CN107784866A - A kind of flight management system transverse direction navigation accuracy is taken a flight test AIRSPACE PLANNING method - Google Patents
A kind of flight management system transverse direction navigation accuracy is taken a flight test AIRSPACE PLANNING method Download PDFInfo
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Abstract
Taken a flight test AIRSPACE PLANNING method the invention provides a kind of flight management system transverse direction navigation accuracy, its feature comprises the following steps:It is determined that region tentatively to be flown, count correlation navigation platform position of the electromagnetism coverage in terminal airspace, including longitude, latitude and height, according to the intervisibility of each flying height guidance station signal in the spatial domain of terrain analysis check machine field, it is determined that the region that at least 2 guidance station radio signals cover is preliminary region to be flown simultaneously.
Description
Technical Field
The invention belongs to airworthiness approval test flight technology of navigation systems of civil aircrafts and transport aircrafts, and particularly relates to a transverse navigation precision test flight airspace planning method of a flight management system.
Background
The FMS transverse navigation accuracy test flight is the verification of the horizontal navigation accuracy of an airborne navigation system based on Regional Navigation (RNAV). RNAV was proposed in the united states in the seventies and eighties of the 20 th century, and RNAV navigation equipment can automatically determine the position of an aircraft by using multi-sensor input, so that the operation efficiency of the aircraft can be greatly improved, and organizations such as International Civil Aviation Organization (ICAO) and Federal Aviation Administration (FAA) in the united states have successively provided a large number of operation specifications and guidance files to guide the operation and popularization of RNAV technology in the world. China introduced the RNAV technology in 2005, listed as one of the core technologies for building a new generation of air transportation system in China, and promulgated the performance-based navigation implementation roadmap of China civil aviation in 10 months in 2009.
Available navigation sources for RNAV lateral navigation include VOR/DME, DME/DME, INS or IRS, GNSS, etc. The INS/IRS is a self-contained navigation source, the navigation precision of the INS/IRS is not influenced by other factors except the navigation equipment, and a positioning error prediction method of the INS/IRS is relatively mature. At present, domestic research on RNAV lateral navigation accuracy mainly focuses on the field of GNSS error analysis, and analysis on navigation accuracy of VOR/DME and DME/DME is relatively less. However, at present, RNAV navigation based on VOR/DME and DME/DME is still the navigation mode mainly used in China, and with the recent rapid development of civil passenger aircraft and large transport aircraft, the airworthiness certification work aiming at RNAV lateral navigation accuracy has received important attention.
The RNAV transverse navigation needs the support of navigation facilities/equipment such as a ground-based navigation station, so that the prediction of navigation signal coverage and navigation accuracy in a specified airspace and the judgment of whether the navigation accuracy meets the RNAV navigation performance are very important before the RNAV transverse navigation accuracy test flight is carried out. RNAV transverse navigation precision analysis is proposed by many countries internationally, and the most widely applied software system, namely RNAV-Pro, developed by FAA entrusted American air traffic simulation Limited company and specially used for RNAV airway design and evaluation is provided. In China, because the currently opened RNAV routes are very few and most of the currently opened RNAV routes are in a very busy main route, the development of RNAV transverse navigation accuracy verification test flight is inconvenient, and therefore it is necessary to develop airspace planning of RNAV transverse navigation accuracy verification test flight and verify that the accuracy of the selected navigation facilities meets the corresponding RNAV operation performance requirements through a prediction means.
Disclosure of Invention
The purpose of the invention is:
the method is used for planning the transverse navigation precision airspace of the flight management system of civil aircrafts and large-scale transport aircrafts, selects the trial flight airspace with good radio navigation signal coverage and meeting the RNAV navigation precision requirement, and provides data support and technical support for the verification of the trial flight of the airworthiness examination and approval of the system.
The technical scheme of the invention is as follows:
the invention provides a flight management system transverse navigation precision trial flight airspace planning method, which is characterized by comprising the following steps of:
determining a preliminary region to be flown, counting the positions of relevant navigation stations in the airport airspace in the electromagnetic coverage range, including longitude, latitude and height, checking the visibility of signals of the navigation stations at each flight altitude in the airport airspace according to terrain analysis, and determining the region simultaneously covered by radio signals of at least 2 navigation stations as the preliminary region to be flown.
Further, the step of determining the navigation station update area comprises the steps of:
in the DME/DME navigation mode,
the aircraft test flight airspace is required to be in an update area of 2 DME navigation tables,
the internal requirement is that "(1) the aircraft must be located within a common coverage area of 2 DME stations; (2) ensuring that the included angle between the airplane and two DME stations is between 30 and 150 degrees, and preselecting DME/DME to navigate the region to be flown for test flight according to the requirements;
further: and (3) simulating positioning according to the pre-test flying VOR/DME to obtain a positioning error:
pre-test flight is carried out in a preliminary flying waiting airspace, the position of the airplane is simulated and positioned according to a simulated positioning algorithm, when the airplane adopts a VOR/DME navigation mode, the airplane is simulated and positioned by adopting the VOR/DME simulated positioning algorithm,
the VOR/DME simulated positioning algorithm is characterized in that the aircraft position observation is obtained by continuously recording the distance and the azimuth information when the aircraft arrives at the ground station and reversely deducing the azimuth and the distance information, and the simulated positioning is realized mathematically according to iterative operation, wherein the model is as follows:
iterative operation of an initial value of the aircraft position: the position of the navigation station is determined,
iterative correction:
Lat_err=|ρ×cos(θ)/60|
lon _ err ═ ρ × sin (θ)/(60 × cos (lat)) | (formula-1)
Lat _ err and Lon _ err are latitude and longitude errors between an actual position of the airplane and a VOR/DME navigation station, rho is a distance between the actual position of the airplane and a current iteration value, a calculation method is shown in formula-2, theta is a relative azimuth angle between the actual position of the airplane and the current iteration position, a coordinate system is established by taking a vector from the VOR/DME station to the iteration position as an X axis and a vector from the iteration position to a true north direction as a Y axis, a second quadrant of the coordinate system is a region I, a first quadrant is a region II, three and four quadrants are regions III, when the actual position of the airplane falls in the regions I, II and III, calculation methods of theta are respectively shown in formula-3, formula-4 and formula-5, wherein DME is a distance between the airplane, VOR is a VOR azimuth output by the airplane, BEARING is a true azimuth of the current iteration position, and a distance between the current iteration position and the navigation station,
θ=180-BEARING-acos((RANGE2+ρ2-DME2) /(2X. rho. times. DME)) (zone I) (formula-3)
θ=-180+BEARING+acos((RANGE2+ρ2-DME2) /(2X. rho. times. DME)) (zone II) (formula-4)
θ=180+BEARING-acos((RANGE2+ρ2-DME2) /(2X. rho. times. DME)) (zone III) (formula-5)
And (3) iteration ending conditions: when rho is smaller than a specified value, the iteration is finished, and the algorithm can be accurate to the rho smaller than or equal to 0.0001m
And (3) calculating the result: correcting the position of the VOR/DME by Lat _ err and Lon _ err at the end of iteration to obtain a predicted airplane position;
and calculating the distance between the aircraft realization position and the simulated positioning position to obtain a positioning error.
Further: and (3) simulating positioning according to the pre-test flying DME/DME, and obtaining a positioning error:
pre-test flight is carried out in an initial airspace to be flown, the position of the airplane is simulated and positioned according to a simulated positioning algorithm, when the airplane adopts a DME/DME navigation mode, the DME/DME simulated positioning algorithm is adopted to simulate and position the airplane,
the DME/DME simulated positioning algorithm continuously records the distance information of the airplane to reach 2 different DME navigation stations, calculates the relative position of one of the DME navigation stations according to the distance information of the 2 DME navigation stations, and then obtains the simulated positioning of the current position of the airplane according to the algorithm in step 3:
the method for calculating the azimuth angle of the carrier arriving at any DME station is shown in the formula-6,
θ2=acos((DME12+RANGE2-DME22) /(2 × DME1 × RANGE)) (formula-6)
Wherein:
DME1 is the distance from the carrier to the # 1 DME navigation station, and the unit: the wavelength of the light beam is nm,
DME2 is the distance from the carrier to the # 2 DME navigation station, and the unit is: the wavelength of the light beam is nm,
RANGE is the distance of # 1 DME station from # 2 DME navigation station, in units: the wavelength of the light beam is nm,
and calculating the distance between the actual position of the airplane and the simulated positioning position to obtain the positioning error.
Further, still include: and (3) according to the simulated positioning result and the actual airplane data, performing RNAV navigation precision prediction:
the RNAV navigation precision prediction comprises two parts, namely a Navigation System Error (NSE) and a Flight Technology Error (FTE), wherein the NSE and the FTE mainly comprise low-frequency components and high-frequency components of positioning errors of position information obtained by analog positioning and position information measured by an actual carrier differential GPS, low-pass and high-pass filtering needs to be carried out on the positioning errors obtained in step 3 or step 4, and the filter design method comprises the following steps:
a)NSE
modeling the system function of the low-pass filter with reference to the ICAO angular error:
it is converted into the following differential equation using bilinear transformation:
yi ═ Apfe × (Xi +2 × Xi (n-1) + Xi (n-2)) + Bpfe × Yi (n-1) + Cpfe × Yi (n-2) (formula-8)
Wherein:
Omn=Om0/0.64
Apfe=Omn2/(K2+2×Omn×K+Omn2)
Bpfe=(2×K2-2×Omn2)/(K2+2×Omn×K+Omn2)
Cpfe=-(K2-2×Omn×K+Omn2)/(K2+2×Omn×K+Omn2)
K=Omn/tg(Omn×T/2)
where Xi (n-1) is the positioning error at the previous time, Yi is the current NSE value, T is the continuously measured signal length, and an error of 0.5rad/s in the lateral direction, as specified by ICAO, will not cause the carrier to deviate from the intended lane. The filter cutoff frequency Om0 therefore takes 0.5;
b)FTE
the high pass filter starting frequency Om1 was selected to be 0.3, and the effect on the FTE was further extrapolated by analyzing the wobble characteristic of the estimated position using this filter, equation-9,
using a bilinear transformation method, equation-9 is converted into a difference equation:
zi ═ Dcmn × (Xi-Xi (n-1)) + Ecmn × Zi (n-1) (formula-10)
Wherein,
Dcmn=1/(1+K×Om1)
Ecmn=(1-K×Om1)/(1+K×Om1)
K=tg(Om1×T/2)/Om1
wherein Xi (n-1) is a positioning error at the previous moment, Zi is a current FTE value, Zi (n-1) is an FTE value at the previous moment, T is a continuously measured signal length, corresponding prediction NSE and FTE values can be obtained by filtering the positioning error, and the trial flight airspace can be determined when the error meets the index requirement.
The invention has the advantages that:
in China, airspace terrain prediction and radio coverage area prediction are applied to transverse navigation precision test flight for the first time, a VOR/DME, DME/DME simulation positioning and navigation precision prediction technology is used for initially selecting a test flight airspace, the technology can be applied to airspace selection of test flight of radio communication navigation subjects, and test flight efficiency can be greatly improved.
The method can be used for screening routes which accord with RNAV trial flight in unpublished airspace, greatly widens airspace resources of RNAV trial flight in China, overcomes the difficulty that the RNAV navigation precision verification trial flight is inconvenient because the RNAV navigation precision is less in the RNAV routes in China and most routes are in busy main routes or remote western routes, and provides a feasible and effective method for subsequent development of RNAV related navigation precision verification trial flight.
Drawings
FIG. 1 is a dual DME navigation station update area;
FIG. 2 is a schematic diagram of VOR/DME simulated localization iterative calculation;
FIG. 3 is a schematic diagram of a DME/DME simulated localization algorithm;
fig. 4 shows the positioning error prediction results.
Detailed Description
Firstly, determining a preliminary flying area:
determining a preliminary region to be flown, counting the positions of relevant navigation stations in the airport airspace in the electromagnetic coverage range, including longitude, latitude and height, checking the visibility of signals of the navigation stations at each flight altitude in the airport airspace according to terrain analysis, and determining the region simultaneously covered by radio signals of at least 2 navigation stations as the preliminary region to be flown.
Secondly, determining an update area of the navigation platform:
in the DME/DME navigation mode, the aircraft test flight airspace is required to be in the updating area of 2 DME navigation stations, "(1) the aircraft must be in the common coverage range of the 2 DME stations; (2) ensuring that the included angle between the airplane and two DME stations is between 30 and 150 degrees, and preselecting DME/DME to navigate the area to be flown for test flight according to the requirements, as shown in figure 1;
thirdly, obtaining a positioning error according to the simulated positioning of the pre-test flying VOR/DME:
pre-test flight is carried out in a preliminary flying waiting airspace, the position of the airplane is simulated and positioned according to a simulated positioning algorithm, when the airplane adopts a VOR/DME navigation mode, the airplane is simulated and positioned by adopting the VOR/DME simulated positioning algorithm,
the VOR/DME simulated positioning algorithm is characterized in that the distance and the azimuth information of an airplane to a ground platform are continuously recorded, the azimuth and the distance information are reversely deduced to obtain the position observation of the airplane, the simulation positioning is realized according to iterative operation in mathematics, the reference figure 2 shows that theta is the relative azimuth angle between the real position of the airplane and the current iterative position, a coordinate system is established by taking the vector from the VOR/DME platform to the iterative position as an X axis and taking the vector from the iterative position to the true north direction as a Y axis, the coordinate system can be an orthogonal coordinate system or a non-orthogonal coordinate system, the second quadrant of the coordinate system is an I area, the first quadrant is an II area, the third quadrant and the fourth quadrant are III areas, and when the actual position of the airplane falls in the I area, the II area and the III area. The model is as follows:
iterative operation of an initial value of the aircraft position: the position of the navigation station is determined,
iterative correction:
Lat_err=|ρ×cos(θ)/60|
lon _ err ═ ρ × sin (θ)/(60 × cos (lat)) | (formula-1)
θ=180-BEARING-acos((RANGE2+ρ2-DME2) /(2X. rho. times. DME)) (zone I) (formula-3)
θ=-180+BEARING+acos((RANGE2+ρ2-DME2) /(2X. rho. times. DME)) (zone II) (formula-4)
θ=180+BEARING-acos((RANGE2+ρ2-DME2) /(2X. rho. times. DME)) (zone III) (formula-5)
And (3) iteration ending conditions: when rho is smaller than a specified value, the iteration is finished, and the algorithm can be accurate to the rho smaller than or equal to 0.0001m
And (3) calculating the result: correcting the position of the VOR/DME by Lat _ err and Lon _ err at the end of iteration to obtain a predicted airplane position;
and calculating the distance between the aircraft realization position and the simulated positioning position to obtain a positioning error.
Fourthly, positioning error is obtained according to the pre-test flying DME/DME simulated positioning:
pre-test flight is carried out in an initial airspace to be flown, the position of the airplane is simulated and positioned according to a simulated positioning algorithm, when the airplane adopts a DME/DME navigation mode, the DME/DME simulated positioning algorithm is adopted to simulate and position the airplane, as shown in figure 3,
the DME/DME simulated positioning algorithm continuously records the distance information of the airplane to reach 2 different DME navigation stations, calculates the relative position of one of the DME navigation stations according to the distance information of the 2 DME navigation stations, and then obtains the simulated positioning of the current position of the airplane according to the algorithm in step 3:
the method for calculating the azimuth angle of the carrier arriving at any DME station is shown in the formula-7.
θ2=acos((DME12+RANGE2-DME22) /(2 × DME1 × RANGE)) (formula-7)
And calculating the distance between the actual position of the airplane and the simulated positioning position to obtain the positioning error.
The fifth step: prediction of RNAV navigation precision according to simulation positioning result and actual airplane data
RNAV navigation accuracy prediction includes two parts, Navigation System Error (NSE) and Flight Technique Error (FTE). The NSE and the FTE mainly comprise low-frequency components and high-frequency components of positioning errors of position information obtained by analog positioning and position information measured by actual carrier differential GPS, low-pass and high-pass filtering needs to be carried out on the positioning errors obtained in step 3 or step 4, and a filter design method is as follows.
c)NSE
Modeling the system function of the low-pass filter with reference to the ICAO angular error:
it is converted into the following differential equation using bilinear transformation:
yi ═ Apfe × (Xi +2 × Xi (n-1) + Xi (n-2)) + Bpfe × Yi (n-1) + Cpfe × Yi (n-2) (formula-4)
Wherein:
Omn=Om0/0.64
Apfe=Omn2/(K2+2×Omn×K+Omn2)
Bpfe=(2×K2-2×Omn2)/(K2+2×Omn×K+Omn2)
Cpfe=-(K2-2×Omn×K+Omn2)/(K2+2×Omn×K+Omn2)
K=Omn/tg(Omn×T/2)
with reference to the ICAO specification, an error of 0.5rad/s in the lateral direction will not cause the carrier to deviate from the intended course. The filter cutoff frequency Om0 therefore takes 0.5.
d)FTE
The high pass filter start frequency was selected to be 0.3, and the filter was used to analyze the wobble characteristics of the estimated position, thereby further estimating the effect on the FTE, equation 5.
Using a bilinear transformation method, equation-5 is converted into a difference equation:
zi ═ Dcmn × (Xi-Xi (n-1)) + Ecmn × Zi (n-1) (formula-6)
Wherein,
Dcmn=1/(1+K×Om1)
Ecmn=(1-K×Om1)/(1+K×Om1)
K=tg(Om1×T/2)/Om1
the positioning error is filtered to obtain corresponding predicted NSE and FTE values, the error meets the index requirement, a test flight airspace can be determined, and a diagram 4 shows the error prediction result of the RNAV transverse navigation precision test flight of a civil passenger plane at an airport.
Claims (5)
1. A flight management system transverse navigation precision trial flight airspace planning method is characterized by comprising the following steps:
determining a preliminary region to be flown, counting the positions of relevant navigation stations in the airport airspace in the electromagnetic coverage range, including longitude, latitude and height, checking the visibility of signals of the navigation stations at each flight altitude in the airport airspace according to terrain analysis, and determining the region simultaneously covered by radio signals of at least 2 navigation stations as the preliminary region to be flown.
2. The method for planning the trial flight airspace of the flight management system with the lateral navigation precision as set forth in claim 1, further comprising: determining an update area of the navigation station:
in the DME/DME navigation mode,
the aircraft test flight airspace is required to be in an update area of 2 DME navigation tables,
the internal requirement is that "(1) the aircraft must be located within a common coverage area of 2 DME stations; (2) and ensuring that the included angle between the airplane and two DME stations is between 30 and 150 degrees, and pre-selecting the DME/DME to navigate the region to be flown for test flight according to the requirements.
3. The method for planning the trial flight airspace of the flight management system with the lateral navigation precision as set forth in claim 1, further comprising: and (3) simulating positioning according to the pre-test flying VOR/DME to obtain a positioning error:
pre-test flight is carried out in a preliminary flying waiting airspace, the position of the airplane is simulated and positioned according to a simulated positioning algorithm, when the airplane adopts a VOR/DME navigation mode, the airplane is simulated and positioned by adopting the VOR/DME simulated positioning algorithm,
the VOR/DME simulated positioning algorithm is characterized in that the aircraft position observation is obtained by continuously recording the distance and the azimuth information when the aircraft arrives at the ground station and reversely deducing the azimuth and the distance information, and the simulated positioning is realized mathematically according to iterative operation, wherein the model is as follows:
iterative operation of an initial value of the aircraft position: the position of the navigation station is determined,
iterative correction:
Lat_err=|ρ×cos(θ)/60|
lon _ err ═ ρ × sin (θ)/(60 × cos (lat)) | (formula-1)
Lat _ err and Lon _ err are latitude and longitude errors between an actual position of the airplane and a VOR/DME navigation station, rho is a distance between the actual position of the airplane and a current iteration value, a calculation method is shown in formula-2, theta is a relative azimuth angle between the actual position of the airplane and the current iteration position, a coordinate system is established by taking a vector from the VOR/DME station to the iteration position as an X axis and a vector from the iteration position to a true north direction as a Y axis, a second quadrant of the coordinate system is a region I, a first quadrant is a region II, three and four quadrants are regions III, when the actual position of the airplane falls in the regions I, II and III, calculation methods of theta are respectively shown in formula-3, formula-4 and formula-5, wherein DME is a distance between the airplane, VOR is a VOR azimuth output by the airplane, BEARING is a true azimuth of the current iteration position, and a distance between the current iteration position and the navigation station,
θ=180-BEARING-a cos((RANGE2+ρ2-DME2) /(2X. rho. times. DME)) (zone I) (formula-3)
θ=-180+BEARING+a cos((RANGE2+ρ2-DME2) /(2X. rho. times. DME)) (zone II) (formula-4)
θ=180+BEARING-a cos((RANGE2+ρ2-DME2) /(2X. rho. times. DME)) (zone III) (formula-5)
And (3) iteration ending conditions: when rho is smaller than a specified value, the iteration is finished, and the algorithm can be accurate to the rho smaller than or equal to 0.0001m
And (3) calculating the result: correcting the position of the VOR/DME by Lat _ err and Lon _ err at the end of iteration to obtain a predicted airplane position;
and calculating the distance between the aircraft realization position and the simulated positioning position to obtain a positioning error.
4. The method for planning the trial flight airspace of the flight management system with the lateral navigation precision as set forth in claim 1 or 2, further comprising: and (3) simulating positioning according to the pre-test flying DME/DME, and obtaining a positioning error:
pre-test flight is carried out in an initial airspace to be flown, the position of the airplane is simulated and positioned according to a simulated positioning algorithm, when the airplane adopts a DME/DME navigation mode, the DME/DME simulated positioning algorithm is adopted to simulate and position the airplane,
the DME/DME simulated positioning algorithm continuously records the distance information of the airplane to reach 2 different DME navigation stations, calculates the relative position of one of the DME navigation stations according to the distance information of the 2 DME navigation stations, and then obtains the simulated positioning of the current position of the airplane according to the algorithm in step 3:
the method for calculating the azimuth angle of the carrier arriving at any DME station is shown in the formula-6,
θ2=acos((DME12+RANGE2-DME22) /(2 × DME1 × RANGE)) (formula-6)
Wherein:
DME1 is the distance from the carrier to the # 1 DME navigation station, and the unit: the wavelength of the light beam is nm,
DME2 is the distance from the carrier to the # 2 DME navigation station, and the unit is: the wavelength of the light beam is nm,
RANGE is the distance of # 1 DME station from # 2 DME navigation station, in units: the wavelength of the light beam is nm,
and calculating the distance between the actual position of the airplane and the simulated positioning position to obtain the positioning error.
5. The method for planning the trial flight airspace of the flight management system with the lateral navigation precision as set forth in claim 3 or 4, further comprising: and (3) according to the simulated positioning result and the actual airplane data, performing RNAV navigation precision prediction:
the RNAV navigation precision prediction comprises two parts, namely a Navigation System Error (NSE) and a Flight Technology Error (FTE), wherein the NSE and the FTE mainly comprise low-frequency components and high-frequency components of positioning errors of position information obtained by analog positioning and position information measured by an actual carrier differential GPS, low-pass and high-pass filtering needs to be carried out on the positioning errors obtained in step 3 or step 4, and the filter design method comprises the following steps:
a)NSE
modeling the system function of the low-pass filter with reference to the ICAO angular error:
it is converted into the following differential equation using bilinear transformation:
yi ═ Apfe × (Xi +2 × Xi (n-1) + Xi (n-2)) + Bpfe × Yi (n-1) + Cpfe × Yi (n-2) (formula-8)
Wherein:
Omn=Om0/0.64
Apfe=Omn2/(K2+2×Omn×K+Omn2)
Bpfe=(2×K2-2×Omn2)/(K2+2×Omn×K+Omn2)
Cpfe=-(K2-2×Omn×K+Omn2)/(K2+2×Omn×K+Omn2)
K=Omn/tg(Omn×T/2)
where Xi (n-1) is the positioning error at the previous time, Yi is the current NSE value, T is the continuously measured signal length, and an error of 0.5rad/s in the lateral direction, as specified by ICAO, will not cause the carrier to deviate from the intended lane. The filter cutoff frequency Om0 therefore takes 0.5;
b)FTE
the high pass filter is selected to have an initial frequency of 0.3, and the filter is used to analyze the wobble characteristics of the estimated position to further deduce the effect on the FTE, formula-9,
using a bilinear transformation method, equation-9 is converted into a difference equation:
zi ═ Dcmn × (Xi-Xi (n-1)) + Ecmn × Zi (n-1) (formula-10)
Wherein,
Dcmn=1/(1+K×Om1)
Ecmn=(1-K×Om1)/(1+K×Om1)
K=tg(Om1×T/2)/Om1
wherein Xi (n-1) is a positioning error at the previous moment, Zi is a current FTE value, Zi (n-1) is an FTE value at the previous moment, T is a continuously measured signal length, corresponding prediction NSE and FTE values can be obtained by filtering the positioning error, and the trial flight airspace can be determined when the error meets the index requirement.
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