioning high-precision positioning result.
1) And establishing a filtering linear kinematics model and an observation model. The observation equation and the state equation can be expressed as
In the formula, XkIs the state vector at time t (k) including receiver position, velocity, receiver clock error, tropospheric wet delay, and carrier phase integer ambiguity. Phik,k-1The one-step transition matrix of the system state from the time t (k-1) to the time t (k) is that the coordinate and the integer ambiguity are constant for static GNSS users, the state transition matrix is correspondingly 1, and the receiver coordinate and the clock offset can be expressed as a random walk or a first-order gaussian markov process for dynamic GNSS users, and the integer ambiguity is constant.k-1For system noise-driven arrays, Wk-1Is a systematic noise vector, LkIs the observation vector at time t (k), HkFor an array of coefficients of an observation equation, VkTo observe the noise.
The system noise and the observation noise are zero mean gaussian white noise which are not correlated with each other, and the corresponding random model can be expressed as:
in the formula, QkAnd RkRespectively become a variance matrix of the system noise sequence (symmetrical non-negative array) and a variance matrix of the measured noise (symmetrical positive array).
2) Time updating
Pk,k-1＝Φk,k-1Pk-1ΦT k,k-1+k-1Qk-1 T k-1
In the formula (I), the compound is shown in the specification,
Pk,k-1the predicted values and their variance-covariance matrix are obtained. Wherein the recursive filtering initial value X0 is set according to specific conditions; when the equipment is initially powered on and started, a filtering initial value is given by GNSS single-point rough positioning; and if the tunnel navigation signal is re-filtered after being temporarily unlocked, the initial filtering value is given by the positioning result of the integrated navigation system.
3) Measurement update
Pk＝(I-KkHk)Pk,k-1(I-KkHk)T+KkRkKk T
In the formula, I is a unit matrix, KkIn order to be a matrix of gains, the gain matrix,
Pkthe filtered estimates and their variance-covariance matrices, respectively.
The third step may include the following steps:
step 301: and obtaining a position velocity difference value according to the high-precision positioning result of the satellite navigation system and the result of the inertial navigation system, wherein the processing mode can be a difference between the two.
Step 302: establishing an integrated navigation Kalman filtering state equation:
Xk＝Φk,k-1Xk-1+Wk
in the formula:
state vector X ═ rx,ry,rz,vx,vy,vz,θx,θy,θz,dx,dy,dz,bx,by,bz]TThe method comprises the steps of detecting a position error, a speed error, a platform misalignment error, a gyro drift random component and an acceleration zero-offset random component;
Φk,k-1representing an excess matrix; wkFor system noise, ∑ WkIs a system noise covariance matrix
Δ t is the sampling time interval, QkIs the system noise spectral density.
Step 303: establishing a measurement equation of the integrated navigation system:
L＝AX+V
in the formula (I), the compound is shown in the specification,
the subscript represents the output position and speed of the GPS or INS, and the coordinate system conversion is needed to be carried out on the result when the coordinate systems of the output results of different systems are different.
V is the observation noise, V-N (0, R), R is the observation noise covariance matrix.
Step 304: performing Kalman filtering recursion:
The obtained error estimation value is used as an output correction value and a feedback correction value, the output correction and the feedback correction are carried out in the initial stage, and the feedback correction frequency is lower than that of the output correction, such as 1 time per second of the output correction and 1 time per 10 seconds of the feedback correction; after stabilization, only feedback correction is carried out, and output correction is not carried out.
The fourth step comprises: and when the satellite navigation signal is unlocked, the inertial navigation independent positioning mode is entered.
When a user of equipment such as a ground receiver loses locking on all satellite navigation signals due to building obstruction or tunnel entrance, or the received navigation signals are less than four satellites, the satellite navigation signals are considered to be unlocked, and the system enters an inertial navigation independent positioning mode.
The fifth step is: when the satellite navigation signal is locked again, the current positioning precision is calculated according to the lock losing time and the precision of the inertial navigation system equipment.
And when the working environment of the ground user receiver is recovered to be normal and the received satellite navigation signal is locked again, the unlocking time can be calculated, and the drifting error of the inertial navigation positioning result of the unlocking time is calculated according to the configuration accuracy of the gyroscope and the accelerometer of the current inertial navigation system, so that the current positioning accuracy is obtained.
The sixth step comprises: and judging whether the current positioning precision is smaller than the system coarse positioning precision or not, and when the judgment result is smaller than the system coarse positioning precision, re-initializing the combined non-poor precision single-point positioning module by using the current positioning result. In particular, the amount of the solvent to be used,
step 601: if the result is less than the predetermined threshold, setting an initial value of the filter of the joint non-differential precision single-point positioning module by using the current positioning result, that is, setting the initial value of the filter in step 204;
step 602: and performing joint non-differential precise single-point positioning again, and performing combined navigation filtering to obtain optimal estimation.
The seventh step comprises: and judging whether the current positioning precision is smaller than the system coarse positioning precision or not, and when the judgment result is not smaller than the system coarse positioning precision, using the coarse positioning result to reinitialize the combined non-poor precision single point positioning module. In particular, the amount of the solvent to be used,
step 701: if the result is not less than the predetermined value, setting an initial value of the filter of the joint non-differential precision single-point positioning module by using the coarse positioning result, that is, setting the initial value of the filter in step 204;
step 702: and performing joint non-differential precise single-point positioning again, and performing combined navigation filtering to obtain optimal estimation.
Accordingly, the device for GNSS/INS integrated navigation under low-earth-orbit navigation augmentation herein includes a satellite navigation system, an inertial navigation system, and an integrated navigation kalman filter module, which may perform some or all of the aforementioned steps.
While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and those skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope of the invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (8)
1. A method for GNSS/INS integrated navigation under low-orbit navigation enhancement is characterized by comprising the following steps:
the method comprises the following steps: receiving GNSS signals, realizing coarse positioning, and performing initialization setting according to a coarse positioning result;
step two: receiving a low-orbit navigation enhancement signal, and performing combined real-time non-differential precise single-point positioning;
step three: obtaining an optimal estimation result and feedback correction according to a high-precision positioning result of a satellite navigation system and a result of an inertial navigation system;
step four: when the satellite navigation signal is unlocked, the inertial navigation independent positioning mode is entered;
step five: when the satellite navigation signal is locked again, the current positioning precision is calculated through the lock losing time and the precision of the inertial navigation system equipment;
step six: judging whether the current positioning precision is smaller than the system coarse positioning precision or not, and when the judgment result is smaller than the system coarse positioning precision, using the current positioning result to reinitialize the combined non-poor precision single-point positioning module;
step seven: and judging whether the current positioning precision is smaller than the system coarse positioning precision or not, and when the judgment result is larger than the system coarse positioning precision, using the coarse positioning result to reinitialize the combined non-poor precision single point positioning module.
2. The method of claim 1, wherein the step one comprises:
step 101: the method comprises the steps of obtaining a pseudo-range measurement value and a carrier phase measurement value by receiving and processing GNSS signals, analyzing broadcast messages in the GNSS signals, and calculating to obtain the corresponding GNSS satellite position;
step 102: and performing positioning calculation according to the pseudo-range measurement value and the GNSS satellite position to obtain a user coarse positioning result including position speed, and then performing initialization assignment on the inertial navigation system according to the position speed.
3. The method of claim 1, wherein the step two comprises:
step 201: performing data preprocessing on the received pseudo-range carrier phase observation value of the GNSS and the received pseudo-range carrier phase observation value of the LEO-NA;
step 202: analyzing an enhanced message in the LEO-NA signal, and acquiring GNSS satellite precision orbit data, GNSS satellite precision clock error data, GNSS code deviation correction, earth rotation parameters, ionosphere correction and low-orbit satellite precision orbit and clock error;
step 203: according to the enhanced correction information, carrying out error correction on the observation data;
step 204: according to a joint observation equation, parameter estimation and integer ambiguity fixing processing are carried out through kalman filtering, and a precise single-point positioning high-precision positioning result is obtained;
step 205: and performing filtering iteration by using a Kalman filtering algorithm, and calculating the integer ambiguity to obtain a combined real-time high-precision position and speed.
4. The method of claim 1, wherein the step three comprises:
step 301: obtaining a position velocity difference value according to a high-precision positioning result of the satellite navigation system and a result of the inertial navigation system, wherein the processing mode can be a difference between the two;
step 302: establishing a combined navigation Kalman filtering state equation;
step 303: establishing a measurement equation of the integrated navigation system;
step 304: and performing Kalman filtering recursion.
5. The method of claim 1, wherein the step six comprises:
step 601: if the result is less than the predetermined threshold, setting an initial value of the filter of the joint non-differential precision single-point positioning module by using the current positioning result, that is, setting the initial value of the filter in step 204;
step 602: and performing joint non-differential precise single-point positioning again, and performing combined navigation filtering to obtain optimal estimation.
6. The method of claim 1, wherein the step seven comprises:
step 701: if the result is not less than the predetermined value, setting an initial value of the filter of the joint non-differential precision single-point positioning module by using the coarse positioning result, that is, setting the initial value of the filter in step 204;
step 702: and performing joint non-differential precise single-point positioning again, and performing combined navigation filtering to obtain optimal estimation.
7. An apparatus for performing GNSS/INS integrated navigation under low-earth-orbit navigation augmentation, comprising a satellite navigation system, an inertial navigation system and an integrated navigation kalman filter module, and being capable of performing the method for performing GNSS/INS integrated navigation under low-earth-orbit navigation augmentation according to any one of claims 1 to 6.
8. A device for GNSS/INS integrated navigation under low-orbit navigation enhancement is characterized by comprising a satellite navigation system, an inertial navigation system and an integrated navigation Kalman filtering module, wherein,
the satellite navigation system receives and processes the GNSS signal and the LEO enhanced signal respectively through the GNSS receiving and processing module and the LEO enhanced signal receiving and processing module to obtain a GNSS observation data coarse positioning result, LEO observation data and an enhanced signal, and then outputs the GNSS observation data coarse positioning result, the LEO observation data and the enhanced signal to the combined non-differential precise single-point positioning module for processing to obtain the final output position and speed of the satellite navigation system;
the inertial navigation system carries out initialization assignment, carries out integral operation according to the initial position, the accelerometer and the gyro measurement data and outputs the current position and speed result;
and the integrated navigation Kalman filtering module is used for performing integrated operation according to the positioning result of the satellite navigation system and the positioning result of the inertial navigation system to obtain an optimal estimation result.
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Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112764067A (en) * | 2020-12-23 | 2021-05-07 | 深圳创维数字技术有限公司 | Method and device for acquiring ephemeris data of GPS (Global positioning System) satellite, and vehicle-mounted and readable storage medium |
| CN113126128A (en) * | 2021-04-20 | 2021-07-16 | 东方红卫星移动通信有限公司 | DCB correction-based Beidou satellite navigation system frequency point precise point positioning method |
| CN114002726A (en) * | 2021-11-15 | 2022-02-01 | 北京北斗华大科技有限公司 | GNSS/INS combined navigation positioning system |
| CN114475655A (en) * | 2022-01-29 | 2022-05-13 | 智道网联科技(北京)有限公司 | Early warning method and device for automatic driving and computer readable storage medium |
| CN115061175A (en) * | 2022-07-28 | 2022-09-16 | 知微空间智能科技(苏州)有限公司 | GNSS RTK and INS semi-tight combined positioning navigation method, device and system |
| CN117194869A (en) * | 2023-11-07 | 2023-12-08 | 中国科学院国家授时中心 | Attitude-considered low-orbit satellite antenna phase center forecasting and fitting method |
| CN117388900A (en) * | 2023-12-13 | 2024-01-12 | 深圳大学 | GNSS/INS combined ocean dynamic reference station construction method |
Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20110238307A1 (en) * | 2010-03-26 | 2011-09-29 | Mark Lockwood Psiaki | Vehicle navigation using non-gps leo signals and on-board sensors |
| US20160131485A1 (en) * | 2014-11-07 | 2016-05-12 | Thales | Method of determining a radius of protection associated with a navigation parameter of a hybrid inertial navigation system, and associated system |
| CN108226985A (en) * | 2017-12-25 | 2018-06-29 | 北京交通大学 | Train Combinated navigation method based on Static Precise Point Positioning |
| CN109061677A (en) * | 2018-06-28 | 2018-12-21 | 上海卫星工程研究所 | The method for carrying out satellite-based navigation enhancing using low orbit satellite |
| CN110161542A (en) * | 2019-06-14 | 2019-08-23 | 火眼位置数智科技服务有限公司 | Compatible appraisal procedure between a kind of low rail navigation system and middle high rail navigation system |
| CN110187364A (en) * | 2019-06-14 | 2019-08-30 | 火眼位置数智科技服务有限公司 | A kind of low rail navigation enhancing is accurate to correct data generation, upper injection system and method |
| CN110793528A (en) * | 2019-09-27 | 2020-02-14 | 西安空间无线电技术研究所 | Low-orbit satellite-based anchoring-based Beidou navigation constellation autonomous orbit determination method |
| CN110988926A (en) * | 2019-12-20 | 2020-04-10 | 福建海峡北斗导航科技研究院有限公司 | Method for realizing position accurate fixed point deception migration in loose GNSS/INS combined navigation mode |
-
2020
- 2020-07-27 CN CN202010730262.9A patent/CN111896987A/en active Pending
Patent Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20110238307A1 (en) * | 2010-03-26 | 2011-09-29 | Mark Lockwood Psiaki | Vehicle navigation using non-gps leo signals and on-board sensors |
| US20160131485A1 (en) * | 2014-11-07 | 2016-05-12 | Thales | Method of determining a radius of protection associated with a navigation parameter of a hybrid inertial navigation system, and associated system |
| CN108226985A (en) * | 2017-12-25 | 2018-06-29 | 北京交通大学 | Train Combinated navigation method based on Static Precise Point Positioning |
| CN109061677A (en) * | 2018-06-28 | 2018-12-21 | 上海卫星工程研究所 | The method for carrying out satellite-based navigation enhancing using low orbit satellite |
| CN110161542A (en) * | 2019-06-14 | 2019-08-23 | 火眼位置数智科技服务有限公司 | Compatible appraisal procedure between a kind of low rail navigation system and middle high rail navigation system |
| CN110187364A (en) * | 2019-06-14 | 2019-08-30 | 火眼位置数智科技服务有限公司 | A kind of low rail navigation enhancing is accurate to correct data generation, upper injection system and method |
| CN110793528A (en) * | 2019-09-27 | 2020-02-14 | 西安空间无线电技术研究所 | Low-orbit satellite-based anchoring-based Beidou navigation constellation autonomous orbit determination method |
| CN110988926A (en) * | 2019-12-20 | 2020-04-10 | 福建海峡北斗导航科技研究院有限公司 | Method for realizing position accurate fixed point deception migration in loose GNSS/INS combined navigation mode |
Non-Patent Citations (4)
| Title |
|---|
| 吴连大, 中国科学技术出版社 * |
| 梁尔涛: "基于低轨卫星增强的非差高精度导航定位技术与在轨试验验证", 《上海航天》 * |
| 王小峰等: "MEMS-INS/GPS双星组合定位方法研究", 《现代导航》 * |
| 王玮等: "卫星/伪卫星/惯性组合着舰导引算法", 《系统工程与电子技术》 * |
Cited By (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112764067A (en) * | 2020-12-23 | 2021-05-07 | 深圳创维数字技术有限公司 | Method and device for acquiring ephemeris data of GPS (Global positioning System) satellite, and vehicle-mounted and readable storage medium |
| CN112764067B (en) * | 2020-12-23 | 2023-07-07 | 深圳创维数字技术有限公司 | GPS satellite ephemeris data acquisition method and device, vehicle-mounted and readable storage medium |
| CN113126128A (en) * | 2021-04-20 | 2021-07-16 | 东方红卫星移动通信有限公司 | DCB correction-based Beidou satellite navigation system frequency point precise point positioning method |
| CN114002726A (en) * | 2021-11-15 | 2022-02-01 | 北京北斗华大科技有限公司 | GNSS/INS combined navigation positioning system |
| CN114475655A (en) * | 2022-01-29 | 2022-05-13 | 智道网联科技(北京)有限公司 | Early warning method and device for automatic driving and computer readable storage medium |
| CN114475655B (en) * | 2022-01-29 | 2024-05-03 | 智道网联科技(北京)有限公司 | Early warning method and device for automatic driving and computer readable storage medium |
| CN115061175A (en) * | 2022-07-28 | 2022-09-16 | 知微空间智能科技(苏州)有限公司 | GNSS RTK and INS semi-tight combined positioning navigation method, device and system |
| CN117194869A (en) * | 2023-11-07 | 2023-12-08 | 中国科学院国家授时中心 | Attitude-considered low-orbit satellite antenna phase center forecasting and fitting method |
| CN117194869B (en) * | 2023-11-07 | 2024-03-19 | 中国科学院国家授时中心 | Attitude-considered low-orbit satellite antenna phase center forecasting and fitting method |
| CN117388900A (en) * | 2023-12-13 | 2024-01-12 | 深圳大学 | GNSS/INS combined ocean dynamic reference station construction method |
| CN117388900B (en) * | 2023-12-13 | 2024-03-08 | 深圳大学 | GNSS/INS combined ocean dynamic reference station construction method |
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