CN112731502A - Unmanned aerial vehicle aerial refueling inertia-assisted Beidou three-frequency precise relative navigation method - Google Patents

Unmanned aerial vehicle aerial refueling inertia-assisted Beidou three-frequency precise relative navigation method Download PDF

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CN112731502A
CN112731502A CN202011318607.6A CN202011318607A CN112731502A CN 112731502 A CN112731502 A CN 112731502A CN 202011318607 A CN202011318607 A CN 202011318607A CN 112731502 A CN112731502 A CN 112731502A
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ambiguity
satellite
navigation system
beidou
observed quantity
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CN112731502B (en
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吴玲
孙永荣
赵伟
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/42—Determining position
    • G01S19/45—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement
    • G01S19/47—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement the supplementary measurement being an inertial measurement, e.g. tightly coupled inertial
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64D—EQUIPMENT FOR FITTING IN OR TO AIRCRAFT; FLIGHT SUITS; PARACHUTES; ARRANGEMENTS OR MOUNTING OF POWER PLANTS OR PROPULSION TRANSMISSIONS IN AIRCRAFT
    • B64D39/00—Refuelling during flight
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12—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
    • G01C21/16—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
    • 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
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/42—Determining position
    • G01S19/43—Determining position using carrier phase measurements, e.g. kinematic positioning; using long or short baseline interferometry
    • G01S19/44—Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method

Abstract

The invention discloses an unmanned aerial vehicle aerial refueling inertia-assisted Beidou tri-band precise relative navigation method, which comprises an oiling machine and an oil receiving machine, wherein inertial navigation on the oiling machine and original data of a Beidou satellite navigation system are tightly combined to obtain real-time position and attitude information of the oiling machine and are transmitted to the oil receiving machine through a data chain; selecting an oiling machine as a mobile reference station and an oil receiving machine as a mobile station, and establishing a combined double-difference carrier phase and pseudo-range observation equation; the method comprises the steps of replacing pseudo-range observed quantity with inertial navigation prediction satellite-to-earth distance, establishing a short-baseline multi-path error model by adopting an improved TCAR method, solving and fixing original carrier ambiguity by adopting a Kalman Filter model and an LAMBDA method which expand multi-path parameters, and carrying out BDS/INS tight combination on an oil receiving machine to obtain two-carrier precise relative navigation parameters. The method has the advantages of high navigation precision, strong real-time property and high reliability.

Description

Unmanned aerial vehicle aerial refueling inertia-assisted Beidou three-frequency precise relative navigation method
Technical Field
The invention relates to the technical field of inertia/satellite integrated navigation, in particular to an unmanned aerial vehicle aerial refueling inertia-assisted Beidou tri-band precise relative navigation method.
Background
Autonomous air refueling can greatly improve the cruising ability of the unmanned aerial vehicle, and has important influence on the military strength in the air. In the refueling stage, the heights, the speeds and the relative positions of the fuel receiving machine and the fuel dispenser must be strictly kept unchanged. When a part of fuel is added into the fuel receiving machine, the weight of the airplane is increased, the weight of the fuel adding machine is reduced, the speed and the posture of the airplane must be adjusted at any time by the two machines so as to ensure smooth oiling, wherein a relative navigation method between the fuel adding machine and the fuel receiving machine is a key technology for implementing the process.
The traditional differential satellite navigation technology based on carrier phase can realize centimeter-level relative positioning accuracy, but a fixed reference station with known accurate position is required to provide differential correction numbers for the rover station, and the communication distance is limited; secondly, correct fixation of the carrier phase whole-cycle ambiguity is a key for realizing high-precision relative positioning, but in a single-frequency signal, due to the carrier wavelength length, the high sampling rate of data output and the inaccuracy of an initial coordinate, the satellite observation data of a single epoch can cause the normal matrix of an observation equation to be seriously ill-conditioned, the ambiguity real number solution obtained by direct calculation has a large difference with a true value, and the ambiguity is difficult to be fixed correctly. With the construction and development of the Beidou satellite navigation system in China, the Beidou satellite navigation system broadcasts three-frequency signals in a full constellation public way, and the combined observed quantity with long wavelength and low noise can be obtained in a three-frequency signal linear combination mode, so that the possibility of single-epoch high-precision navigation is provided. In the oil filling stage in air oil filling, on one hand, the oil receiving machine is positioned behind and below the oil filling machine with a large volume, the satellites are partially shielded, the number of visible satellites is reduced, and the geometric structure of the satellites is influenced, so that the precision of satellite navigation is seriously reduced; on the other hand, the oil adding machine and the oil receiving machine have high flight speed and high dynamic, and the satellite navigation data updating rate is low, so that the requirement of real-time navigation is difficult to meet. Therefore, a simple satellite navigation system cannot meet the requirements of high precision and high reliability of the air refueling in the refueling stage.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention aims to provide an unmanned aerial vehicle air refueling inertia auxiliary Beidou three-frequency precise relative navigation method, and the technical problems to be solved by the invention are as follows: in the air refueling stage, on one hand, the receiving oil engine is positioned behind and below the refueling machine with large volume, the satellite is partially shielded, the number of visible satellites is reduced, and the geometric structure of the satellite is influenced, so that the precision of satellite navigation is seriously reduced; on the other hand, the oil adding and receiving machine has high flying speed, high dynamic and low satellite navigation data updating rate, and is difficult to meet the requirement of real-time navigation.
In order to achieve the purpose, the invention provides the following technical scheme: an unmanned aerial vehicle aerial refueling inertia assisted Beidou tri-band precise relative navigation method comprises a refueling machine and a receiving machine, and comprises the following steps:
the method comprises the steps that firstly, an inertial navigation system on the oiling machine and original data of a Beidou satellite navigation system (BDS/INS) are tightly combined to obtain real-time position and attitude information of the oiling machine, and the real-time position and attitude information of the oiling machine is transmitted to an oil receiving machine through a data chain;
selecting an oiling machine as a mobile reference station and an oil receiving machine as a mobile station, and establishing three groups of optimal tri-frequency linear combination double-difference carrier phase and pseudo-range observation equations;
thirdly, the inertial navigation system is used for predicting the satellite-to-ground distance to replace pseudo range observed quantity, and the dual-difference ambiguity of the Extra Wide Lane (EWL) is directly obtained through rounding based on a Gemoty-free (GF) model;
constructing an accurate pseudorange observed quantity by using the Extra Wide Lane observed quantity with fixed ambiguity, solving Wide Lane (WL) double-difference ambiguity based on a Gemoty-base (GB) model by adopting an ILS method, and searching and fixing through LAMBDA;
constructing accurate pseudo-range observed quantity by using the Wide Lane observed quantity with fixed ambiguity, establishing a short-baseline multi-path error model, solving the original frequency double-difference integer ambiguity based on the Gemotry-Base model by using a Kalman Filter model with an extended multi-path parameter, and searching and fixing through LAMBDA;
and step six, the precise relative navigation parameters of the two moving carriers are solved in real time by adopting the carrier phase with fixed original ambiguity, the pseudo range, the Doppler observed quantity and the prediction information of the inertial navigation system to be tightly combined on the oil receiving machine.
In a preferred embodiment, in the first step, the state equation of the navigation system is tightly combined by the inertial navigation system and the raw data of the beidou satellite navigation system on the fuel dispenser, and the expression is as follows:
Figure BDA0002792088380000031
the combined system state quantity is:
Figure BDA0002792088380000032
W(t)＝[ωgx ωgy ωgz ωrx ωry ωrz ωax ωay ωaz ωtu ωtru]T，
wherein the content of the first and second substances,
Figure BDA0002792088380000033
as attitude angle error, δ ve δvn δvuFor velocity errors, δ L δ λ δ h for position errors, εx εyεzFor gyro constant drift, epsilonmx εmy εmzIn order to provide a top first order markov drift,
Figure BDA0002792088380000034
for zero offset, δ t, of the accelerometeruδtruDistance error caused by equivalent clock error and distance rate error caused by equivalent clock frequency error;
in a system state equation of combined navigation, a Beidou satellite navigation system state transition matrix FB(t) and a state noise system matrix GB(t), inertial navigation System State matrix FI(t) and the State noise coefficient matrix GI(t) selecting pseudo-range difference and pseudo-range difference between the Beidou satellite navigation system and the inertial navigation system by tightly combining the observed quantities, and tabulatingThe expression is as follows:
Figure BDA0002792088380000035
wherein Z isρ(t)，
Figure BDA0002792088380000036
Difference and difference of pseudoranges for BDS and SINS, Hρ(t)，
Figure BDA0002792088380000037
Is a unit vector of direction, Vρ(t)，
Figure BDA0002792088380000038
To observe the noise.
In a preferred embodiment, in the second step, the double difference carrier phase and pseudorange observation equation expression is as follows:
Figure BDA0002792088380000039
in the formula (I), the compound is shown in the specification,
Figure BDA00027920883800000310
represents the double difference operator, i.e.:
Figure BDA00027920883800000311
Figure BDA00027920883800000312
Figure BDA00027920883800000313
and
Figure BDA00027920883800000314
respectively, at frequency f (f is 1,2,3) to satellite s (s is 1,2)1,2, …, n), the expression:
Figure BDA0002792088380000041
wherein the content of the first and second substances,
Figure BDA0002792088380000042
representing the geometric distance of the receiver r from the satellite s, c being the speed of light, trAnd tsRespectively representing the receiver clock error and the satellite clock error,
Figure BDA00027920883800000412
denotes first order ionospheric delay, betafIn order to be the ionospheric delay factor,
Figure BDA0002792088380000043
the delay in the troposphere is indicated,
Figure BDA0002792088380000044
and
Figure BDA0002792088380000045
respectively, the error of each of the multiple paths,
Figure BDA0002792088380000046
is the integer ambiguity, λfIs the carrier wavelength, epsilonPAnd εΦRespectively receiver code noise and carrier noise.
In a preferred embodiment, in the third step, the satellite ranges are predicted by the inertial navigation system and the Beidou satellite navigation system satellite ephemeris is used for calculating the predicted satellite ranges by the inertial navigation system
Figure BDA0002792088380000047
And in rhoINSReplacing pseudo range observed quantity, and calculating the ambiguity of the whole circle of the ultra-wide lane by adopting a geometry-free model as follows:
Figure BDA0002792088380000048
in a preferred embodiment, in the fourth step, after the ambiguity of the Extra Wide Lane is rounded and determined, the ambiguity-fixed Extra Wide Lane carrier observed quantity is regarded as an accurate pseudorange observed quantity, and the Wide Lane ambiguity is assisted to be solved; the expression is as follows:
Figure BDA0002792088380000049
then, solving Wide Lane ambiguity by adopting a geometry-based model and an ILS method, and searching and fixing by adopting an LAMBDA method; the geometry-based model is as follows:
Figure BDA00027920883800000410
in a preferred embodiment, in the fifth step, after determining the Wide Lane ambiguity, the Wide Lane carrier observed quantity with fixed ambiguity is regarded as the accurate pseudorange observed quantity, and the basic ambiguity is further assisted to be solved; the expression is as follows:
Figure BDA00027920883800000411
in a preferred embodiment, in the step six, the precise relative navigation parameters of the two moving carriers use the carrier phase with fixed ambiguity, the pseudorange, the doppler observation and the INS prediction information to construct a DGNSS/INS tightly-combined filter model, which is as follows:
Figure BDA0002792088380000051
in the formula, ρINSThe inertial prediction geodetic distance is represented,
Figure BDA0002792088380000052
representing the relative velocity of the inertial prediction vehicle and the satellite.
The invention has the technical effects and advantages that:
1. the precision is improved:
the differential satellite navigation technology based on the carrier phase can obtain the relative positioning precision of the cm level, the key technology lies in the rapid and accurate fixation of the whole-cycle ambiguity, and under the condition of single-frequency signals, due to the fact that the carrier wavelength is short and under the high-dynamic condition, the satellite observation data correlation of a single epoch is strong, the matrix of the observation equation method is seriously ill-conditioned, and the ambiguity is difficult to fix correctly. The Beidou satellite navigation system is a satellite navigation system which is independently constructed and independently operated in China, a full constellation broadcasts three-frequency signals in a public way, and three-frequency linear combination is adopted to facilitate the construction of combined observed quantity with long wavelength and low noise, so that the accurate fixation of the integer ambiguity of a single epoch is facilitated, and the advantages of high inertial navigation output rate and short-term precision are utilized to predict satellite pseudorange instead of satellite pseudorange observed quantity, thereby further reducing pseudorange errors, facilitating the fixation of the ambiguity of the single epoch and improving the fixation success rate of the ambiguity.
2. The reliability is improved:
the satellite navigation technology has the advantages of globality, all-weather and high-precision positioning, but satellite signals are easily shielded and easily interfered by the outside, and under the high dynamic condition, the receiver is very easy to have the phenomena of signal lock losing and the like, so that the whole-cycle ambiguity needs to be fixed again and the cycle slip frequently occurs, thereby seriously affecting the navigation positioning result. The inertial navigation is an autonomous navigation mode, has strong anti-interference capability, fast data updating and high short-term precision, and can not be used independently for a long time due to error accumulation. The inertial/satellite combined navigation system can achieve advantage complementation, can obtain continuous, stable and high-precision navigation results in a complex environment, and improves the reliability of the system.
3. The method has the following real-time property:
in dynamic application, although the sampling rate of satellite positioning data can reach 1-10 Hz, the satellite positioning data is still difficult to be applied to a high dynamic environment of a flight carrier, the data sampling rate of inertial navigation generally can reach more than 100Hz, when the satellite positioning data and the inertial navigation data are combined for application, inertial errors can be corrected when the satellite data are intact, the inertial navigation precision is greatly improved, meanwhile, corrected inertial navigation has better stability and can predict navigation parameters with high precision, the data sampling rate of a navigation system is improved, a smoother navigation result is provided, and the real-time performance of the system is improved.
Drawings
Fig. 1 is a schematic diagram of relative navigation in a fueling phase in airborne fueling according to the present invention.
FIG. 2 is a flow chart of inertia-assisted Beidou tri-band precise relative positioning based on a mobile reference station.
Figure 3 is a diagram of a mobile reference station inertial/differential satellite tight combination architecture in which the present invention is implemented.
FIG. 4 is a flow chart of improved inertia-assisted Beidou tri-band integer ambiguity fixing implemented by the present invention.
FIG. 5 is a graph of the relationship between the combined observations and the number of lanes in accordance with the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1-5, the invention provides an unmanned aerial vehicle aerial refueling inertia-assisted Beidou three-frequency precise relative navigation method, which comprises the following specific steps:
1. and the BDS/INS tightly-combined absolute positioning is realized on the oiling machine, namely the error state quantity of the Beidou satellite navigation system and the error state quantity of the inertial system are combined to be jointly used as the state quantity of the combined navigation system. In general, the form of the equation of state is expressed as
Figure BDA0002792088380000071
The state equation of the BDS/INS combined navigation system can be obtained by connecting two state equations, and the expression is as follows:
Figure BDA0002792088380000072
the combined system state quantity is
Figure BDA0002792088380000073
W(t)＝[ωgx ωgy ωgz ωrx ωry ωrz ωax ωay ωaz ωtu ωtru]TWherein the content of the first and second substances,
Figure BDA0002792088380000074
as attitude angle error, δ ve δvn δvuFor velocity errors, δ L δ λ δ h for position errors, εx εy εzFor gyro constant drift, epsilonmxεmy εmzIn order to provide a top first order markov drift,
Figure BDA00027920883800000712
for zero offset, δ t, of the accelerometeru δtruThe range error caused by the equivalent clock error and the range rate error caused by the equivalent clock frequency error. In a system state equation of the integrated navigation, in a Beidou navigation system state equation, a Beidou navigation system state transition matrix FB(t) and a state noise system matrix GB(t), inertial navigation State matrix FI(t) and the State noise coefficient matrix GI(t) of (d). And tightly combining the observation quantity to select the pseudo-range difference and the pseudo-range difference of the BDS and the SINS, wherein the expression is as follows:
Figure BDA0002792088380000075
Zρ(t)，
Figure BDA0002792088380000076
as sum of pseudoranges differences between BDS and SINSDifference in pseudorange, Hρ(t)，
Figure BDA0002792088380000077
Is a unit vector of direction, Vρ(t)，
Figure BDA0002792088380000078
To observe the noise.
2. The original satellite pseudo range and the carrier phase observed quantity of the oiling machine are transmitted to the oil receiving machine through a data link, and a double-difference pseudo range and carrier phase observation equation is established by taking the oiling machine as a mobile reference station. The expression is as follows:
Figure BDA0002792088380000079
Figure BDA00027920883800000710
in the formula (I), the compound is shown in the specification,
Figure BDA00027920883800000711
represents the double difference operator, i.e.:
Figure BDA0002792088380000081
Figure BDA0002792088380000082
Figure BDA0002792088380000083
and
Figure BDA0002792088380000084
the pseudoranges and carrier observations from the receiver r (r is 1,2) to the satellite s (s is 1,2, …, n) at the frequency f (f is 1,2,3), respectively, are expressed as follows:
Figure BDA0002792088380000085
Figure BDA0002792088380000086
wherein the content of the first and second substances,
Figure BDA0002792088380000087
representing the geometric distance of the receiver r from the satellite s, c being the speed of light, trAnd tsRespectively representing the receiver clock error and the satellite clock error,
Figure BDA0002792088380000088
denotes first order ionospheric delay, betafIn order to be the ionospheric delay factor,
Figure BDA0002792088380000089
the delay in the troposphere is indicated,
Figure BDA00027920883800000810
and
Figure BDA00027920883800000811
respectively, the error of each of the multiple paths,
Figure BDA00027920883800000812
is the integer ambiguity (unit: week), lambdafIs the carrier wavelength, epsilonPAnd εΦRespectively receiver code noise and carrier noise.
Constructing virtual observed quantities through three-frequency linear combination, wherein the combined observed quantities and relevant parameters thereof are defined as follows:
Figure BDA00027920883800000813
Figure BDA00027920883800000814
wherein i, j, k are integer coefficients. The combined wavelength and integer ambiguity are:
Figure BDA00027920883800000815
N(i,j,k)＝i·N1+j·N2+k·N3 (8)
first order ionospheric scale factor (relative to carrier phase Φ)1) And the combined pseudorange and carrier phase multipath errors are respectively:
Figure BDA00027920883800000816
Figure BDA00027920883800000817
Figure BDA00027920883800000818
assumed code observation noise epsilonPi(i ═ 1,2,3) and carrier phase observation noise
Figure BDA0002792088380000091
Independent and equal at each frequency, the combined code and carrier observed noise variance can be expressed as:
Figure BDA0002792088380000092
Figure BDA0002792088380000093
the carrier phase noise factor is defined as:
Figure BDA0002792088380000094
define the overall noise level (TNL) as:
Figure BDA0002792088380000095
let f1,f2,f3Respectively corresponding to frequency points of Beidou B1, B2 and B3, and taking the greatest common divisor as the Beidou reference frequency f02.046MHz, then f1＝763f0，f2＝590f0，f3＝620f0Let the number of lanes KC763 · i +590 · j +620 · k, the combined wavelength
Figure BDA0002792088380000096
λ0146.53m corresponds to f0Is the wavelength of (c). When selecting the combination coefficient, the optimal three linearly independent combinations are selected, and when K is usedCLess than or equal to 50 is an ultra-wide lane combination, and K is more than 50CIs a wide lane combination of less than or equal to 195, KCAnd more than 195 is a narrow lane combination. Take i, j, k ∈ [ -10,10]，KCUseful combination coefficients < 2000 are shown in Table 1.
TABLE 1 useful combination coefficients and observed quantity coefficients
Figure BDA0002792088380000101
The combination coefficients corresponding to the combination characteristics are preferably selected from i + j + k ═ 0, where (0, -1, 1) is a combination having a long wavelength, a small ionospheric amplification factor and a small noise amplification factor, and the first linear combination can be set regardless of the base line length. The second combination choice is linearly independent of (0, -1, 1) and for short baselines, ionospheric and tropospheric errors are almost completely eliminated by double differencing, where observation noise and multipath errors are the major sources of error, and the combination chosen should have a small noise amplification factor and a longer wavelength, with both (1, 0, -1) and (1, -1, 0) being reasonable choices. The third combination needs to be independent of the first and second combinations linearly, considering that the screening from i + j + k ═ 1, for a short baseline, the selected combination should also have a smaller noise amplification factor and a longer wavelength, and obviously, the original observations (1, 0, 0), (0, 1, 0) and (0, 0, 1) have the smallest noise amplification factor and are the most reasonable choices. Therefore, three sets of combination coefficients (0, -1, 1), (1, 0, -1), (1, 0, 0) are finally selected. The combined observations are shown in fig. 5.
3. Calculating INS predicted satellite distance by using INS predicted position and BDS satellite ephemeris
Figure BDA0002792088380000111
And in rhoINSReplacing pseudo range observed quantity, and calculating the ambiguity of the whole circle of the ultra-wide lane by adopting a geometry-free model as follows:
Figure BDA0002792088380000112
to make the above formula correct, the error amount needs to be satisfied
Figure BDA0002792088380000113
Neglecting residual atmospheric delay and multipath error effects, there are:
Figure BDA0002792088380000114
and if the standard deviation of the BDS single-frequency carrier noise is 0.002m, the standard deviation of the double-difference carrier noise is 0.004, and 3 sigma is taken according to a 99.7% confidence interval, namely 0.012 m. According to the combination error propagation formula, the carrier noise amplification factor of the EWL is 28.5, so that the double-difference carrier noise of the EWL is 0.342 m. Therefore, the temperature of the molten metal is controlled,
Figure BDA0002792088380000115
ignoring the reference station position error, then:
Figure BDA0002792088380000116
in the formula: lp，lqRepresenting mobile station receivers to reference stars p and satellites, respectivelyUnit direction vector of star q; dXI＝[dxI dyI dzI]TFor INS position error, if | lp-lqIf 1 and the INS predicted position has equal errors in three directions, then there are
Figure BDA0002792088380000117
Therefore, the feasibility of the algorithm needs to meet the condition that the accumulation of the single-direction position errors in the filtering period of the adopted IMU device is less than 1.5 m.
4. After the EWL ambiguity is rounded and determined, the EWL carrier observed quantity with fixed ambiguity can be regarded as an accurate pseudorange observed quantity, and the WL ambiguity is assisted to be solved. The expression is as follows:
Figure BDA0002792088380000118
then, solving the WL ambiguity by using a geometry-based (GB) model and an ILS method, and searching and fixing by using an LAMBDA method. The GB model is as follows:
Figure BDA0002792088380000119
5. after the WL ambiguity is determined, similarly, the WL carrier observed with fixed ambiguity is regarded as an accurate pseudorange observed, which further assists in solving the basic ambiguity. The expression is as follows:
Figure BDA0002792088380000121
because in the short baseline situation, the double difference eliminates most errors, including satellite and receiver clock differences, orbit errors, atmospheric delay and the like, except multipath errors and observation noise. Therefore, to further provide the precision of the basic ambiguity float solution, the multipath error is modeled and solved as a state parameter. On the other hand, the position information obtained by the INS prediction can be used as an additional constraint observed value, and the double difference equation is linearized at the INS prediction position. The observation equation based on the GB model is adopted as follows:
Figure BDA0002792088380000122
assuming double-difference carrier phase multipath
Figure BDA0002792088380000123
Modeling is a first order Gauss-Markov random process, i.e.:
Figure BDA0002792088380000124
where η is the time correlation constant of the multipath. The discretization equation is:
Figure BDA0002792088380000125
wherein T is a sampling period and q is a spectral density constant.
6. And (2) constructing a DGNSS/INS tight combination filtering model by adopting the carrier phase, the pseudo range and the Doppler observed quantity with fixed ambiguity and INS prediction information, wherein the error quantity of a satellite system is not considered, and the equation form and other state quantities are equal to Eq (1). The observation model is as follows:
Figure BDA0002792088380000126
in the formula, ρINSThe inertial prediction geodetic distance is represented,
Figure BDA0002792088380000127
representing the relative velocity of the inertial prediction vehicle and the satellite.
7. The effect of the moving reference station position offset on the baseline measurement can be expressed as: delta X2＝δX1+δΔX12It can be seen that it mainly comprises two parts: one is to make the baseline vector produce a translation deltaX1In a space rectangular coordinate system, the influence relationship is simple, and the value of the influence relationship only depends on the change of the coordinates of the starting point; secondly, the deviation of the initial point coordinate, through the GNSS relative positioning model, affects the solved baseline vector, namely: delta X12＝Q·δX1Here, the value of Q matrixIs related to many factors such as the length of the base line, the azimuth, the location of the starting point, and the geometric distribution of the measured satellite. The influence of the position deviation of the reference station on the measured baseline is mainly closely related to the length of the baseline, and the influence can be generally estimated according to the following formula: δ S is 0.60 · 10-4.·D·δX1D is the base length in km, deltaX1δ S is the baseline error for the positional deviation of the moving reference station. When the baseline accuracy requirement is less than 1cm, the mobile reference station position deviation should be less than 16.7m for a baseline length within 10 km. Considering that the BDS/INS tight combination positioning precision of the oiling machine can generally reach m-level precision, the influence of the position deviation of the mobile reference station on the baseline result is less than 1cm, and the requirement of relative positioning precision is met.
It should be noted that:
firstly, the invention adopts the prior art without specific description;
secondly, the method comprises the following steps: in the drawings of the disclosed embodiments of the invention, only the structures related to the disclosed embodiments are referred to, other structures can refer to common designs, and the same embodiment and different embodiments of the invention can be combined with each other without conflict;
and finally: the above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that are within the spirit and principle of the present invention are intended to be included in the scope of the present invention.

Claims (7)

1. The utility model provides an unmanned aerial vehicle aerial refueling inertia-assisted Beidou tri-band precise relative navigation method, which comprises a refueling machine and a receiving machine, and is characterized in that: the method comprises the following steps:
the method comprises the following steps that firstly, an inertial navigation system on the oiling machine and original data of a Beidou satellite navigation system are tightly combined to obtain real-time position and attitude information of the oiling machine, and the real-time position and attitude information of the oiling machine is transmitted to an oil receiving machine through a data link;
selecting an oiling machine as a mobile reference station and an oil receiving machine as a mobile station, and establishing three groups of optimal tri-frequency linear combination double-difference carrier phase and pseudo-range observation equations;
thirdly, the inertial navigation system is used for predicting the satellite-to-ground distance to replace pseudo range observed quantity, and the Extra Wide Lane double-difference ambiguity is directly obtained through rounding and solving based on a Gemotry-Free model;
constructing an accurate pseudorange observed quantity by using the Extra Wide Lane observed quantity with fixed ambiguity, solving Wide Lane double-difference ambiguity based on a Gemotry-Base model by adopting an ILS method, and searching and fixing through LAMBDA;
constructing accurate pseudo-range observed quantity by using the Wide Lane observed quantity with fixed ambiguity, establishing a short-baseline multi-path error model, solving the original frequency double-difference integer ambiguity based on the Gemotry-Base model by using a Kalman Filter model with an extended multi-path parameter, and searching and fixing through LAMBDA;
and step six, the precise relative navigation parameters of the two moving carriers are solved in real time by adopting the carrier phase with fixed original ambiguity, the pseudo range, the Doppler observed quantity and the prediction information of the inertial navigation system to be tightly combined on the oil receiving machine.
2. The unmanned aerial vehicle aerial refueling inertia-assisted Beidou three-frequency precise relative navigation method as claimed in claim 1, characterized in that: in the first step, the state equation of the navigation system is tightly combined by the original data of the inertial navigation system and the Beidou satellite navigation system on the oiling machine, and the expression is as follows:
Figure FDA0002792088370000011
the combined system state quantity is:
Figure FDA0002792088370000012
W(t)＝[ωgx ωgy ωgz ωrx ωry ωrz ωax ωay ωaz ωtu ωtru]T，
wherein the content of the first and second substances,
Figure FDA0002792088370000013
as attitude angle error, δ ve δvn δvuFor velocity errors, δ L δ λ δ h for position errors, εx εy εzFor gyro constant drift, epsilonmx εmy εmzIn order to provide a top first order markov drift,
Figure FDA0002792088370000021
for zero offset, δ t, of the accelerometeru δtruDistance error caused by equivalent clock error and distance rate error caused by equivalent clock frequency error;
in a system state equation of combined navigation, a Beidou satellite navigation system state transition matrix FB(t) and a state noise system matrix GB(t), inertial navigation System State matrix FI(t) and the State noise coefficient matrix GI(t), selecting pseudo-range difference and pseudo-range difference between the Beidou satellite navigation system and the inertial navigation system by combining the observed quantities, wherein the expression is as follows:
Figure FDA0002792088370000022
wherein Z isρ(t)，
Figure FDA00027920883700000212
Difference and difference of pseudoranges for BDS and SINS, Hρ(t)，
Figure FDA00027920883700000213
Is a unit vector of direction, Vρ(t)，
Figure FDA00027920883700000214
To observe the noise.
3. The unmanned aerial vehicle aerial refueling inertia-assisted Beidou three-frequency precise relative navigation method as claimed in claim 1, characterized in that: in the second step, the expression of the double-difference carrier phase and pseudo-range observation equation is as follows:
Figure FDA0002792088370000023
in the formula (I), the compound is shown in the specification,
Figure FDA0002792088370000024
represents the double difference operator, i.e.:
Figure FDA0002792088370000025
Figure FDA0002792088370000026
Figure FDA0002792088370000027
and
Figure FDA0002792088370000028
the pseudoranges and carrier observations from the receiver r (r is 1,2) to the satellite s (s is 1,2, …, n) at the frequency f (f is 1,2,3), respectively, are expressed as follows:
Figure FDA0002792088370000029
wherein the content of the first and second substances,
Figure FDA00027920883700000210
representing the geometric distance of the receiver r from the satellite s, c being the speed of light, trAnd tsRespectively representing the receiver clock error and the satellite clock error,
Figure FDA00027920883700000211
denotes first order ionospheric delay, betafIn order to be the ionospheric delay factor,
Figure FDA0002792088370000031
the delay in the troposphere is indicated,
Figure FDA0002792088370000032
and
Figure FDA0002792088370000033
respectively, the error of each of the multiple paths,
Figure FDA0002792088370000034
is the integer ambiguity, λfIs the carrier wavelength, epsilonPAnd εΦRespectively receiver code noise and carrier noise.
4. The unmanned aerial vehicle aerial refueling inertia-assisted Beidou three-frequency precise relative navigation method as claimed in claim 1, characterized in that: in the third step, the satellite distance adopts the inertial navigation system to predict the position and the Beidou satellite navigation system satellite ephemeris to calculate the satellite distance predicted by the inertial navigation system
Figure FDA0002792088370000035
And in rhoINSReplacing pseudo range observed quantity, and calculating the ambiguity of the whole circle of the ultra-wide lane by adopting a geometry-free model as follows:
Figure FDA0002792088370000036
5. the unmanned aerial vehicle aerial refueling inertia-assisted Beidou three-frequency precise relative navigation method as claimed in claim 1, characterized in that: in the fourth step, after the ambiguity of the Extra Wide Lane is rounded and determined, the Extra Wide Lane carrier observed quantity with fixed ambiguity is taken as an accurate pseudorange observed quantity, and the Wide Lane ambiguity is solved in an auxiliary manner; the expression is as follows:
Figure FDA0002792088370000037
then, solving Wide Lane ambiguity by adopting a geometry-based model and an ILS method, and searching and fixing by adopting an LAMBDA method; the geometry-based model is as follows:
Figure FDA0002792088370000038
6. the unmanned aerial vehicle aerial refueling inertia-assisted Beidou three-frequency precise relative navigation method as claimed in claim 1, characterized in that: in the fifth step, after the WidLane ambiguity is determined, the WidLane carrier observed quantity with fixed ambiguity is taken as an accurate pseudo-range observed quantity, and basic ambiguity is further assisted to be solved; the expression is as follows:
Figure FDA0002792088370000039
7. the unmanned aerial vehicle aerial refueling inertia-assisted Beidou three-frequency precise relative navigation method as claimed in claim 1, characterized in that: in the sixth step, the precise relative navigation parameters of the two moving carriers adopt the carrier phase with fixed ambiguity, the pseudo range, the Doppler observed quantity and the INS prediction information to construct a DGNSS/INS tight combination filtering model, and the model is as follows:
Figure FDA0002792088370000041
in the formula, ρINSThe inertial prediction geodetic distance is represented,
Figure FDA0002792088370000042
representing the relative velocity of the inertial prediction carrier and the satellite。
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