A multi-frequency BDS / INS integrated relative navigation system and method for aerial refueling

Abstract

The application discloses a kind of multi-frequency BDS / INS combined aerial refueling relative navigation system and method, navigation system includes tanker and receiver, respectively installs multi-frequency Beidou satellite navigation system and inertial navigation system;The navigation method of the present application is as follows: tanker obtains the real-time position, velocity and attitude information of tanker by tight combination, and is transmitted to receiver by data link;Receiver establishes the relative measurement model of tanker as mobile reference station, receiver as flow station, using cascaded filtering fusion structure, the relative navigation information between tanker and receiver is obtained, to provide guarantee for aerial refueling task.The present application improves the accuracy of relative state error model, effectively suppresses the divergence of solution result, improves the precision and reliability of relative navigation system.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation and integrated navigation technology, and in particular to a multi-frequency BDS / INS integrated aerial refueling relative navigation system and method. Background Technology

[0002] Unmanned aerial vehicles (UAVs) have advantages such as small size, light weight, and low cost, leading to their wide range of applications. However, the amount of fuel they carry limits their takeoff weight and endurance. In-flight refueling technology can improve the flight range and loiter time of UAVs, enhancing their performance advantages and is currently one of the key research directions for UAVs.

[0003] Determining the relative position, speed, and attitude relationship between the tanker and receiver aircraft during aerial refueling is crucial for its successful completion. Currently, commonly used relative navigation methods include satellite-based differential relative navigation and absolute navigation information differential relative navigation. However, satellite-based differential relative navigation relies on satellite signals and cannot function when these signals are blocked, resulting in poor robustness. While absolute navigation information differential relative navigation compensates for this, it lacks the establishment of relative relationships between targets and a relative state estimation feedback loop, often limiting its navigation accuracy and failing to meet the high reliability and precision requirements of aerial refueling. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to improve the navigation accuracy and reliability of relative navigation in complex aerial refueling scenarios, provide navigation technology support for aerial refueling missions, and design a multi-frequency BDS / INS combined aerial refueling relative navigation system and method.

[0005] Technical solution: The multi-frequency BDS / INS combined aerial refueling relative navigation system of the present invention includes: a tanker aircraft navigation system and a receiver aircraft navigation system;

[0006] The refueling machine navigation system includes 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 calculation device, and a first power supply device;

[0007] The receiver aircraft navigation system includes a second multi-frequency satellite signal receiving device, a second inertial measurement unit, a second data storage device, a receiver aircraft data communication device, a receiver aircraft online navigation calculation device, a second power supply device, and a guidance and flight control device;

[0008] The data communication equipment of the fuel dispenser and the data communication equipment of the receiving machine can communicate with each other.

[0009] The first multi-frequency satellite signal receiving device and the second multi-frequency satellite signal receiving device are used to receive BeiDou multi-frequency satellite signals in real time, respectively. The first multi-frequency satellite signal receiving device is connected to 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 to the second data storage device and stores the received BeiDou multi-frequency satellite signals in the second data storage device.

[0010] The first inertial measurement unit and the second inertial measurement unit are used to measure the angular velocity and linear acceleration of the carrier online, respectively; the first inertial measurement unit is connected to the first data storage device, and the second inertial measurement unit is connected to the second data storage device.

[0011] First data storage device: used to record and store the raw data collected by the first multi-frequency satellite signal receiving device and the first inertial measurement unit; Second data storage device: used to record and store the raw data collected by the second multi-frequency satellite signal receiving device and the second inertial measurement unit;

[0012] The output of the fuel dispenser online navigation calculation equipment is transmitted to the receiving aircraft via the fuel dispenser data communication equipment; the receiving aircraft data communication equipment synchronously receives the data and sends the received data to the receiving aircraft online navigation calculation equipment.

[0013] The online navigation calculation equipment for the refueling machine and the online navigation calculation equipment for the receiving machine are respectively loaded with and run the software part of the system, which is used to run the navigation information calculation program online, including: real-time data acquisition and alignment, calculation of the position, speed and attitude information of the refueling machine / receiving machine and output of the calculation results;

[0014] The first power supply equipment and the second power supply equipment provide power support for the navigation systems of the refueling machine and the receiving machine, respectively;

[0015] The guidance and flight control equipment is connected to the online navigation calculation equipment of the receiving aircraft. It uses the estimated real-time relative position, speed, and attitude information of the receiving aircraft and the tanker as reference input, and adjusts the flight attitude of the receiving aircraft through guidance law and servo control.

[0016] A multi-frequency BDS / INS combined aerial refueling relative navigation method includes the following steps:

[0017] S1, based on the BeiDou satellite navigation system and inertial navigation system of the refueling aircraft and the receiving aircraft, constructs the multi-frequency BDS system measurement equations of the receiving aircraft and the refueling aircraft respectively, and corrects the INS solution results through absolute state filtering of BDS / INS tight combination; at the same time, the refueling aircraft sends real-time absolute navigation information and raw data to the receiving aircraft through data link;

[0018] S2, using the refueling aircraft as the mobile reference station and the receiving aircraft as the rover station, establish carrier phase double-difference observation equations and Doppler double-difference observation equations;

[0019] S3 separates the integer ambiguity in the carrier phase from the filter parameter estimation, selects three sets of Beidou coefficients to form an ultra-wide lane-wide lane-narrow lane combination, and replaces the pseudorange observation with the satellite-to-ground distance predicted by the inertial navigation system. Based on the geometric-free model and the geometric model, the double-difference integer ambiguity is obtained lane by lane.

[0020] S4. A relative state filter is introduced to establish a multi-frequency BeiDou differential relative measurement equation based on a mobile reference station. Combined with the relative state error recursive model of the SINS navigation system, a DGNSS / INS compact combination relative filtering model is constructed. The relative information data is fused using the extended Kalman filter data fusion method to complete the calculation of the relative navigation parameters between the refueling aircraft and the receiving aircraft.

[0021] Furthermore, in step S1, the expression for the recursive equation of the tightly coupled state of the receiver's inertial navigation system and the BeiDou navigation system is as follows:

[0022]

[0023] The state variables are selected as follows:

[0024] X r =[(δp) T (δv) T φ T (δb rg ) T (δb ra ) T δt u δt ru ] T

[0025] In the formula, (δp) T =[δp E δp N δp U [δv] represents the positional error in the ENU direction. T =[δv E δv N δv U ] represents the velocity error in the ENU direction; φ T =[φ E φ N φ U [δb] represents the attitude error in the ENU direction; rg ) T 、(δb ra ) TThese are the random constant drift errors of the receiver gyroscope and the accelerometer, respectively; δt u δt is the distance corresponding to the equivalent clock error. ru The distance rate corresponding to the equivalent clock frequency error; "T" indicates matrix transpose;

[0026] The expression for the recursive equation of the tightly coupled state of the inertial navigation system and the BeiDou navigation system of the refueling aircraft is the same as that of the tightly coupled state of the inertial navigation system and the BeiDou navigation system of the receiving aircraft.

[0027] Furthermore, in step S1, the measurement equation for the receiver's multi-frequency BDS system is:

[0028]

[0029] In the formula, P r,n and D r,n These respectively indicate that the receiver aircraft is in the BeiDou B navigation system. n Pseudorange and Doppler observations at frequencies, n = 1, 2, 3; H r (t) is the measurement coefficient matrix of the oil receiver, V r (t) represents the receiver noise matrix. These are the pseudorange calculated by the receiver aircraft and the pseudorange rate calculated by the receiver aircraft, respectively.

[0030] The measurement equations for the multi-frequency BDS system of the refueling machine are the same as those for the multi-frequency BDS system of the receiving machine.

[0031] Furthermore, in step S2, the refueling aircraft m observes satellites i and j, while the receiving aircraft r observes satellites i and j simultaneously. Both the refueling aircraft m and the receiving aircraft r receive tri-frequency BDS signals, obtaining multiple sets of observations in the B1 / B2 / B3 frequency bands. The carrier phase double-difference observation equation and the Doppler double-difference observation equation are as follows:

[0032]

[0033]

[0034] In the formula, ▽Δ represents the double difference operator, φ is the carrier phase in meters, N is the integer ambiguity, D is the Doppler observation, and ρ is the geometric distance between the satellite and the receiver. The geometric distance between the satellite and the receiver is the rate of change; n represents BeiDou B. n Frequency bands, n = 1, 2, 3; λ n Indicates Beidou B n The wavelength corresponding to the frequency band, I represents the ionospheric delay error, T represents the tropospheric delay error, and the superscript "·" represents the rate of change; This represents the carrier phase noise error term. This represents the noise error term in the Doppler observations; Let r be the satellite-to-ground geometric distance between the receiver and satellite i. Let r be the satellite-to-ground geometric distance between the receiver and satellite j; Let the refueling aircraft m correspond to the satellite i in terms of satellite-to-ground geometric distance. Let m be the satellite-to-ground geometric distance between the refueling aircraft and satellite j; To enable refueling aircraft m and receiving aircraft r to synchronously observe satellites i and j, forming B n Frequency band double-difference carrier phase; To enable refueling aircraft m and receiving aircraft r to synchronously observe satellites i and j, forming B n Frequency band double-difference integer ambiguity; To enable refueling aircraft m and receiving aircraft r to synchronously observe satellites i and j, forming B n Frequency band double-difference ionospheric delay error; To enable refueling aircraft m and receiving aircraft r to synchronously observe satellites i and j, forming B n Frequency band double-difference tropospheric delay error.

[0035] Furthermore, in step S4, the process of constructing the relative measurement error equation is as follows:

[0036] Let the position coordinates of the refueling machine in the Earth-centered geodetic coordinate system be... The approximate location is estimated as follows The correction number is The receiver's position coordinates are The approximate location is estimated as follows The correction number is The position vector of receiver r relative to refueling unit m in the ECEF coordinate system is Approximate position is Position error is Define the projection of a physical quantity M in coordinate system a relative to coordinate system b onto coordinate system c as follows: Let represent the attitude transformation matrix from coordinate system a to coordinate system b; I represents the inertial coordinate system.

[0037] Let the position of satellite i be (x i ,y i ,z i ) T Then the receiver r corresponds to the satellite i's geometric distance from Earth. The calculation is as follows:

[0038]

[0039] Taylor linearization expansion of the nonlinear terms in the above equation:

[0040]

[0041] In the formula, For the estimated geometric distance between the satellite and the receiver, [I x I y I z Let ] be the line-of-sight vector, and let the subscripts x, y, and z represent the components of the line-of-sight vector in the x, y, and z directions, respectively; let Let m be the line-of-sight vector between the refueling aircraft m and satellite i. Let r be the line-of-sight vector between the receiver r and the satellite i, then:

[0042]

[0043] The relative positions in the ECEF coordinate system and the relative positions in the mechanical system have the following relationship:

[0044]

[0045] In the formula, Let represent the positions of the refueling aircraft and the receiving aircraft in the ECEF coordinate system, respectively. Projecting the relative positions onto the refueling aircraft's body coordinate system, the receiving aircraft in the ECEF coordinate system... The expression is rewritten as:

[0046]

[0047] Considering Therefore, the positional error of the oil engine for:

[0048]

[0049] Where, δα mr This refers to the relative attitude angle error;

[0050] The final result is:

[0051]

[0052] Similarly, we can obtain:

[0053]

[0054] Ignore the positional error of the fuel dispenser Regarding the impact of relative navigation, inter-station and inter-satellite differentials are performed for the refueling aircraft and the receiving aircraft, and the residual errors in the ionosphere and troposphere after double differential are ignored. The expression for the relative measurement error equation is as follows:

[0055]

[0056] Simultaneous observation of M satellites yields a multi-frequency carrier phase observation equation consisting of M-1 observation equations:

[0057]

[0058] In the formula, φ represents the M-1 dimensional carrier phase vector, and N represents the M-1 dimensional integer ambiguity vector. Let K1 and K2 represent the M-1 dimension satellite distance prediction vector, and K1 and K2 are the coefficient matrices formed by the M-1 set of equations;

[0059] The following relationship exists between the pseudorange change rate and the relative velocities of the refueling aircraft and the receiving aircraft:

[0060]

[0061] In the formula, This is an estimate of the rate of change of the geometric distance between the satellite and the receiver;

[0062] Depend on

[0063]

[0064] Then there is

[0065] then:

[0066]

[0067] Combining the error models of the gyroscope and accelerometer, we can obtain:

[0068]

[0069] Ignoring the refueling aircraft speed error and substituting it into the Doppler observation equation, we get:

[0070]

[0071] Ignoring the double-difference residual error term, the multi-frequency Doppler observation equation can finally be written as:

[0072]

[0073] In the formula, D represents the M-1 dimension Doppler observation vector. Let Q1, Q2, Q3, and Q4 represent the M-1 dimensional predicted satellite-to-Earth distance change rate, and Q4 be the coefficient matrix of the M-1 set of equations.

[0074] Compared with the prior art, the significant advantages of this invention are as follows:

[0075] 1. Compared to single-frequency, this invention adopts a multi-frequency form in the observation, which can increase the redundancy of observation information and improve the fault tolerance of the system; the use of multi-frequency signals can provide a large number of combined observations with excellent performance, which is conducive to the rapid solution and fixation of single-epoch integer ambiguity; at the same time, the use of inertial prediction satellite-to-ground distance to assist in ambiguity fixation is conducive to suppressing the influence of pseudorange gross errors and multipath effects on ambiguity fixation, thereby improving the ambiguity fixation rate and navigation and positioning accuracy.

[0076] 2. Satellite navigation features all-day, all-weather, high-precision positioning and navigation. However, during the refueling process, satellite signals are easily blocked, and under external interference and high dynamic conditions, the receiver is prone to signal loss, which seriously affects the navigation and positioning results. This invention uses an inertial / satellite integrated navigation system, which can complement each other's advantages, make up for the discontinuity of satellite relative positioning results, and achieve continuous, stable, and high-precision navigation results even in complex environments, thus improving the stability of the system.

[0077] 3. Conventional integrated navigation schemes often employ a loose combination approach, which is easy to implement. However, when fewer than four satellites are observed, the system degenerates into a single inertial navigation system, resulting in significant error accumulation and rapid divergence. In contrast, this invention utilizes a tight combination scheme based on the original observations, offering high accuracy and robustness. This approach is more suitable for environments where satellite signals are susceptible to interference, maintaining a certain level of endurance even during short-term signal loss, and providing continuous navigation services. Furthermore, this invention uses satellite information from both the refueling aircraft and the receiving aircraft to first correct its own absolute positioning results and also modifies the measurements from the gyroscope and accelerometer. Due to the presence of a local state filter, the accuracy of the relative state error model is improved, effectively suppressing the divergence of the solution results and enhancing the system's reliability. Attached Figure Description

[0078] Figure 1 This is a schematic diagram of the relative navigation system for aerial refueling of unmanned aerial vehicles (UAVs) according to the present invention.

[0079] Figure 2 This is a schematic diagram of the relative navigation method for aerial refueling of unmanned aerial vehicles according to the present invention;

[0080] Figure 3 This is a vector diagram showing the relationship between the tanker and the receiver aircraft in aerial refueling according to the present invention;

[0081] Figure 4(a) is a diagram of the relative position error in the x-direction during relative navigation according to the present invention;

[0082] Figure 4(b) is a diagram showing the relative position error in the y-direction during relative navigation according to the present invention;

[0083] Figure 4(c) is a diagram of the relative position error in the z-direction during relative navigation according to the present invention;

[0084] Figure 5(a) is a diagram of the relative velocity error in the x-direction during relative navigation according to the present invention;

[0085] Figure 5(b) is a diagram showing the relative velocity error in the y-direction during relative navigation according to the present invention;

[0086] Figure 5(c) is a diagram of the relative velocity error in the z-direction during relative navigation according to the present invention;

[0087] Figure 6(a) is a diagram of relative roll angle error in relative navigation according to the present invention;

[0088] Figure 6(b) is a diagram of relative pitch angle error in relative navigation according to the present invention;

[0089] Figure 6(c) is a diagram of relative heading angle error in relative navigation according to the present invention. Detailed Implementation

[0090] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0091] like Figure 1 As shown, this invention provides a multi-frequency BDS / INS (BDS: BeiDou Navigation Satellite System, INS: Inertial Navigation System) combined relative navigation system for aerial refueling of unmanned aerial vehicles (UAVs). The system includes a tanker navigation system and a receiver aircraft navigation system. The tanker navigation system includes a first multi-frequency satellite signal receiving device, a first inertial measurement unit, a first data storage device, a tanker data communication device, a tanker online navigation calculation device, and a first power supply device. The receiver aircraft navigation system includes a second multi-frequency satellite signal receiving device, a second inertial measurement unit, a second data storage device, a receiver aircraft data communication device, a receiver aircraft online navigation calculation device, a second power supply device, and guidance and flight control equipment. Data communication occurs between the tanker data communication device and the receiver aircraft data communication device.

[0092] The first multi-frequency satellite signal receiving device and the second multi-frequency satellite signal receiving device include, but are not limited to, satellite signal receiving antennas and satellite navigation integrated boards, respectively, for receiving BeiDou multi-frequency satellite signals in real time; the first multi-frequency satellite signal receiving device is connected to the first data storage device to store the received BeiDou multi-frequency satellite signals in the first data storage device; the second multi-frequency satellite signal receiving device is connected to the second data storage device to store the received BeiDou multi-frequency satellite signals in the second data storage device.

[0093] The first inertial measurement unit and the second inertial measurement unit each include a gyroscope and an accelerometer, used for online measurement of the angular velocity and linear acceleration of the carrier; the first inertial measurement unit is connected to the first data storage device, and the second inertial measurement unit is connected to the second data storage device.

[0094] First data storage device: used to record and store the raw data collected by the first multi-frequency satellite signal receiving device and the first inertial measurement unit; Second data storage device: used to record and store the raw data collected by the second multi-frequency satellite signal receiving device and the second inertial measurement unit.

[0095] The output of the fuel dispenser's online navigation calculation equipment is transmitted to the receiving aircraft via the fuel dispenser's data communication equipment; the receiving aircraft's data communication equipment synchronously receives the data and sends the received data to the receiving aircraft's online navigation calculation equipment. The fuel dispenser (or receiving aircraft) data communication equipment may use, but is not limited to, a WDS high-speed frequency hopping radio-SDR400L and a wireless transmission antenna.

[0096] The software component of the online navigation calculation equipment for refueling aircraft (or receiving aircraft) is used to run navigation information calculation programs online, including: real-time data acquisition and alignment, calculation of the position, speed, and attitude information of the refueling aircraft / receiving aircraft, and output of the calculation results; it adopts, but is not limited to, NVIDIA Jetson TX2 development boards, and is suitable for building airborne embedded platforms to complete tasks such as real-time navigation data calculation.

[0097] The first power supply equipment and the second power supply equipment provide power support for the navigation systems of the refueling machine and the receiving machine, respectively.

[0098] The guidance and flight control equipment is connected to the online navigation calculation equipment of the receiving aircraft. It uses the estimated real-time relative position, speed and attitude information of the receiving aircraft and the tanker as reference input, and adjusts the flight attitude of the receiving aircraft through guidance law and servo control.

[0099] The relative navigation system of this invention, in complex aerial refueling mission scenarios, utilizes a multi-frequency BeiDou satellite navigation system and an inertial navigation system to establish a relative measurement model with the tanker aircraft as a mobile reference station and the receiver aircraft as a rover station. Employing a cascaded filtering fusion structure, it obtains relative navigation information between the tanker and receiver aircraft, providing support for aerial refueling missions. The specific working steps are as follows:

[0100] Step A1: Assemble the system software and hardware, turn on the power, perform system initialization operations, and check the system's working status.

[0101] Step A2: The refueling aircraft and receiver aircraft use multi-frequency satellite signal receiving equipment and inertial measurement units to collect airborne data;

[0102] Step A3: The fuel dispenser online navigation calculation device receives data from the data storage device and performs absolute state filtering;

[0103] Step A4: The refueling tanker's data communication equipment sends the filtering results, carrier phase, Doppler observations, and gyroscope and accelerometer outputs to the receiving tanker's data communication equipment. Both the refueling tanker's and receiving tanker's data communication equipment use wireless transmission. The data transmission and reception frequencies and baud rates of the two data communication devices must be consistent. The communication protocol uses, but is not limited to, radio, network, and other communication methods.

[0104] Step A5: The receiver aircraft online navigation solution device receives data from the data storage device and the data communication device. For the receiver aircraft online navigation solution device, this further includes key algorithms such as data synchronization, absolute state filtering, integer ambiguity solution, and relative state filtering.

[0105] Step A6: Using the estimated real-time relative position, speed, and attitude information of the receiver aircraft and the tanker aircraft as reference input, the flight attitude of the receiver aircraft is adjusted through guidance law and servo control.

[0106] This invention also provides a multi-frequency BDS / INS combined relative navigation method for aerial refueling of unmanned aerial vehicles (UAVs). The relative navigation system for aerial refueling will be further described below with reference to the software and hardware structure diagrams of this invention.

[0107] like Figure 2 The diagram shows a flowchart of a relative navigation method for aerial refueling of unmanned aerial vehicles (UAVs). The specific steps of the key technologies and implementation methods for each step in this embodiment are as follows:

[0108] Step one: Both the refueling aircraft and the receiving aircraft are equipped with the BeiDou satellite navigation system and inertial navigation system to collect raw observation data, construct an absolute state filter, and correct errors in the inertial devices through BDS / INS tightly coupled data fusion. Simultaneously, the refueling aircraft transmits real-time absolute navigation information and raw data to the receiving aircraft via data link.

[0109] Taking the receiving aircraft as an example, considering the errors of the combined BeiDou satellite navigation system and the state variables of the inertial navigation system as the state variables of the integrated navigation system, and using the pseudorange and Doppler observations of the BDS as measurements, the INS solution results are corrected through absolute state filtering of the BDS / INS tightly integrated system, and the carrier's navigation information is estimated. The same principle applies to the refueling aircraft. The system's state recursive equation is as follows:

[0110]

[0111] The state variables are selected as follows:

[0112] X r =[(δp) T (δv) T φ T (δb rg )T (δb ra ) T δt u δt ru ] T (2)

[0113] In the formula, (δp) T =[δp E δp N δp U [δv] represents the positional error in the East-North-Up (ENU) direction; T =[δv E δv N δv U ] represents the velocity error in the ENU direction; φ T =[φ E φ N φ U [δb] represents the attitude error in the ENU direction; rg ) T 、(δb ra ) T These are the random constant drift errors of the receiver gyroscope and the accelerometer, respectively; δt u δt is the distance corresponding to the equivalent clock error. ru The distance rate is the equivalent clock frequency error, and "T" represents the matrix transpose.

[0114] The measurement equation for a multi-frequency system is:

[0115]

[0116] In the formula, P r,n and D r,n (n = 1, 2, 3) represent Beidou B respectively. n Pseudorange and Doppler observations at frequencies, H r (t) is the measurement coefficient matrix, V r (t) is the measurement noise matrix. These are for calculating pseudorange and pseudorange rate, respectively.

[0117] Step 2: Using the refueling aircraft as the mobile reference station and the receiving aircraft as the rover station, establish a double-difference observation equation;

[0118] Tanker aircraft m observes satellites i and j, while receiver aircraft r simultaneously observes satellites i and j. Both tanker aircraft m and receiver aircraft r receive tri-frequency BDS signals, enabling the acquisition of multiple sets of observations in the B1 / B2 / B3 frequency bands. The carrier phase double-difference observation equation is as follows:

[0119]

[0120] The Doppler double-difference observation equation is:

[0121]

[0122] In the formula, ▽Δ represents the double difference operator, φ is the carrier phase in meters, D is the Doppler observation, N is the integer ambiguity, and ρ is the geometric distance between the satellite and the receiver. Let n represent the rate of change of the geometric distance between the satellite and the receiver, and n represent the distance between the BeiDou B satellite and the receiver. n Frequency band (n=1,2,3), λ n Indicates Beidou B n The wavelength corresponding to the frequency band, I represents the ionospheric delay error, T represents the tropospheric delay error, the superscript "·" indicates the rate of change, and ε represents the noise error term. For example, it means that the receiver r corresponds to the satellite i's geometric distance from the ground; For example, it means that the refueling aircraft m and the receiving aircraft r synchronously observe the B formation formed by satellites i and j. n The interpretation of each term in Equation (4) and Equation (5) is similar for the frequency band double-difference carrier phase.

[0123] Step 3: Separate the ambiguity from the filter parameter estimation. Based on the wavelength, ionospheric amplification factor, and combined noise amplification factor of the combined observations, select three sets of BeiDou optimal coefficients to form an ultra-wide lane-wide lane-narrow lane combination. Replace the pseudorange observation with the satellite-to-ground distance predicted by the inertial navigation system. Calculate the double-difference integer ambiguity for each lane based on the geometric-free model and the geometric model.

[0124] Carrier phase is a distance measurement with high observation accuracy. It is commonly used in GNSS precision positioning and is currently the most widely used GNSS high-precision positioning technology. However, due to the characteristics of carrier signals, there is an integer ambiguity problem in its measurement. Once the integer ambiguity is correctly solved, high-precision distance measurement values ​​can be obtained.

[0125] It is worth noting that the ambiguity resolution adopts a step-by-step ambiguity fixing strategy of Extra Wide Lane - Wide Lane - Narrow Lane. The ambiguity combinations of Extra Wide Lane and Wide Lane should have a certain linear relationship to facilitate the solution. Combinations that can be used, but are not limited to, Extra Wide Lane (EWL): (0,-1,1), Wide Lane (WL): (1,-1,0), (1,0,-1), Narrow Lane (NL): (1,0,0), (0,1,0), (0,0,1) are acceptable. The steps involved in integer ambiguity resolution are further described below using the above combinations as an example.

[0126] Step 31, using the inertial prediction quantity ρ INSInstead of pseudorange observations, ultrawide aisle ambiguity is calculated using a geometry-free (GF) model.

[0127]

[0128]

[0129] In the formula, ρ INS For inertial prediction of satellite-to-Earth distance, (x s ,y s ,z s (x) represents the satellite position in the Earth-Centered Earth-Fixed (ECEF) coordinate system. INS ,y INS ,z INS ) represents the inertial prediction position in the ECEF coordinate system, N represents the integer ambiguity, φ represents the carrier phase, λ represents the wavelength, and the subscripts "EWL", "WL", and "NL" represent the physical quantities corresponding to the ultra-wide lane, wide lane, and narrow lane, respectively.

[0130] Step 32, using the known ambiguity of the ultra-wide alley combination (0,-1,1) Estimate high-precision satellite-to-Earth distance

[0131]

[0132] Step 33, calculate the ambiguity of the wide lane (1,-1,0).

[0133]

[0134] Step 34, using the known ambiguity of the width alley (1,-1,0) Estimate high-precision satellite-to-Earth distance

[0135]

[0136] Step 35: For the ambiguities of the ultra-wide alley and wide alley, the aforementioned GF model is used to improve the solution efficiency. For the narrow alley ambiguities that are difficult to fix, a geometric-based (GB) model is established, and the LAMBDA algorithm is used to search for and fix the integer frequency ambiguities of B1 / B2 / B3. The observation equations of the GB model are as follows:

[0137]

[0138] In the formula, The relative positions of the oil receiving and receiving units in the ECEF coordinate system. For Bn Frequency band carrier phase, For B n Frequency band double-difference integer ambiguity, For B n Frequency band carrier phase noise, A is the design matrix. I c Let be a c-dimensional identity matrix, ε be the observation error term, and the other physical quantities be the same as before.

[0139] Step four: Introduce a relative state filter. Utilize multi-frequency BeiDou differential relative measurement information based on a mobile reference station, combined with the relative state error recursive model of the SINS navigation system, and calculate the relative navigation parameters between the refueling aircraft and the receiving aircraft through BDS / INS tight combination relative state filtering.

[0140] Further consideration is given to the error relationship between the two targets to minimize the error in relative state estimation, thereby improving relative navigation accuracy. While collecting raw observation data, the receiver aircraft also receives carrier phase and Doppler observation information from the refueling aircraft via data link. This information, together with the receiver aircraft's satellite observations, constitutes the carrier phase and Doppler double-difference observation equations.

[0141] The receiver aircraft's system filtering module consists of two parts: an absolute state filter, which outputs absolute navigation information and corrects gyroscope and acceleration errors through a tight combination of BDS / INS; and a relative state filter, which utilizes multi-frequency BeiDou differential relative measurement information based on a mobile reference station, combined with the state error recursive model of the SINS navigation system, to achieve optimal estimation of the relative inertial state of the differential BDS / INS tight combination, thereby improving the accuracy of the relative navigation system solution of the BDS / INS combination. The relative navigation filtering process comprises three parts: the relative state error equation, the relative measurement error equation, and information fusion, as follows:

[0142] (1) Relative state error equation

[0143] General interpretation of physical quantities: Define a physical quantity M in frame a relative to frame b as the projection of its value into frame c. This represents the attitude transformation matrix from system a to system b; all physical quantities in this embodiment are defined in this manner.

[0144] The relative positions between the refueling pump m and the receiving pump r are: According to the general interpretation, it means the projection of the receiver's position relative to the refueling tanker onto the receiver's system. Further:

[0145]

[0146] In the formula, subscript I represents the inertial coordinate system. Equation (12) differentiated with respect to time:

[0147]

[0148] In the formula, Let represent velocity, [(·)×] represent the cross product operation, and ω represent the angular velocity of rotation. Differentiating equation (13) again with respect to time:

[0149]

[0150] Substituting equation (13) into equation (14) yields:

[0151]

[0152] In the formula, Indicates acceleration. Let The differential equation for relative velocity error is defined as follows:

[0153]

[0154] In the formula, the superscript "^" indicates the estimated value, and δ represents the error amount, the same below. Considering the error of the inertial device, the relative velocity error equation can be obtained by rearranging:

[0155]

[0156] In the formula, w rg w ra These are the Gaussian white noise of the gyroscope and the Gaussian white noise of the accelerometer, respectively. δα mr Let q be the relative attitude angle error. Define the attitude quaternion q of the receiver r relative to the refueling unit m. mr Represented as:

[0157]

[0158] In the formula, q represents a quaternion, q mr =[q mr0 q mr13 ] T ;q m Let q be the attitude quaternion of the refueling aircraft. r This is the quaternion for the receiver aircraft's attitude. (Definition) For quaternion operators, it is conventionally defined as follows: in,

[0159] Taking the first derivative of equation (18), we get:

[0160]

[0161] Based on the quaternion differential equation:

[0162]

[0163] Similarly, For the attitude quaternion q of the refueling aircraft m Given:

[0164]

[0165] Taking the first derivative of equation (21), we get:

[0166]

[0167] then:

[0168]

[0169] Substituting and rearranging, we get:

[0170]

[0171] Similar to the kinematic equations of relative attitude, the relative attitude estimation error in the state variables is represented in quaternion form:

[0172]

[0173] Taking the first-order differential from both sides simultaneously, we get:

[0174]

[0175] Let δα mr =2δq mr13 Combining the error model of inertial devices, we can deduce:

[0176]

[0177] (2) Relative measurement error equation

[0178] Let the position coordinates of the refueling machine in the Earth-centered geodetic coordinate system be... The approximate location is estimated as follows The correction number is The receiver's position coordinates are The approximate location is estimated as follows The correction number is The position vector of the receiver aircraft relative to the refueling aircraft in the ECEF coordinate system is Approximate position is Position error is The relationship between the refueling aircraft, the receiving aircraft, and the satellite is as follows: Figure 3 As shown. The refueling aircraft m observes satellites i and j, while the receiving aircraft r observes satellites i and j simultaneously. The carrier phase double difference observation equation is shown in equation (4).

[0179] Let the position of satellite i be (x i ,y i ,z i )T In equation (4) For example, it can be calculated using the following formula:

[0180]

[0181] Taylor linearization expansion of the nonlinear terms in equation (28):

[0182]

[0183] In the formula, For the estimated geometric distance between the satellite and the receiver, [I x I y I z Let ] be the line-of-sight vector, and the subscripts x, y, and z represent the components of the line-of-sight vector in the x, y, and z directions, respectively. Let Let i be the line-of-sight vector between the refueling aircraft and satellite i. Let i be the line-of-sight vector between the receiver and satellite i. Substituting this into equation (29) and subtracting the two equations, we get:

[0184]

[0185] For the position coordinates of the fuel dispenser in the ECEF coordinate system and receiver The relative positions in the ECEF coordinate system and the relative positions in the mechanical system have the following relationship:

[0186]

[0187] In the formula, Let represent the positions of the refueling aircraft and the receiving aircraft in the ECEF coordinate system, respectively. Since refueling aircraft are generally equipped with high-precision navigation sensors, their positions can be considered precisely known. Therefore, their relative positions can be projected onto the refueling aircraft's body coordinate system. Thus, the receiving aircraft in the ECEF coordinate system... The expression can be rewritten as:

[0188]

[0189] Considering Therefore, the positional error of the oil engine for:

[0190]

[0191] Substituting equation (33) into equation (30) yields:

[0192]

[0193] for Item, considering Then we have:

[0194]

[0195] If we assume When the baseline length At that time, the position error of the fuel dispenser satisfies At this time, the impact on baseline error can be less than 2cm. According to the publicly available service performance specification (Ver 3.0) of the BeiDou Navigation Satellite System, the BeiDou satellite constellation consists of GEO, MEO, and IGSO, all with orbital altitudes above 20,000km. The position error of the refueling aircraft has a small impact on relative navigation and can be ignored.

[0196] Similarly, for geostationary observation satellite j, we can obtain:

[0197]

[0198] Performing inter-station and inter-satellite differential measurements on the refueling aircraft and receiving aircraft, and neglecting the refueling aircraft position error, ionospheric and tropospheric residual errors after double-difference, the carrier phase double-difference observation equation is as follows:

[0199]

[0200] The integer ambiguity in the formula is calculated using an integer ambiguity resolution filter. After obtaining the integer ambiguity, the carrier phase can be used as a high-precision range measurement. Simultaneous observation of M satellites yields a multi-frequency carrier phase observation equation consisting of M-1 observation equations:

[0201]

[0202] In the formula, φ represents the M-1 dimensional carrier phase vector, and N represents the M-1 dimensional integer ambiguity vector. Let K1 and K2 represent the M-1 dimension satellite distance prediction vector, and K1 and K2 are the coefficient matrices formed by the M-1 set of equations.

[0203] Doppler observations are extractable observations from a receiver that represent the difference between the received and transmitted signal frequencies. This is due to the change in the received signal frequency caused by the relative motion between the signal transmitter and receiver. The Doppler observation equations for the synchronous observations of satellites i and j by the refueling and receiving aircraft are shown in equation (5).

[0204] The following relationship exists between the pseudorange change rate and the relative velocity between the two machines:

[0205]

[0206] In the formula, To estimate the rate of change of the geometric distance between the satellite and the receiver, differentiate both sides of equation (32):

[0207]

[0208] Right now

[0209]

[0210] then:

[0211]

[0212] Combining the error models of the gyroscope and accelerometer, we can obtain:

[0213]

[0214] Ignoring the refueling aircraft speed error and substituting it into the Doppler observation equation, we get:

[0215]

[0216] Similar to equation (38), and ignoring the double-difference residual error term, the multi-frequency Doppler observation equation can finally be written as:

[0217]

[0218] In the formula, D represents the M-1 dimension Doppler observation vector. Let Q1, Q2, Q3, and Q4 represent the M-1 dimensional predicted satellite-to-Earth distance change rate, and Q4 be the coefficient matrix of the M-1 set of equations.

[0219] (3) Information fusion

[0220] A DGNSS / INS tightly coupled relative filtering model is constructed using the Extended Kalman Filter (EKF) data fusion method, employing carrier phase and Doppler observations with known ambiguity, to fuse relative information data. The selected state variables are:

[0221]

[0222] Calculate the state prediction value using EKF time updates. and its variance matrix P k,k-1 .

[0223]

[0224] In the formula, P k-1 These are the posterior state vector and covariance matrix at time k-1, respectively. P k,k-1 These are the prior state vector and covariance matrix at time k, respectively, Φ k,k-1 Let Γ be the state transition matrix from time k-1 to time k.k-1 Let Q be the system noise matrix. k-1 Let K be the system noise variance matrix. Then, perform measurement updates and calculate the gain matrix K. k Filtered estimate Variance matrix P k .

[0225]

[0226] In the formula, Z k H is the measurement vector. k For the measurement matrix, R k To measure the noise variance matrix, P k Let be the posterior state vector and covariance matrix at time k, respectively, and I be the identity matrix.

[0227] This invention employs digital simulation. The simulation conditions are as follows: the inertial navigation system has a sampling frequency of 200Hz, a random constant of 0.1° / h, and white noise of 0.01° / h; the accelerometer has a random constant and white noise of 1mg; the BeiDou satellite navigation system has a sampling frequency of 1Hz, with identical observation accuracy for all three frequencies, including a pseudorange accuracy of 0.3m, a carrier phase observation accuracy of 0.01 cycles, a Doppler observation accuracy of 0.01m / s, and a cutoff altitude angle of 15°. During aerial refueling, the tanker and receiver aircraft maintain formation flight. A set of comparative experiments was designed to obtain the following results: Figures 4(a) to 4(c) , Figures 5(a) to 5(c) , Figures 6(a) to 6(c) The simulation results are shown in the figure. Figures 4(a) to 4(c) This is a diagram showing the relative position error in relative navigation. Figures 5(a) to 5(c) This is a diagram of relative velocity error in relative navigation. Figures 6(a) to 6(c) This is a diagram of relative attitude error in relative navigation. The solid curve in the diagram represents the conventional relative navigation method based on differential absolute navigation information, while the dashed curve represents a multi-frequency BDS / INS combined aerial refueling relative navigation method presented in this invention.

[0228] Simulation results show that the relative navigation method for UAV aerial refueling of the present invention can effectively suppress the divergence of the inertial navigation system. Compared with the conventional relative navigation method based on the difference of absolute navigation information, it can effectively improve the accuracy of relative position, velocity and attitude estimation.

Claims

1. A method for multi-frequency BDS / INS integrated relative navigation for aerial refueling, characterized in that, Includes the following steps: S1, based on the BeiDou satellite navigation system and inertial navigation system of the refueling aircraft and the receiving aircraft, constructs the multi-frequency BDS system measurement equations of the receiving aircraft and the refueling aircraft respectively, and corrects the INS solution results through absolute state filtering of BDS / INS tight combination; at the same time, the refueling aircraft sends real-time absolute navigation information and raw data to the receiving aircraft through data link; S2, using the refueling aircraft as the mobile reference station and the receiving aircraft as the rover station, establish carrier phase double-difference observation equations and Doppler double-difference observation equations; S3 separates the integer ambiguity in the carrier phase from the filter parameter estimation, selects three sets of Beidou coefficients to form an ultra-wide lane-wide lane-narrow lane combination, and replaces the pseudorange observation with the satellite-to-ground distance predicted by the inertial navigation system. Based on the geometric-free model and the geometric model, the double-difference integer ambiguity is obtained lane by lane. S4. A relative state filter is introduced to establish a multi-frequency BeiDou differential relative measurement error equation based on a mobile reference station. Combined with the relative state error recursive model of the SINS navigation system, a DGNSS / INS compact combination relative filtering model is constructed. The relative information data is fused by the extended Kalman filter data fusion method to complete the calculation of the relative navigation parameters between the refueling aircraft and the receiving aircraft. The process of constructing the relative measurement error equation is as follows: Let the position coordinates of the refueling machine in the Earth-centered geodetic coordinate system be... The approximate location is estimated as follows: The corrected number is The receiver's position coordinates are: The approximate location is estimated as follows: The corrected number is Oil receiver Compared to fuel dispensers The position vector in the ECEF coordinate system is Approximate position is The positional error is ;definition coordinate system relative to Physical quantities of a coordinate system ,exist Projection in coordinate system is ; express coordinate system to The attitude transformation matrix of the coordinate system; "T" indicates an inertial coordinate system; "T" indicates matrix transpose. Set up satellite The position is For the receiving machine Corresponding to satellite Geometric distance between satellite and Earth fuel dispensers Corresponding to satellite Geometric distance between satellite and Earth Taylor linearization expansion of the nonlinear terms: ， In the formula, This is an estimate of the geometric distance between the satellite and the receiver. The line-of-sight vector, with subscripts , , These represent the line-of-sight vectors at... Towards, Towards, The component of the direction; let For refueling machines With satellite The line-of-sight vector between them For oil receiver With satellite Given the line-of-sight vectors between them, we have: ， The relative positions in the ECEF coordinate system and the relative positions in the mechanical system have the following relationship: ， In the formula, , Let represent the positions of the refueling aircraft and the receiving aircraft in the ECEF coordinate system, respectively. Projecting the relative positions onto the refueling aircraft's body coordinate system, the receiving aircraft in the ECEF coordinate system... The expression is rewritten as: ， Considering , the position error of the oil receiver is: ， wherein, is the relative attitude angle error; The final result is: ， Similarly, we can obtain: ， Ignore the positional error of the fuel dispenser Regarding the impact of relative navigation, inter-station and inter-satellite differentials are performed for the refueling aircraft and the receiving aircraft, and the residual errors in the ionosphere and troposphere after double differential are ignored. The expression for the relative measurement error equation is as follows: ， Synchronous observation of a satellite, resulting in a multi-frequency carrier phase observation equation composed of observation equations ， In the formula, express 3D carrier phase vector, express 3D integer ambiguity vector express Predicted distance vector between the satellite and the ground. , for The coefficient matrix formed by the set of equations; The following relationship exists between the pseudorange change rate and the relative velocities of the refueling aircraft and the receiving aircraft: ， wherein is an estimate of the rate of change of the geometric range between the satellite and the receiver; By , ， Then there is , then: ， Combining the error models of the gyroscope and accelerometer, we obtain: ， Ignoring the refueling aircraft speed error and substituting it into the Doppler observation equation, we get: ， Ignoring the double-difference residual error term, the multi-frequency Doppler observation equation is finally written as: ， In the formula, express Widopler observation vector, express Predict the rate of change of satellite-to-Earth distance. , , and for The coefficient matrix formed by the set of equations.

2. The multi-frequency BDS / INS integrated relative navigation method for airborne refueling according to claim 1, wherein, In step S1, the expression for the recursive equation of the tightly coupled state of the receiver aircraft's inertial navigation system and the BeiDou navigation system is as follows: ， The state variables are selected as follows: ， In the formula, for Orientation and position error; for Directional velocity error; for Orientation and attitude error; , These are the random constant drift error of the receiver gyroscope and the random constant drift error of the accelerometer, respectively. The distance corresponding to the equivalent clock error. The distance rate corresponding to the equivalent clock frequency error; The expression for the recursive equation of the tightly coupled state of the inertial navigation system and the BeiDou navigation system of the refueling aircraft is the same as that of the tightly coupled state of the inertial navigation system and the BeiDou navigation system of the receiving aircraft.

3. The multi-frequency BDS / INS integrated relative navigation method for airborne refueling according to claim 2, characterized in that, In step S1, the measurement equation for the receiver's multi-frequency BDS system is: ， In the formula, and These respectively indicate that the receiver aircraft is in Beidou Pseudorange and Doppler observations at frequencies ; This is the measurement coefficient matrix of the receiver engine. The noise matrix for measuring the receiver engine. , These are the pseudorange calculated by the receiver aircraft and the pseudorange rate calculated by the receiver aircraft, respectively. This refers to the wavelength corresponding to the BeiDou B1 band. This refers to the wavelength corresponding to the BeiDou B2 band. This refers to the wavelength corresponding to the BeiDou B3 frequency band. The measurement equations for the multi-frequency BDS system of the refueling machine are the same as those for the multi-frequency BDS system of the receiving machine.

4. The multi-frequency BDS / INS integrated relative navigation method for airborne refueling according to claim 3, wherein, In step S2, the refueling machine Observation satellite , At the same time, the oil receiving machine Observation satellite , fuel dispenser and receiver The system receives tri-frequency BDS signals and obtains multiple sets of observations in the B1 / B2 / B3 frequency bands; the carrier phase double-difference observation equation and the Doppler double-difference observation equation are as follows: ， ， In the formula, This represents the double difference operator. The carrier phase is expressed in meters. For integer ambiguity, For Doppler observations, The geometric distance between the satellite and the receiver. The geometric distance between the satellite and the receiver is the rate of change; n represents BeiDou. frequency band ; Beidou The wavelength corresponding to the frequency band Indicates ionospheric delay error. This indicates the tropospheric delay error, with the superscript "·" indicating the rate of change. This represents the carrier phase noise error term. This represents the noise error term in the Doppler observations; For oil receiver Corresponding to satellite The geometric distance between the satellite and the Earth. For oil receiver Corresponding to satellite Geometric distance between the satellite and the ground; For refueling machines Corresponding to satellite The geometric distance between the satellite and the Earth. For refueling machines Corresponding to satellite Geometric distance between the satellite and the ground; For refueling machines With the receiver Synchronous observation satellite and Formed Frequency band double-difference carrier phase; For refueling machines With the receiver Synchronous observation satellite and Formed Frequency band double-difference integer ambiguity; For refueling machines With the receiver Synchronous observation satellite and Formed Frequency band double-difference ionospheric delay error; For refueling machines With the receiver Synchronous observation satellite and Formed Frequency band double-difference tropospheric delay error.

Images