CN116878498A - Multi-frequency BDS/INS combined air refueling relative navigation system and method - Google Patents

Multi-frequency BDS/INS combined air refueling relative navigation system and method Download PDF

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Publication number
CN116878498A
CN116878498A CN202310824341.XA CN202310824341A CN116878498A CN 116878498 A CN116878498 A CN 116878498A CN 202310824341 A CN202310824341 A CN 202310824341A CN 116878498 A CN116878498 A CN 116878498A
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machine
frequency
oil receiving
relative
navigation
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付希禹
孙永荣
吴玲
王凯锋
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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
    • 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
    • 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
    • G01C21/183—Compensation of inertial measurements, e.g. for temperature effects
    • 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

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  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Position Fixing By Use Of Radio Waves (AREA)

Abstract

The invention discloses a multi-frequency BDS/INS combined air refueling relative navigation system and a method, wherein the navigation system comprises a refueling machine and an oil receiving machine, and a multi-frequency Beidou satellite navigation system and an inertial navigation system are respectively installed; the navigation method of the invention is as follows: the oiling machine obtains real-time position, speed and attitude information of the oiling machine through tight combination and transmits the information to the oil receiving machine through a data chain; the oil receiving machine establishes a relative measurement model with the oiling machine as a mobile reference station and the oil receiving machine as a mobile station, and adopts a fusion structure of cascading filtering to obtain relative navigation information between the oiling machine and the oil receiving machine, thereby providing guarantee for an aerial oiling task. The invention improves the accuracy of the relative state error model, effectively inhibits the divergence of the resolving result and improves the accuracy and the reliability of the relative navigation system.

Description

Multi-frequency BDS/INS combined air refueling relative navigation system and method
Technical Field
The invention relates to the technical field of satellite navigation and integrated navigation, in particular to a multi-frequency BDS/INS integrated air refueling relative navigation system and method.
Background
The unmanned plane has the advantages of small volume, light weight, low cost and the like, and has wide application. But the amount of oil it carries limits its take-off weight and cruising ability. The unmanned aerial vehicle aerial refueling technology can improve the flight distance and the air time of the unmanned aerial vehicle, improves the performance advantage of the unmanned aerial vehicle, and is one of the important directions of the current unmanned aerial vehicle research.
In the air refueling process, determining the relative position, speed and posture relation between the oiling machine and the oil receiving machine is an important ring for smoothly completing the air refueling process. The current common relative navigation methods include methods of relative navigation based on satellite difference, relative navigation based on absolute navigation information difference and the like. However, the satellite differential relative navigation is dependent on satellite signals, and cannot work when the satellite signals are shielded, so that the robustness is not strong. While the relative navigation of absolute navigation information difference makes up the point, the relative relation between targets is not established, a relative state estimation feedback loop is not established, the navigation precision is often limited, and the requirements of high reliability and high precision of air refueling cannot be met.
Disclosure of Invention
The invention aims to: the invention aims to improve the navigation precision and reliability of relative navigation under a complex air refueling scene, provide navigation technical support for an air refueling task, and designs a multi-frequency BDS/INS combined air refueling relative navigation system and method.
The technical scheme is as follows: the multi-frequency BDS/INS combined air refueling relative navigation system of the invention comprises: the oiling machine navigation system and the oil receiving machine navigation system;
the oiling machine navigation system comprises a first multi-frequency satellite signal receiving device, a first inertial measurement unit, a first data storage device, an oiling machine data communication device, an oiling machine online navigation resolving device and a first power supply device;
the oil receiving machine navigation system comprises a second multi-frequency satellite signal receiving device, a second inertial measurement unit, a second data storage device, an oil receiving machine data communication device, an oil receiving machine online navigation resolving device, a second power supply device and a guidance and flight control device;
the data communication between the oiling machine data communication equipment and the oil receiving machine data communication equipment can be realized;
the first multi-frequency satellite signal receiving device and the second multi-frequency satellite signal receiving device are respectively used for receiving Beidou multi-frequency satellite signals in real time; the first multi-frequency satellite signal receiving device is connected with the first data storage device and stores the received Beidou multi-frequency satellite signals in the first data storage device; the second multi-frequency satellite signal receiving device is connected with the second data storage device and stores the received Beidou multi-frequency satellite signals in the second data storage device;
the first inertial measurement unit and the second inertial measurement unit are respectively used for measuring the angular velocity and the linear acceleration of the carrier on line; the first inertia measurement unit is connected with the first data storage device, and the second inertia measurement unit is connected with the second data storage device;
a first data storage device: the system comprises a first multi-frequency satellite signal receiving device, a first inertial measurement unit and a second inertial measurement unit, wherein the first multi-frequency satellite signal receiving device is used for receiving and storing original data acquired by the first multi-frequency satellite signal receiving device and the first inertial measurement unit; a second data storage device: the system comprises a first multi-frequency satellite signal receiving device, a second multi-frequency satellite signal receiving device, a first inertial measurement unit and a second inertial measurement unit, wherein the first multi-frequency satellite signal receiving device is used for receiving and storing the primary data acquired by the first multi-frequency satellite signal receiving device and the second inertial measurement unit;
the output of the oiling machine online navigation resolving equipment transmits data to the oil receiving machine through the oiling machine data communication equipment; the oil receiving machine data communication equipment synchronously receives the data and sends the received data to the oil receiving machine on-line navigation resolving equipment;
the online navigation resolving device of the oiling machine and the online navigation resolving device of the oil receiving machine are respectively loaded and run with software parts of a system, and are used for processing an online running navigation information resolving program, and the online navigation resolving device comprises: the data are collected and aligned in real time, the position, speed and attitude information of the oiling machine/oil receiving machine are calculated, and a calculation result is output;
the first power supply device and the second power supply device respectively provide power supply support for a navigation system of the oiling machine and the oil receiving machine;
the guidance and flight control equipment is connected with the oil receiving machine on-line navigation resolving equipment, the estimated real-time relative position, speed and attitude information of the oil receiving machine and the oiling machine are used as reference input, and the flight attitude of the oil receiving machine is adjusted through guidance law and steering engine control.
A multi-frequency BDS/INS combined air refueling relative navigation method comprises the following steps:
s1, respectively constructing multifrequency BDS system measurement equations of the oil receiver and the oil receiver based on a Beidou satellite navigation system and an inertial navigation system of the oil receiver and the inertial navigation system, and correcting a solution result of the INS through absolute state filtering of BDS/INS tight combination; meanwhile, the oiling machine sends real-time absolute navigation information and original data to the oil receiving machine through a data link;
s2, using an oiling machine as a mobile reference station and an oil receiving machine as an mobile station, and establishing a carrier phase double-difference observation equation and a Doppler double-difference observation equation;
s3, separating the integer ambiguity in the carrier phase from the filter parameter estimation, screening three groups of Beidou coefficients to form an ultra-wide lane-narrow lane combination, replacing pseudo-range observed quantity with the satellite distance predicted by an inertial navigation system, and solving the double-difference integer ambiguity lane by lane based on a geometric model and a geometric model;
s4, introducing a relative state filter, and establishing a multi-frequency Beidou differential relative measurement equation based on the mobile reference station; and constructing a DGNSS/INS tightly-combined relative filtering model by combining a relative state error recurrence model of the SINS navigation system, and fusing relative information data by expanding a Kalman filtering data fusion method to complete the calculation of relative navigation parameters of the oiling machine and the oil receiving machine.
Further, in step S1, the expression of the state recurrence equation of the tight combination of the inertial navigation system of the oil receiving machine and the beidou navigation system is:
the selected state variables are:
X r ＝[(δp) T (δv) T φ T (δb rg ) T (δb ra ) T δt u δt ru ] T
in (δp) T ＝[δp E δp N δp U ]Is an ENU directional position error; (δv) T ＝[δv E δv N δv U ]Is an ENU directional velocity error; phi (phi) T ＝[φ E φ N φ U ]Is an ENU direction attitude error; (δb) rg ) T 、(δb ra ) T The random constant drift error of the oil receiving machine gyroscope and the random constant drift error of the accelerometer are respectively; δt u For equivalent clock error corresponding distance δt ru The distance rate corresponding to the equivalent clock frequency error; "T" represents the matrix transpose;
the expression of the state recurrence equation of the tight combination of the inertial navigation system and the Beidou navigation system of the oiling machine is the same as the state recurrence equation of the tight combination of the inertial navigation system and the Beidou navigation system of the oil receiving machine.
Further, in step S1, the measurement equation of the multi-frequency BDS system of the oil receiving machine is:
wherein P is r,n And D r,n Respectively indicate that the oil receiving machine is in the big dipper B n Pseudo-range and Doppler observations over frequency, n=1, 2,3; h r (t) is the measurement coefficient matrix of the oil receiving machine, V r (t) is the measurement noise matrix of the oil receiving machine,calculating pseudo ranges and pseudo range rates for the oil receiving machines respectively;
the multi-frequency BDS system measurement equation of the oiling machine is the same as the multi-frequency BDS system measurement equation of the oil receiving machine.
In step S2, the oiling machine m observes satellites i and j, and meanwhile, the oil receiving machine r observes satellites i and j, and the oiling machine m and the oil receiving machine r receive three-frequency BDS signals to obtain a plurality of groups of observation values under the frequency bands B1/B2/B3; the carrier phase double-difference observation equation and the Doppler double-difference observation equation are as follows:
where, Δ represents a double difference operator, φ is carrier phase in meters, N is integer ambiguity, D is Doppler observed quantity, ρ is the geometric distance of the satellite and the receiver,the change rate of the geometric distance between the satellite and the receiver is shown; n represents Beidou B n Frequency band, n=1, 2,3; lambda (lambda) n Representing Beidou B n The wavelength corresponding to the frequency band, I represents ionosphere delay error, T represents troposphere delay error, and superscript "·" represents change rate; />Representing carrier phase noise error term,/->Representing Doppler observed quantity noise error items; />For the satellite geometry distance of the oil receiver r corresponding to satellite i>The geometrical distance of the oil receiver r corresponding to the satellite j is the satellite ground; />For the dispenser m the geometrical distance of the satellite i corresponding to the satellite i +.>The geometrical distance of the satellite corresponding to the satellite j is provided for the oiling machine m;synchronous observation for oiling machine m and oil receiving machine rB formed by satellites i and j n Frequency band double difference carrier phase; />B formed by the synchronous observation satellites i and j of the oiling machine m and the oil receiving machine r n Frequency band double-difference integer ambiguity; />B formed by the synchronous observation satellites i and j of the oiling machine m and the oil receiving machine r n Frequency band double difference ionosphere delay error; />B formed by the synchronous observation satellites i and j of the oiling machine m and the oil receiving machine r n Frequency band double difference troposphere delay error.
Further, in step S4, the construction process of the relative measurement error equation is as follows:
set the position coordinate of the oiling machine under the geodetic fixed coordinate system of the geodetic center asEstimating the approximate position asThe correction is +.>The position coordinate of the oil receiving machine is->Estimating the approximate position as +.>The correction is +.>The position vector of the oil receiver r relative to the oil filler m in the ECEF coordinate system is +.>The approximate position is +.>Position error is +.>Defining the physical quantity M of the a-coordinate system relative to the b-coordinate system, the projection under the c-coordinate system is +.> Representing a gesture conversion matrix from an a coordinate system to a b coordinate system; i represents an inertial coordinate system;
let the position of satellite i be (x i ,y i ,z i ) T The oil receiver r corresponds to the geometrical distance of the satellite i from the groundIs calculated as follows:
taylor linear expansion is carried out on nonlinear terms in the above method:
in the method, in the process of the invention,for satellite and receiver geometric distance estimation, [ I ] x I y I z ]As the sight line vector, subscripts x, y and z respectively represent components of the sight line vector in x direction, y direction and z direction; let->For the line of sight vector between the fuel dispenser m and satellite i,/->The line of sight vector between the oil receiver r and the satellite i is:
the relative position under the ECEF coordinate system has the following relation with the relative position under the machine system:
in the method, in the process of the invention,representing the positions of the oiling machine and the oil receiving machine in the ECEF coordinate system respectively, and projecting the relative positions to the oiling machine body coordinate system, wherein the oil receiving machine in the ECEF coordinate system is a box-shaped oil receiving machine>The expression is rewritten as:
taking into account thatThus, the position error of the oil receiving machine->The method comprises the following steps:
wherein δα mr Is the error of relative attitude angleDifference;
finally, the method comprises the following steps:
similarly, the following can be obtained:
ignoring position errors of fuel dispensersThe relative navigation is influenced, the difference between stations and stars is made for the oiling machine and the oil receiving machine, and the residual errors of the ionosphere and the troposphere after double differences are ignored, so that the expression of the relative measurement error equation is as follows:
synchronously observing M satellites to obtain a multi-frequency carrier phase observation equation consisting of M-1 observation equations:
where phi represents an M-1 dimensional carrier phase vector, N represents an M-1 dimensional integer ambiguity vector,represents M-1 dimension guard distance predictive vector, K 1 、K 2 A coefficient matrix formed by M-1 sets of equations;
the following relationship exists for the pseudorange rate of change, the relative speeds of the fuel dispenser and the fuel receiver:
in the method, in the process of the invention,an estimated value of the geometric distance change rate of the satellite and the receiver;
from the following components
Then there is
Then:
error models combining gyroscopes and accelerometers can be obtained:
ignoring the fuel dispenser speed error and substituting into the doppler observation equation, then:
and ignoring the double difference residual error term, the multi-frequency Doppler observation equation can be finally written as:
wherein D represents an M-1-dimensional Doppler observed vector,represents M-1 dimension prediction of the change rate of the distance between the guard and the ground, Q 1 、Q 2 、Q 3 Q and Q 4 A coefficient matrix for the M-1 set of equations.
Compared with the prior art, the invention has the following remarkable effects:
1. compared with single frequency, the invention adopts a multi-frequency form on the observed quantity, can increase the redundancy of the observed information and improve the fault tolerance of the system; the multi-frequency signal can provide a large number of combined observables with excellent performance, thereby being beneficial to the rapid solving and fixing of single epoch integer ambiguity; meanwhile, inertial prediction is adopted to assist in fixing the ambiguity, so that the influence of coarse difference of pseudo range and multipath effect on the ambiguity fixing is restrained, and the ambiguity fixing rate and the navigation positioning accuracy are improved;
2. satellite navigation has the characteristics of all-day and all-weather high-precision positioning navigation, but satellite signals are easily shielded in the tail approaching and docking oiling processes of an oil receiving machine, and the phenomena of signal lock losing and the like of a receiver are easily caused under the conditions of external interference and high dynamic state, so that the navigation positioning result is seriously influenced; the invention adopts an inertial/satellite combined navigation system, can complement advantages, makes up for the defect of discontinuous positioning results of satellites, can obtain continuous, stable and high-precision navigation results in complex environments, and improves the stability of the system;
3. the common combined navigation scheme adopts a loose combination mode, so that the implementation difficulty is low, but when the number of the observation satellites is less than four, the system is degenerated to single inertial navigation, the error accumulation is obvious, and the divergence is fast; the tight combination scheme of the original observed quantity combination has high precision and strong poor resistance, is more suitable for being applied to the environment where satellite signals are easily interfered, has certain endurance capacity when the signals lose lock for a short time, and can provide continuous navigation service; meanwhile, the satellite information on the oiling machine and the oil receiving machine is utilized to correct the absolute positioning result of the satellite information on the oiling machine and the oil receiving machine, and the measurement information of the gyroscope and the accelerometer is corrected, so that the accuracy of a relative state error model is improved due to the existence of a local state filter, the divergence of a resolving result is effectively restrained, and the reliability of the system is improved.
Drawings
FIG. 1 is a schematic diagram of an aerial fueling relative navigation system of the present invention;
FIG. 2 is a flow chart of a relative navigation method for aerial refueling of the unmanned aerial vehicle according to the present invention;
FIG. 3 is a vector relationship diagram of an air-fuelling and oil receiving machine of the present invention;
FIG. 4 (a) is a graph of relative position error in the x-direction of relative navigation according to the present invention;
FIG. 4 (b) is a graph of relative position error in the y-direction of the relative navigation of the present invention;
FIG. 4 (c) is a graph of relative position error in the z-direction of relative navigation in accordance with the present invention;
FIG. 5 (a) is a graph of relative velocity error in the x-direction of relative navigation in accordance with the present invention;
FIG. 5 (b) is a graph of the relative velocity error in the y-direction of the relative navigation of the present invention;
FIG. 5 (c) is a graph of the relative velocity error in the z-direction of the relative navigation of the present invention;
FIG. 6 (a) is a graph of relative roll angle error in relative navigation of the present invention;
FIG. 6 (b) is a graph of relative pitch angle error in relative navigation of the present invention;
FIG. 6 (c) is a graph of relative heading angle error in relative navigation according to the present invention.
Detailed Description
The invention is described in further detail below with reference to the drawings and the detailed description.
As shown in fig. 1, the invention provides a multi-frequency BDS/INS (BDS: bei Dou system Beidou satellite navigation system, INS: inertial navigation system) combined relative navigation system for unmanned aerial vehicle aerial refueling, which comprises a refueling machine navigation system and an oil receiving machine navigation system, wherein the refueling machine navigation system comprises a first multi-frequency satellite signal receiving device, a first inertial measurement unit, a first data storage device, a refueling machine data communication device, a refueling machine online navigation resolving device and a first power supply device; the oil receiving machine navigation system comprises a second multi-frequency satellite signal receiving device, a second inertial measurement unit, a second data storage device, an oil receiving machine data communication device, an oil receiving machine online navigation resolving device, a second power supply device and a guidance and flight control device; and the data communication device of the oiling machine and the data communication device of the oil receiving machine are used for data communication.
The first multi-frequency satellite signal receiving device and the second multi-frequency satellite signal receiving device respectively comprise, but are not limited to, a satellite signal receiving antenna, a satellite navigation integrated board card and the like, and are used for receiving Beidou multi-frequency satellite signals in real time; the first multi-frequency satellite signal receiving device is connected with the first data storage device and stores the received Beidou multi-frequency satellite signals in the first data storage device; the second multi-frequency satellite signal receiving device is connected with the second data storage device and stores the received Beidou multi-frequency satellite signals in the second data storage device.
The first inertial measurement unit and the second inertial measurement unit respectively comprise a gyroscope and an accelerometer and are used for measuring the angular velocity and the linear acceleration of the carrier on line; the first inertial measurement unit is coupled to the first data storage device and the second inertial measurement unit is coupled to the second data storage device.
A first data storage device: the system comprises a first multi-frequency satellite signal receiving device, a first inertial measurement unit and a second inertial measurement unit, wherein the first multi-frequency satellite signal receiving device is used for receiving and storing original data acquired by the first multi-frequency satellite signal receiving device and the first inertial measurement unit; a second data storage device: the system is used for recording and storing the original data acquired by the second multi-frequency satellite signal receiving device and the second inertial measurement unit.
The output of the oiling machine online navigation resolving equipment transmits data to the oil receiving machine through the oiling machine data communication equipment; and the oil receiving machine data communication equipment synchronously receives the data and transmits the received data to the oil receiving machine on-line navigation resolving equipment. The fuel dispenser (or oil receiver) data communication device may employ, but is not limited to, WDS high speed frequency hopping station-SDR 400L and a wireless transmission antenna.
The software part of the system is loaded and operated by the online navigation resolving equipment of the oiling machine (or the oil receiving machine) and is used for processing the online navigation information resolving program, and the software part comprises the following components: the data are collected and aligned in real time, and the position, speed and attitude information of the oiling machine/oil receiving machine are calculated and a calculation result is output; the method is applicable to building an onboard embedded platform by adopting, but not limited to, NVIDIA Jetson TX2 development boards and the like so as to complete tasks such as real-time navigation data calculation and the like.
The first power supply device and the second power supply device respectively provide power supply support for a navigation system of the oiling machine and the oil receiving machine.
The guidance and flight control equipment is connected with the oil receiving machine on-line navigation resolving equipment, the estimated real-time relative position, speed and attitude information of the oil receiving machine and the oiling machine are used as reference input, and the flight attitude of the oil receiving machine is adjusted through guidance law and steering engine control.
The relative navigation system of the invention establishes a relative measurement model with the oiling machine as a mobile reference station and the oil receiver as a mobile station by utilizing a multi-frequency Beidou satellite navigation system and an inertial navigation system under the scene of a complex aerial oiling task, and adopts a fusion structure of cascade filtering to obtain relative navigation information between the oiling machine and the oil receiver, thereby providing guarantee for the aerial oiling task, and the specific working steps are as follows:
step A1, assembling system software and hardware, turning on a power supply, powering on to execute system initialization operation, and checking the working condition of the system;
a2, acquiring airborne data by the oiling machine, the oil receiving machine multi-frequency satellite signal receiving equipment and the inertial measurement unit;
a3, the oiling machine online navigation resolving equipment receives data from the data storage equipment and performs absolute state filtering;
and A4, transmitting the filtering result, the carrier phase, the Doppler observed quantity, the gyroscope and the accelerometer output by the oiling machine data communication equipment to the oil receiving machine data communication equipment for receiving. The data communication equipment of the oiling machine and the data communication equipment of the oil receiving machine are in wireless transmission modes, the data receiving and transmitting frequency and the baud rate of the two data communication equipment are required to be kept consistent, and the communication protocol adopts communication modes such as radio, network and the like;
step A5, the oil receiving machine online navigation resolving equipment receives data from the data storage equipment and the data communication equipment, and for the oil receiving machine online navigation resolving equipment, key algorithms such as data synchronization, absolute state filtering, integer ambiguity resolving, relative state filtering and the like are further included;
and A6, taking the estimated real-time relative position, speed and attitude information of the oil receiver and the oiling machine as reference input, and adjusting the flight attitude of the oil receiver through guidance law and steering engine control.
The invention also provides a multi-frequency BDS/INS combined relative navigation method for the air refueling of the unmanned aerial vehicle, and the relative navigation system for the air refueling is further described below by combining the software and hardware structure diagrams of the invention.
As shown in fig. 2, a flowchart of a relative navigation method for air refueling of an unmanned aerial vehicle is shown, and the key technology and implementation method of each step in this embodiment are as follows:
step one, the oiling machine and the oil receiving machine are both provided with a Beidou satellite navigation system and an inertial navigation system, original observation data are collected, an absolute state filter is constructed, and errors of inertial devices are corrected through data fusion of BDS/INS tight combination. Meanwhile, the oiling machine sends real-time absolute navigation information and original data to the oil receiving machine through a data link.
Taking an oil receiver as an example, taking the error of a combined Beidou satellite navigation system and the state quantity of an inertial navigation system as the state quantity of the combined navigation system, taking the pseudo range and Doppler observed quantity of BDS as measurement, correcting the solution result of the INS through the absolute state filtering of BDS/INS tight combination, estimating the navigation information of a carrier, and the oiling machine is the same. The state recurrence equation of the system is:
the selected state variables are:
X r ＝[(δp) T (δv) T φ T (δb rg ) T (δb ra ) T δt u δt ru ] T (2)
in (δp) T ＝[δp E δp N δp U ]In the northeast-North-Up (ENU) directionPosition error; (δv) T ＝[δv E δv N δv U ]Is an ENU directional velocity error; phi (phi) T ＝[φ E φ N φ U ]Is an ENU direction attitude error; (δb) rg ) T 、(δb ra ) T The random constant drift error of the oil receiving machine gyroscope and the random constant drift error of the accelerometer are respectively; δt u For equivalent clock error corresponding distance δt ru For a distance rate corresponding to an equivalent clock frequency error, "T" represents a matrix transpose.
The measurement equation of the multi-frequency system is:
wherein P is r,n And D r,n (n=1, 2, 3) respectively represents Beidou B n Pseudo-range and Doppler observations over frequency, H r (t) is a measurement coefficient matrix, V r (t) is a measurement noise matrix,and respectively calculating pseudo ranges and pseudo range rates.
Step two, an oiling machine is used as a mobile reference station, an oil receiving machine is used as a mobile station, and a double-difference observation equation is established;
the oiling machine m observes satellites i and j, and the oil receiving machine r observes satellites i and j, and both the oiling machine m and the oil receiving machine r receive three-frequency BDS signals, so that multiple groups of observation values under the frequency band of B1/B2/B3 can be obtained. The carrier phase double difference observation equation is:
the Doppler double difference observation equation is:
in the method, in the process of the invention,delta represents a double difference operator, phi is carrier phase in meters, D is Doppler observed quantity, N is integer ambiguity, ρ is geometric distance of satellite and receiver,for the change rate of the geometric distance between the satellite and the receiver, n represents Beidou B n Frequency band (n=1, 2, 3), λ n Representing Beidou B n The wavelength corresponding to the frequency band, I represents the ionospheric delay error, T represents the tropospheric delay error, superscript "·" represents the rate of change, epsilon represents the noise error term. To->By way of example, it means that the oil receiver r corresponds to the geometrical distance of the satellite i from the ground; to->By way of example, it means that fuel dispenser m and fuel receiver r synchronously observe B formed by satellites i and j n The explanations of the band double difference carrier phase, equation (4), equation (5) and so on.
Step three, separating the ambiguity from the filter parameter estimation, selecting three groups of Beidou optimal coefficients according to comprehensive consideration of wavelength of combined observables, ionosphere amplification factors, combined noise amplification factors and the like to form an ultra-wide lane-narrow lane combination, replacing the pseudo-range observables with the satellite-ground distance predicted by an inertial navigation system, and solving the double-difference integer ambiguity lane by lane based on a geometric model and a geometric model;
the carrier phase is a distance observation quantity, has higher observation precision, is generally applied to GNSS precise positioning, is the most widely applied GNSS high-precision positioning technology at present, but has the problem of integer ambiguity in measurement according to the characteristics of carrier signals, and can obtain high-precision distance measurement value once the integer ambiguity is correctly solved.
It should be noted that the ambiguity resolution adopts a step-by-step ambiguity fixing strategy of ultra-Wide Lane-narrow Lane, and the combination of ultra-Wide Lane and Wide Lane ambiguities should have a certain linear relationship to facilitate the resolution, and may be, but not limited to, ultra-Wide Lane (EWL): (0, -1, 1), wide Lane (WL): (1, -1, 0), (1, 0, -1), narrow Lane (Narrow Lane, NL): (1, 0), (0, 1, 0), (0, 1) combinations. The steps involved in the whole cycle ambiguity resolution will be further described below taking the above combinations as examples.
Step 31, predicting the amount ρ by inertia INS Instead of pseudo-range observations, ultra-wide lane ambiguities are computed by a Geometry-Free (GF) model
Wherein ρ is INS Predicting the distance between the guard and the ground for inertia, (x) s ,y s ,z s ) Is the satellite position (x) in the Earth's center Fixed coordinate system (Earth-Centered Earth-Fixed, ECEF) INS ,y INS ,z INS ) For the inertia prediction position under the ECEF coordinate system, N represents the whole-cycle ambiguity, phi is the carrier phase, lambda is the wavelength, and subscripts "EWL", "WL", "NL" respectively represent physical quantities corresponding to the ultra-wide lane, the wide lane and the narrow lane.
Step 32, combining (0, -1, 1) ambiguities by known ultra-wide lanesEstimating high precision distance between guard and ground
Step 33, calculating the ambiguity of the wide lane (1, -1, 0)
Step 34, ambiguity by known wide lane (1, -1, 0)Estimating high-precision distance between the ground and the earth>
And 35, improving the resolving efficiency of the ultra-wide lane and the wide lane ambiguity by adopting the GF model. For narrow-lane ambiguity which is difficult to fix, a geometric-based (GB) model is built, and the fixed is searched through an LAMBDA algorithm to determine the B1/B2/B3 frequency integer ambiguity. The GB model observation equation is as follows:
in the method, in the process of the invention,for ECEF coordinate system down-oil filling/receiving machine relative position +.>Is B n Frequency band carrier phase>Is B n Frequency band double-difference integer ambiguity, +.>Is B n Frequency band carrier phase noise, A is the design matrix. I c For the c-dimensional identity matrix, ε is the observation error term and the other physical quantities are the same as above.
And step four, introducing a relative state filter, and solving relative navigation parameters of the oiling machine and the oil receiving machine through BDS/INS tight combination relative state filtering by utilizing multi-frequency Beidou differential relative measurement information based on the mobile reference station and combining a relative state error recurrence model of the SINS navigation system.
The error relation between the two targets is further considered, so that the error of the relative state estimation is minimized, and the relative navigation precision is improved. The oil receiver is used for collecting original observation data, and simultaneously receiving carrier phase and Doppler observation information of the oiling machine from a data chain, and forming a carrier phase and Doppler double difference observation equation with satellite observation quantity of the oil receiver.
The system filtering module of the oil receiving machine is divided into two parts: the absolute state filter outputs absolute navigation information through BDS/INS tight combination, and corrects gyroscope and acceleration error; meanwhile, a relative state filter is introduced, and by utilizing multi-frequency Beidou differential relative measurement information based on a mobile reference station and combining a state error recurrence model of the SINS navigation system, the differential BDS/INS tight combination is realized, and the optimal estimation of the relative inertial state is carried out, so that the calculation precision of the BDS/INS combined relative navigation system is improved. The relative state error equation, the relative measurement error equation and the information fusion of the relative navigation filtering process are as follows:
(1) Equation of relative state error
General physical quantity interpretation: definition of the physical quantity M of the a-system relative to the b-system, projection under the c-system is Representing a posture conversion matrix from a system to b system; the physical quantities in this embodiment are defined in this manner.
Between the oiling machine m and the oil receiving machine rThe relative position isAccording to a general interpretation, it is meant the projection of the position of the oil receiver relative to the fuel dispenser under the oil receiver system. Further:
in the formula, the angle mark I represents an inertial coordinate system. The equation (12) derives time:
in the method, in the process of the invention,express speed, [ (. Times.) x]Represents a cross multiplication operation, and ω represents a rotational angular velocity. Again deriving equation (13) over time:
substitution of formula (13) into formula (14) yields:
in the method, in the process of the invention,indicating acceleration. Let->The differential equation for the relative velocity error is defined as:
where the superscript "≡" denotes the estimated value, δ denotes the error amount, and the same applies. And (3) considering the error of the inertial device, and finishing an available relative speed error equation:
wherein w is rg 、w ra The white gaussian noise of the gyroscope and the white gaussian noise of the accelerometer, respectively. Delta alpha mr Is the relative attitude angle error. Defining the attitude quaternion q of the oil receiver r relative to the oiling machine m mr Expressed as:
wherein q represents a quaternion, q mr ＝[q mr0 q mr13 ] T ；q m Is the attitude quaternion of the oiling machine, q r Is an oil receiving machine attitude quaternion. Definition of the definitionIs a quaternion operator, agreed as +.>Wherein (1)>
Taking the first derivative of equation (18), we can obtain:
according to the quaternion differential equation:
in the same way, the processing method comprises the steps of,attitude quaternion q for fuel dispenser m It is known that:
taking the first derivative of equation (21), we can obtain:
then:
substitution arrangement can be obtained:
like the relative-pose kinematic equation, the relative-pose estimation error in the state variable is represented by a quaternion form:
the two sides simultaneously calculate first-order differentiation, and the method can obtain:
let delta alpha mr ＝2δq mr13 . Combining an inertial device error model, and finishing to obtain:
(2) Equation of relative measurement error
Set the position coordinate of the oiling machine under the geodetic fixed coordinate system of the geodetic center asEstimating the approximate position asThe correction is +.>The position coordinate of the oil receiving machine is->Estimating the approximate position as +.>The correction is +.>The position vector of the oil receiver relative to the oiling machine in the ECEF coordinate system is +.>The approximate position is +.>Position error is +.>The relationship among the fuel dispenser, the fuel receiver and the satellite is shown in fig. 3. The oiling machine m observes satellites i and j, and meanwhile the oil receiving machine r observes satellites i and j, and a carrier phase double difference observation equation is shown as (4).
Let the position of satellite i be (x i ,y i ,z i ) T In the formula (4)For example, it can be calculated by the following formula:
taylor linear expansion of the nonlinear term in equation (28):
in the method, in the process of the invention,for satellite and receiver geometric distance estimation, [ I ] x I y I z ]The subscripts x, y, z denote the components of the line-of-sight vector in the x, y, and z directions, respectively, for the line-of-sight vector. Let->For the line of sight vector between the fuel dispenser and satellite i, < >>For the line-of-sight vector between the oil receiver and satellite i, the formula (29) is substituted and subtracted to obtain:
for position coordinate oiling machine under ECEF coordinate systemAnd oil receiver->The relative position under the ECEF coordinate system has the following relation with the relative position under the machine system:
in the method, in the process of the invention,representing the positions of the oiling machine and the oil receiving machine in the ECEF coordinate system respectively, since the general oiling machine is provided with a high-precision navigation sensor, the position of the navigation sensor can be regarded as precisely known, the relative position can be projected to the machine body coordinate system of the oiling machine, and the oil receiving machine in the ECEF coordinate system can be used for receiving oil in the ECEF coordinate system>The expression may be rewritten as:
taking into account thatThus, the position error of the oil receiving machine->The method comprises the following steps:
formula (33) is substituted into formula (30):
for the followingItem, consider->Then there are:
if it is provided withWhen baseline length->When the position error of the oiling machine is satisfiedWhen the baseline error is less than 2cm. According to the Beidou satellite navigation system public service performance specification (Ver 3.0) file, the Beidou satellite space constellation distribution consists of GEO, MEO and IGSO, the orbit heights are higher than 20000km, and the influence of the position error of the oiling machine on the relative navigation is small and can be ignored.
Similarly, for the synchronous observation satellite j, it is possible to obtain:
and (3) carrying out inter-station and inter-satellite difference on the oiling machine and the oil receiving machine, and neglecting the position error of the oiling machine, the ionosphere after double difference and the residual error of the troposphere, wherein the carrier phase double difference observation equation is as follows:
the integer ambiguity in the formula is calculated by adopting an integer ambiguity resolution filter, and after the integer ambiguity is obtained, the carrier phase can be used as a high-precision distance observation quantity. Synchronously observing M satellites to obtain a multi-frequency carrier phase observation equation consisting of M-1 observation equations:
wherein phi represents an M-1-dimensional carrier phase vector, N represents an M-1-dimensional integerThe vector of the degree of ambiguity,represents M-1 dimension guard distance predictive vector, K 1 、K 2 A coefficient matrix for the M-1 set of equations. />
The doppler observed quantity is an extractable observed value in a receiver, representing the difference between the signal reception frequency and the transmission frequency. It is a phenomenon in which the frequency of a received signal changes due to relative movement between a signal transmission source and a receiver. The oil adding and receiving machine synchronously observes satellites i and j, and a Doppler observation equation is shown in a formula (5).
The following relationship exists for the pseudo-range rate of change and the relative speed of the two machines:
in the method, in the process of the invention,for the estimated value of the geometric distance change rate of the satellite and the receiver, deriving two sides of the formula (32):
i.e.
Then:
error models combining gyroscopes and accelerometers can be obtained:
ignoring the fuel dispenser speed error and substituting into the doppler observation equation, then:
similar to equation (38), and ignoring the double difference residual error term, the multi-frequency Doppler observation equation can ultimately be written as:
wherein D represents an M-1-dimensional Doppler observed vector,represents M-1 dimension prediction of the change rate of the distance between the guard and the ground, Q 1 、Q 2 、Q 3 Q and Q 4 A coefficient matrix for the M-1 set of equations.
(3) Information fusion
By the data fusion method of extended Kalman filtering (Extended Kalman Filter, EKF), a DGNSS/INS tightly-combined relative filtering model is constructed by adopting carrier phase and Doppler observed quantity with known ambiguity, and relative information data is fused. The selected state variables are:
/>
calculating state prediction values by EKF time updateVariance matrix P k,k-1 。
In the method, in the process of the invention,P k-1 posterior state vector and covariance matrix at time k-1, respectively, < >>P k,k-1 A priori state vector and a covariance matrix at k time respectively, phi k,k-1 For the state transition matrix from k-1 to k moment, Γ k-1 As a system noise matrix, Q k-1 Is a system noise variance matrix. Then, the measurement is updated to calculate the gain matrix K k Filtering estimate +.>Variance matrix P k 。
Wherein Z is k To measure the vector, H k For measuring matrix, R k In order to measure the noise variance matrix,P k the posterior state vector and the covariance matrix at the moment k are respectively, and the I is an identity matrix.
The invention adopts digital simulation, and the simulation conditions are as follows: the sampling frequency of the inertial navigation system is 200Hz, the random constant value is 0.1 degree/h, the white noise is 0.01 degree/h, and the accelerometer random constant value and the white noise are 1mg; the sampling frequency of the Beidou satellite navigation system is 1Hz, the three-frequency signal observation precision is the same, wherein the pseudo-range precision is 0.3m, the carrier phase observation precision is 0.01 week, the Doppler observation precision is 0.01m/s, and the cut-off height angle is 15 degrees. In the air refueling process, the oiling machine and the oil receiving machine keep a formation flying state. A set of comparative experiments were designed to obtain simulation result graphs as shown in fig. 4 (a) to 4 (c), fig. 5 (a) to 5 (c), and fig. 6 (a) to 6 (c), wherein fig. 4 (a) to 4 (c) are relative position error graphs in relative navigation, fig. 5 (a) to 5 (c) are relative velocity error graphs in relative navigation, and fig. 6 (a) to 6 (c) are relative attitude error graphs in relative navigation. In the figure, a solid curve represents a conventional relative navigation method based on absolute navigation information difference, and a dotted curve represents a multi-frequency BDS/INS combined air refueling relative navigation method.
Simulation results show that: the relative navigation method for the unmanned aerial vehicle air refueling can effectively inhibit the divergence of an inertial navigation system, and can effectively improve the estimation precision of the relative position, speed and gesture compared with the conventional relative navigation method based on absolute navigation information.

Claims (6)

1. A multi-frequency BDS/INS combination air fueling relative navigation system comprising: the oiling machine navigation system and the oil receiving machine navigation system;
the oiling machine navigation system comprises a first multi-frequency satellite signal receiving device, a first inertial measurement unit, a first data storage device, an oiling machine data communication device, an oiling machine online navigation resolving device and a first power supply device;
the oil receiving machine navigation system comprises a second multi-frequency satellite signal receiving device, a second inertial measurement unit, a second data storage device, an oil receiving machine data communication device, an oil receiving machine online navigation resolving device, a second power supply device and a guidance and flight control device;
the data communication between the oiling machine data communication equipment and the oil receiving machine data communication equipment can be realized;
the first multi-frequency satellite signal receiving device and the second multi-frequency satellite signal receiving device are respectively used for receiving Beidou multi-frequency satellite signals in real time; the first multi-frequency satellite signal receiving device is connected with the first data storage device and stores the received Beidou multi-frequency satellite signals in the first data storage device; the second multi-frequency satellite signal receiving device is connected with the second data storage device and stores the received Beidou multi-frequency satellite signals in the second data storage device;
the first inertial measurement unit and the second inertial measurement unit are respectively used for measuring the angular velocity and the linear acceleration of the carrier on line; the first inertia measurement unit is connected with the first data storage device, and the second inertia measurement unit is connected with the second data storage device;
a first data storage device: the system comprises a first multi-frequency satellite signal receiving device, a first inertial measurement unit and a second inertial measurement unit, wherein the first multi-frequency satellite signal receiving device is used for receiving and storing original data acquired by the first multi-frequency satellite signal receiving device and the first inertial measurement unit; a second data storage device: the system comprises a first multi-frequency satellite signal receiving device, a second multi-frequency satellite signal receiving device, a first inertial measurement unit and a second inertial measurement unit, wherein the first multi-frequency satellite signal receiving device is used for receiving and storing the primary data acquired by the first multi-frequency satellite signal receiving device and the second inertial measurement unit;
the output of the oiling machine online navigation resolving equipment transmits data to the oil receiving machine through the oiling machine data communication equipment; the oil receiving machine data communication equipment synchronously receives the data and sends the received data to the oil receiving machine on-line navigation resolving equipment;
the online navigation resolving device of the oiling machine and the online navigation resolving device of the oil receiving machine are respectively loaded and run with software parts of a system, and are used for processing an online running navigation information resolving program, and the online navigation resolving device comprises: the data are collected and aligned in real time, the position, speed and attitude information of the oiling machine/oil receiving machine are calculated, and a calculation result is output;
the first power supply device and the second power supply device respectively provide power supply support for a navigation system of the oiling machine and the oil receiving machine;
the guidance and flight control equipment is connected with the oil receiving machine on-line navigation resolving equipment, the estimated real-time relative position, speed and attitude information of the oil receiving machine and the oiling machine are used as reference input, and the flight attitude of the oil receiving machine is adjusted through guidance law and steering engine control.
2. A multi-frequency BDS/INS combined air refueling relative navigation method is characterized by comprising the following steps:
s1, respectively constructing multifrequency BDS system measurement equations of the oil receiver and the oil receiver based on a Beidou satellite navigation system and an inertial navigation system of the oil receiver and the inertial navigation system, and correcting a solution result of the INS through absolute state filtering of BDS/INS tight combination; meanwhile, the oiling machine sends real-time absolute navigation information and original data to the oil receiving machine through a data link;
s2, using an oiling machine as a mobile reference station and an oil receiving machine as an mobile station, and establishing a carrier phase double-difference observation equation and a Doppler double-difference observation equation;
s3, separating the integer ambiguity in the carrier phase from the filter parameter estimation, screening three groups of Beidou coefficients to form an ultra-wide lane-narrow lane combination, replacing pseudo-range observed quantity with the satellite distance predicted by an inertial navigation system, and solving the double-difference integer ambiguity lane by lane based on a geometric model and a geometric model;
s4, introducing a relative state filter, and establishing a multi-frequency Beidou differential relative measurement equation based on the mobile reference station; and constructing a DGNSS/INS tightly-combined relative filtering model by combining a relative state error recurrence model of the SINS navigation system, and fusing relative information data by expanding a Kalman filtering data fusion method to complete the calculation of relative navigation parameters of the oiling machine and the oil receiving machine.
3. The multi-frequency BDS/INS combined air refueling relative navigation method according to claim 2, wherein in step S1, an expression of a state recurrence equation of a tight combination of an inertial navigation system of an oil receiver and a beidou navigation system is:
the selected state variables are:
X r ＝[(δp) T (δv) T φ T (δb rg ) T (δb ra ) T δt u δt ru ] T
in (δp) T ＝[δp E δp N δp U ]Is an ENU directional position error; (δv) T ＝[δv E δv N δv U ]Is an ENU directional velocity error; phi (phi) T ＝[φ E φ N φ U ]Is an ENU direction attitude error; (δb) rg ) T 、(δb ra ) T The random constant drift error of the oil receiving machine gyroscope and the random constant drift error of the accelerometer are respectively; δt u For equivalent clock error corresponding distance δt ru Is equivalent to clock frequency errorDifference of corresponding distance rate; "T" represents the matrix transpose;
the expression of the state recurrence equation of the tight combination of the inertial navigation system and the Beidou navigation system of the oiling machine is the same as the state recurrence equation of the tight combination of the inertial navigation system and the Beidou navigation system of the oil receiving machine.
4. A multi-frequency BDS/INS combined air fueling relative navigation method as set forth in claim 3 wherein in step S1, the multi-frequency BDS system measurement equation of the fueling receiver is:
wherein P is r,n And D r,n Respectively indicate that the oil receiving machine is in the big dipper B n Pseudo-range and Doppler observations over frequency, n=1, 2,3; h r (t) is the measurement coefficient matrix of the oil receiving machine, V r (t) is the measurement noise matrix of the oil receiving machine,calculating pseudo ranges and pseudo range rates for the oil receiving machines respectively;
the multi-frequency BDS system measurement equation of the oiling machine is the same as the multi-frequency BDS system measurement equation of the oil receiving machine.
5. The multi-frequency BDS/INS combined air refueling relative navigation method according to claim 4, wherein in the step S2, the oiling machine m observes satellites i and j, and meanwhile, the oil receiver r observes satellites i and j, and the oiling machine m and the oil receiver r receive three-frequency BDS signals to obtain a plurality of groups of observation values in the frequency range of B1/B2/B3; the carrier phase double-difference observation equation and the Doppler double-difference observation equation are as follows:
in the method, in the process of the invention,representing a double difference operator, phi being the carrier phase in meters, N being the integer ambiguity, D being the Doppler observed quantity, ρ being the geometric distance of the satellite from the receiver,>the change rate of the geometric distance between the satellite and the receiver is shown; n represents Beidou B n Frequency band, n=1, 2,3; lambda (lambda) n Representing Beidou B n The wavelength corresponding to the frequency band, I represents ionosphere delay error, T represents troposphere delay error, and superscript "·" represents change rate; />Representing carrier phase noise error term,/->Representing Doppler observed quantity noise error items; />For the satellite geometry distance of the oil receiver r corresponding to satellite i>The geometrical distance of the oil receiver r corresponding to the satellite j is the satellite ground; />For the dispenser m the geometrical distance of the satellite i corresponding to the satellite i +.>The geometrical distance of the satellite corresponding to the satellite j is provided for the oiling machine m; />B formed by the synchronous observation satellites i and j of the oiling machine m and the oil receiving machine r n Frequency band doubleDifferential carrier phase; />B formed by the synchronous observation satellites i and j of the oiling machine m and the oil receiving machine r n Frequency band double-difference integer ambiguity; />B formed by the synchronous observation satellites i and j of the oiling machine m and the oil receiving machine r n Frequency band double difference ionosphere delay error; />B formed by the synchronous observation satellites i and j of the oiling machine m and the oil receiving machine r n Frequency band double difference troposphere delay error.
6. The multi-frequency BDS/INS combination air fueling relative navigation method of claim 5 wherein in step S4, said relative measurement error equation is constructed as follows:
set the position coordinate of the oiling machine under the geodetic fixed coordinate system of the geodetic center asEstimating the approximate position asThe correction is +.>The position coordinate of the oil receiving machine is->Estimating the approximate position as +.>The correction is +.>The position vector of the oil receiver r relative to the oil filler m in the ECEF coordinate system is +.>The approximate position is +.>Position error is +.>Defining the physical quantity M of the a-coordinate system relative to the b-coordinate system, the projection under the c-coordinate system is +.>Representing a gesture conversion matrix from an a coordinate system to a b coordinate system; i represents an inertial coordinate system;
let the position of satellite i be (x i ,y i ,z i ) T The oil receiver r corresponds to the geometrical distance of the satellite i from the groundIs calculated as follows:
taylor linear expansion is carried out on nonlinear terms in the above method:
in the method, in the process of the invention,for satellite and receiver geometric distance estimation, [ I ] x I y I z ]As line-of-sight vectors, subscripts x, y, z are dividedComponents of the sight line vector in the x direction, the y direction and the z direction are respectively represented; let->For the line of sight vector between fuel dispenser m and satellite i,the line of sight vector between the oil receiver r and the satellite i is:
the relative position under the ECEF coordinate system has the following relation with the relative position under the machine system:
in the method, in the process of the invention,representing the positions of the oiling machine and the oil receiving machine in the ECEF coordinate system respectively, and projecting the relative positions to the oiling machine body coordinate system, wherein the oil receiving machine in the ECEF coordinate system is a box-shaped oil receiving machine>The expression is rewritten as:
taking into account thatThus, the position error of the oil receiving machine->The method comprises the following steps:
wherein δα mr Is the relative attitude angle error;
finally, the method comprises the following steps:
similarly, the following can be obtained:
ignoring position errors of fuel dispensersThe relative navigation is influenced, the difference between stations and stars is made for the oiling machine and the oil receiving machine, and the residual errors of the ionosphere and the troposphere after double differences are ignored, so that the expression of the relative measurement error equation is as follows:
synchronously observing M satellites to obtain a multi-frequency carrier phase observation equation consisting of M-1 observation equations:
where phi represents an M-1 dimensional carrier phase vector, N represents an M-1 dimensional integer ambiguity vector,representing M-1 dimension guard range pre-emptionMeasuring the quantity, K 1 、K 2 A coefficient matrix formed by M-1 sets of equations;
the following relationship exists for the pseudorange rate of change, the relative speeds of the fuel dispenser and the fuel receiver:
in the method, in the process of the invention,an estimated value of the geometric distance change rate of the satellite and the receiver;
from the following components
Then there is
Then:
combining the error model of the gyroscope and the accelerometer to obtain:
ignoring the fuel dispenser speed error and substituting into the doppler observation equation, then:
and ignoring the double difference residual error term, and finally writing the multi-frequency Doppler observation equation as follows:
wherein D represents an M-1-dimensional Doppler observed vector,represents M-1 dimension prediction of the change rate of the distance between the guard and the ground, Q 1 、Q 2 、Q 3 Q and Q 4 A coefficient matrix for the M-1 set of equations.
CN202310824341.XA 2023-07-06 2023-07-06 Multi-frequency BDS/INS combined air refueling relative navigation system and method Pending CN116878498A (en)

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* Cited by examiner, † Cited by third party
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