CN114235007A - Method and system for positioning and integrity monitoring of APNT service - Google Patents

Method and system for positioning and integrity monitoring of APNT service Download PDF

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CN114235007A
CN114235007A CN202111461447.5A CN202111461447A CN114235007A CN 114235007 A CN114235007 A CN 114235007A CN 202111461447 A CN202111461447 A CN 202111461447A CN 114235007 A CN114235007 A CN 114235007A
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CN114235007B (en
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王志鹏
朱衍波
黄思琪
方堃
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Beihang University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
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Abstract

The invention discloses a method and a system for positioning and monitoring integrity of APNT service, wherein the method comprises the following steps: determining the positioning precision requirement under a target scene; when the positioning precision requirement is high-precision positioning, determining the position of the aircraft by adopting a combined positioning algorithm, and carrying out integrity monitoring on the combined positioning by adopting a multi-solution separation mode; when the positioning precision requirement is low precision positioning, judging whether the aircraft is a high-altitude user; if not, determining the position of the aircraft by adopting an air-to-air positioning algorithm of high-altitude users and low-altitude users based on LDACS, and carrying out integrity monitoring on the air-to-air positioning by adopting a least square residual method. The method can provide a plurality of APNT alternative schemes for the aircraft according to different requirements of users on positioning accuracy and actual application conditions, and carry out fault detection algorithm research aiming at each alternative scheme to realize integrity monitoring of APNT service.

Description

Method and system for positioning and integrity monitoring of APNT service
Technical Field
The invention relates to the technical field of aviation navigation, in particular to a method and a system for monitoring positioning and integrity of an APNT service.
Background
The modernization of air transportation systems places higher demands on the performance of air navigation systems. The Global Navigation Satellite System (GNSS) mainly includes a Global Positioning System (GPS) in the united states, a Global Navigation Satellite System (GLONASS) in russia, a Galileo Satellite Navigation System (Galileo Satellite Navigation System) in europe, and a BeiDou Satellite Navigation System (BDS) in china. By virtue of its high precision and availability, GNSS has become the top system for providing Positioning, Navigation and Timing (PNT) services worldwide.
However, the GNSS signal has low power and a long propagation distance, so the GNSS signal is very easily interrupted by radio frequency interference during the propagation process, and if only the global satellite navigation system is relied on during the flight process, the navigation information may be lost after the aircraft is interrupted by interference, and a flight accident may be caused in a serious case. As a common Navigation system next to GNSS, the error of Inertial Navigation System (INS) is accumulated over time, and its use is limited in time. Therefore, the existing Navigation assistance system must be used as a backup system to provide alternate Positioning, Navigation and time service (APNT) services for the aircraft when the GNSS is unavailable, so as to construct an aviation Navigation network and ensure the continuity and integrity of flight.
The navigation assistance System mainly includes a Distance Measuring Instrument (DME), a very high frequency Omnidirectional Radio (VOR), an Instrument Landing System (ILS), a barometric altimeter, and other novel systems with navigation capability, such as an L-band Digital Aeronautical Communication System (LDACS).
Currently, the Next Generation Air transport System (Next Generation Air transport System, NextGen) in the united states and the Single Sky Air traffic management Research project (SESAR) in europe have both been studied for the APNT service and proposed alternatives (e.g., DME enhancement System, LDACS, SSR-based mode N and eLoran, etc.), but further Research is still needed to determine how to select among these in a sustainable way without risking the implementation of Dual-Frequency Multi-Constellation (DFMC) GNSS. SESAR studies were conducted from three levels, short term, medium term and long term, for the maturity of the APNT service. Among them, short-term studies are mainly based on DME/DME solutions to achieve APNT services; the middle-term research is mainly based on a Multi-DME positioning algorithm with Receiver Autonomous Integrity Monitoring (RAIM) to realize APNT service; long-term goals have planned to achieve APNT services through the advanced architecture of LDACS and eLORAN, which can provide better Performance, and support Performance-Based Navigation (PBN)/Required Navigation Performance (RNP) operations using alternative technologies. Future APNT services will use existing navigation equipment and new navigation technology to make modular combination, and achieve the RNP0.3 goal in the terminal mobile area.
The development of the APNT service faces many problems, among which, the improvement of the positioning accuracy and the integrity monitoring are the most urgent to be solved.
Disclosure of Invention
The invention aims to provide a method and a system for monitoring the positioning and integrity of an APNT service, which realize the integrity monitoring of the APNT service on the premise of ensuring the positioning precision.
In order to achieve the purpose, the invention provides the following scheme:
a method of location and integrity monitoring of an APNT service, comprising:
determining the positioning precision requirement under a target scene;
when the positioning precision requirement is high-precision positioning, determining the position of the aircraft by adopting a combined positioning algorithm, and carrying out integrity monitoring on the combined positioning by adopting a multi-solution separation mode;
when the positioning precision requirement is low precision positioning, judging whether the aircraft is a high-altitude user;
if not, determining the position of the aircraft by adopting an air-to-air positioning algorithm of high-altitude users and low-altitude users based on LDACS, and carrying out integrity monitoring on the air-to-air positioning by adopting a least square residual method.
Optionally, the method further includes: when the aircraft is a high-altitude user, determining the position of the aircraft by adopting a DME/DME-based positioning algorithm, and carrying out integrity monitoring on the DME/DME-based positioning algorithm.
Optionally, the integrity monitoring of the DME/DME-based localization algorithm specifically includes:
calculating the position of the aircraft before the new measuring station is introduced and the position of the aircraft after the new measuring station is introduced;
calculating a protection level of the DME/DME-based positioning algorithm based on the position of the aircraft before the introduction of the new station and the position of the aircraft after the introduction of the new station;
the protection level is compared to a required level warning limit for the route to complete integrity monitoring of the DME/DME based positioning algorithm.
Optionally, the determining the position of the aircraft by using the air-to-air positioning algorithm based on the LDACS for the high-altitude user and the low-altitude user specifically includes:
determining the position information of the high-altitude user by using a Multi-DME positioning algorithm;
determining the measurement distance between the high-altitude user and the low-altitude user based on the two-way distance measurement function of the LDACS;
and determining the position of the aircraft according to the measuring distance and the position information of the high-altitude user.
Optionally, the integrity monitoring of the space-to-space positioning by using the least square residual method specifically includes:
calculating a detection threshold value of the fault according to the false detection probability of the system;
calculating a minimum detectable fault according to the detection threshold and the missed detection probability;
calculating a horizontal precision factor of the system;
calculating a horizontal protection level of the system from the minimum detectable fault and the horizontal precision factor;
and completing the integrity monitoring of the air-to-air positioning based on the horizontal protection level.
Optionally, the determining the position of the aircraft by using the combined positioning algorithm specifically includes:
calculating ranging errors obtained by bidirectional ranging of m DME stations and pseudo-range errors obtained by unidirectional measurement of n LDACS stations;
constructing an observation equation of a ranging system based on the ranging error and the pseudo-range error;
taking the air pressure height as an observed quantity, and introducing an air pressure lift height table into the system to obtain a height observation equation;
constructing an observation model of the system based on the observation equation and the height observation equation;
and solving the observation model by adopting a least square method to determine the position of the aircraft.
Optionally, the integrity monitoring of the combined positioning by using a multi-solution separation method specifically includes:
calculating a state main estimate and a state sub-estimate based on an observation model of the system;
calculating a difference covariance matrix based on the state main estimate and the state sub-estimate;
constructing a horizontal position test statistic based on the difference covariance matrix;
calculating a detection threshold value of the fault according to the false detection probability;
determining whether there is a fault based on the test statistic and the detection threshold;
if the fault exists, isolating the fault and calculating the protection level of the system;
if no fault exists, directly calculating the protection level of the system;
and completing the integrity monitoring of the combined positioning according to the protection level.
A location and integrity monitoring system for APNT services, comprising:
the requirement determining module is used for determining the positioning precision requirement in the target scene;
the first positioning and integrity monitoring module is used for determining the position of the aircraft by adopting a combined positioning algorithm and monitoring the integrity of the combined positioning by adopting a multi-solution separation mode when the positioning precision requirement is high-precision positioning;
the judging module is used for judging whether the aircraft is a high-altitude user or not when the positioning precision requirement is low-precision positioning;
and the second positioning and integrity monitoring module is used for determining the position of the aircraft by adopting an air-to-air positioning algorithm of high-altitude users and low-altitude users based on LDACS when the aircraft is a low-altitude user, and monitoring the integrity of the air-to-air positioning by adopting a least square residual method.
Optionally, the method further includes: and the third positioning and integrity monitoring module is used for determining the position of the aircraft by adopting a DME/DME-based positioning algorithm and carrying out integrity monitoring on the DME/DME-based positioning algorithm when the aircraft is a high-altitude user.
Optionally, in the aspect of determining the position of the aircraft by using the air-to-air positioning algorithm based on the LDACS for the high-altitude users and the low-altitude users, the second positioning and integrity monitoring module specifically includes:
the high-altitude user position information unit is used for determining the position information of the high-altitude users by adopting a Multi-DME positioning algorithm;
the measuring distance determining unit is used for determining the measuring distance between the high-altitude user and the low-altitude user based on the two-way distance measuring function of the LDACS;
and the position determining unit is used for determining the position of the aircraft according to the measuring distance and the position information of the high-altitude user.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides a method and a system for monitoring positioning and integrity of an APNT service, which are used for providing a plurality of APNT alternative schemes for an aircraft according to different requirements of a user on positioning accuracy and actual application conditions under the condition that the accuracy is reduced or even unavailable due to interference of GNSS-based aviation navigation, and carrying out fault detection algorithm research on each alternative scheme to realize the integrity monitoring of the APNT service.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flow chart illustrating a method for location and integrity monitoring of APNT services according to the present invention;
FIG. 2 is a general flow chart of a method for location and integrity monitoring of APNT services according to the present invention;
FIG. 3 is a diagram of a multi-resolution separation method hierarchy according to the present invention;
FIG. 4 is a flow chart of the multiple solution isolated APNT integrity monitoring algorithm of the present invention;
fig. 5 is a schematic diagram of a location and integrity monitoring system of the APNT service according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The most basic APNT method is based on DME/DME to achieve location, but this method requires the user to be able to transmit information with a certain number of DME stations without interruption during the flight. However, for aircraft with low flying height, due to the influence of terrain and urban environment, part of ground DME ranging sources may be shielded, which results in the reduction of positioning accuracy calculated by users, and even renders the APNT unusable when the number of ranging sources is reduced to a certain extent. Aiming at the problem, according to the bidirectional ranging function of the LDACS, the invention utilizes the high-altitude user with higher positioning precision obtained by Multi-DME as an airborne ranging source to provide position information for the low-altitude user, realizes positioning by measuring pseudo range in a similar way to GNSS, realizes air-to-air cooperative positioning integrity monitoring based on least square residual algorithm, and further calculates the protection level of the system by utilizing the minimum detectable fault. However, the positioning accuracy that this method can provide is limited for users with higher positioning accuracy requirements. Aiming at the problem, the invention provides a positioning method combining DME, LDACS and a pneumatic altimeter, positioning is realized by combining three observed quantities of ranging, pseudo-range measurement and height measurement and utilizing a residual error minimization algorithm, and the method can provide higher positioning accuracy for users.
Another important issue facing APNT is the issue of integrity monitoring. RNP requires that On-Board equipment must have On-Board Performance Monitoring and Alerting (OPMA) capabilities, while DME/DME localization may not support such RNP navigation specifications. Therefore, the concept of On-Ground Performance Monitoring and Alerting (GPMA) based On RNP support is proposed, and similar to RAIM algorithm commonly used in GNSS, the integrity Monitoring is carried out On DME/DME system. For a positioning method combining DME, LDACS and a pneumatic altimeter, integrity monitoring is mainly carried out through redundancy measurement.
In view of this, the present invention provides a method and a system for positioning and integrity monitoring of an APNT service, which achieve integrity monitoring of the APNT service on the premise of improving positioning accuracy.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
The purpose of the invention is mainly realized by the following technical scheme:
1. accurate positioning and precision estimation of high altitude users are realized through DME/DME.
2. Determining a fault mode introduced in DME/DME positioning, calculating corresponding position deviation, realizing fault detection by introducing a new measuring station, calculating a system protection level, and simultaneously comparing the protection level with an alarm limit to judge the availability of the system.
3. The positioning of high-altitude users is realized through Multi-DME, and the space-to-space cooperative positioning between the high-altitude users and the low-altitude users is realized based on the LDACS bidirectional ranging function.
4. Determining a fault mode introduced in space-to-space cooperative positioning based on LDACS, designing a fault detection algorithm according to the characteristics of the fault mode, modeling the residual error of the positioning error, and calculating the protection level of the system.
5. And the DME/LDACS/air pressure type altimeter is combined, and the high-precision positioning of the user is realized by using a least square method.
6. And (3) monitoring the integrity of combined positioning by adopting a multi-solution separation algorithm, calculating positioning errors of the complete set and each corresponding subset, detecting and eliminating APNT faults, calculating a system protection level and judging the availability of the system.
Example one
As shown in fig. 1 and fig. 2, the method for locating and monitoring integrity of APNT service provided in this embodiment includes the following steps.
Step 101: determining the positioning precision requirement under a target scene; the target scene is a scene when the GNSS is unavailable.
Step 102: and when the positioning precision requirement is high-precision positioning, determining the position of the aircraft by adopting a combined positioning algorithm, and carrying out integrity monitoring on the combined positioning by adopting a multi-solution separation mode.
Step 103: when the positioning precision requirement is low precision positioning, judging whether the aircraft is a high-altitude user; if not, go to step 104; if yes, go to step 105.
Step 104: the method comprises the steps of determining the position of an aircraft by adopting an air-to-air positioning algorithm of high-altitude users and low-altitude users based on LDACS, and monitoring the integrity of the air-to-air positioning by adopting a least square residual method.
Step 105: when the aircraft is a high-altitude user, determining the position of the aircraft by adopting a DME/DME-based positioning algorithm, and carrying out integrity monitoring on the DME/DME-based positioning algorithm.
Wherein, step 105 specifically comprises:
1. DME/DME-based localization principle
DME refers to a distance measuring instrument, is a distance measuring device widely applied to aviation navigation, and consists of an interrogator at an airborne end and a transponder on the ground. In operation, an interrogator sends an interrogation signal and transponders transmit in sequence a response synchronized with the interrogation signal. In this way, the DME system can measure the pitch between the aircraft and the ground platform. The single DME station cannot realize the positioning of the aircraft, and the position of the aircraft can be determined only when two or more DME stations simultaneously receive signals.
In positioning based on the DME/DME positioning principle, the aircraft must be located within the coverage area of the DME station and be able to receive input signals of at least two DME stations simultaneously. If only two DME station inputs can be received, the angle between the aircraft and the two DME stations is between 30 degrees and 150 degrees. DME/DME is one of the main ways to support Regional Area Navigation (RNAV), which has a positioning accuracy inferior to GNSS.
2. The DME/DME integrity monitoring algorithm specifically comprises the following steps: calculating the position of the aircraft before the new measuring station is introduced and the position of the aircraft after the new measuring station is introduced; calculating a protection level of the DME/DME-based positioning algorithm based on the position of the aircraft before the introduction of the new station and the position of the aircraft after the introduction of the new station; comparing the protection level to a required level warning limit for the route to complete integrity monitoring of the DME/DME-based positioning algorithm; the detailed process is as follows:
the DME signal may be threatened during propagation, on one hand, it may be influenced by terrain to generate multipath effect, resulting in error of ranging information, on the other hand, the signal may be interfered by other signals in the same channel, resulting in error of receiving the signal. The former can be improved by the change of signal waveform and echo suppression mechanism, and the latter needs frequency allocation and compatibility research on signals. The invention herein unifies this as a transponder failure that will be reflected in the DME station position bias, resulting in a non-zero average value of the DME error distribution.
Assuming that the DME errors follow a normal distribution, the mean value of the error of a non-faulty transponder is zero, and the mean value of a faulty transponder is equal to the station bias:
Figure BDA0003388912800000081
wherein the content of the first and second substances,
Figure BDA0003388912800000082
refers to the standard deviation of the ranging deviation of the DME station,
Figure BDA0003388912800000083
σSiS＝0.05NM，σair＝max{0.085NM,0.00125Di}，Dithe finger tilt distance.
Calculating the position based on i, j two DME stations, and obtaining a horizontal position error:
Figure BDA0003388912800000091
wherein alpha isijIs the angle between the aircraft and the two stations,
Figure BDA0003388912800000092
should follow a normal distribution:
Figure BDA0003388912800000093
wherein:
Figure BDA0003388912800000094
Figure BDA0003388912800000095
designing a single fault scene: assuming that the aircraft obtains an initial effective position through two fault-free DME stations, and as the position of the aircraft changes, the initial two stations no longer meet the geometric conditions, a new DME3 station is introduced to replace the initial station, and a Flight Management System (FMS) compares the position of the aircraft before the introduction of the new station with the introduced position to determine a potential ranging deviation, and then calculates the protection level of the position solution.
Order the range error R obtained based on two fault-free initial stations12Compliance
Figure BDA0003388912800000096
Fault DME3 based ranging error R3Obeying N (mu, sigma)D) The fault judgment form is as follows:
|R12-R3|>T→failure (6)；
defining test statistic R ═ R12-R3Wherein
Figure BDA0003388912800000097
If DME3 is not faulty, test statistic R obeys N (0, σ)R) From the false detection probability PfdThe fault detection threshold T can be found:
Figure BDA0003388912800000098
if DME3 is faulty, test statistic R obeys N (mu, sigma)R) From the probability of missed detection PmdAnd a detection threshold value T to obtain a minimum detectable deviation mum：
Figure BDA0003388912800000101
Assuming that the aircraft uses DME3 and DME1 for ranging, the calculation of the system Level Protection Level (HPL) is achieved by deviation detection:
Figure BDA0003388912800000102
the HPL is compared to a required level warning limit for the route and if the protection level is greater than the warning limit, the system is unavailable.
The method for determining the position of the aircraft by adopting the air-to-air positioning algorithm of the high-altitude user and the low-altitude user based on the LDACS specifically comprises the following steps:
determining the position information of the high-altitude user by using a Multi-DME positioning algorithm; determining the measurement distance between the high-altitude user and the low-altitude user based on the two-way distance measurement function of the LDACS; and determining the position of the low-altitude aircraft according to the measuring distance and the position information of the high-altitude user. The detailed process is as follows:
(1) LDACS-based air-to-air positioning algorithm for high-altitude users and low-altitude users
Due to the influence of terrain shielding, the performance of receiving and transmitting navigation signals by low-altitude users is limited, and positioning is difficult to realize. Compared with the method, the high-altitude user can obtain ranging information and ranging error information from more ground ranging sources, for example, accurate positioning is realized by a Multi-DME method, the ranging information and the ranging error information are used as airborne ranging sources to broadcast own position information and covariance matrixes to the low-altitude user, the distance measurement between the high-altitude user and the low-altitude user is realized by combining the air-to-air communication capacity of the LDACS, and the low-altitude user can obtain the own position. Considering the limited number of high-altitude ranging sources, only two-dimensional positioning is carried out, and the height measurement is assisted by the air pressure altimeter.
Measuring y from the position of high-altitude user ranging source AAPerforming empty-to-empty measurement with position error epsilonAObey distribution N (0, Sigma)A). The distance between the low-altitude user and the airborne ranging source n is as follows:
r(n)＝(xu-x(n))·1(n)+T(n)+M(n)+c·(dt(n)-dtu)+ε(n)(10) (ii) a Wherein xuAnd x(n)Respectively the position of the aircraft and the ranging source, ∈(n)For distance measurement error, T(n)For tropospheric delay, M(n)Is a multipath effect, dt(n)Indicating the clock offset, dt, of the onboard ranging sourceuIndicating the clock offset of the subscriber receiver, 1(n)A set of unit vectors along the line connecting the user receiver and the ranging source, referred to herein as the line of Sight (LoS) vectors.
Tropospheric delay T in the context of RNP operation(n)And the effects of multipath M(n)Are negligible, since they usually only give rise to the ratio σrA random error that is orders of magnitude smaller. The pseudorange measurement between an airborne ranging source and a low-altitude user is realized through the two-way ranging function of the LDACS:
Figure BDA0003388912800000111
wherein, ttAnd trRespectively, the time at which the low-altitude user transmits and receives the signal, τ represents the known inherent delay of the high-altitude ranging source from receiving the signal to transmitting the reply signal, and c represents the speed of light.
In the air-to-air positioning algorithm, an airborne ranging source is different from a satellite or a ground ranging source, the position of the airborne ranging source has non-negligible uncertainty, and the airborne ranging source can be regarded as ephemeris error in the satellite, and noise sigma in distance measurementrAdding uncertainty of airborne ranging source along LoS to obtain ranging error epsilon of low-altitude user j(n)Can be approximated as a zero mean Gaussian distribution N (0, sigma)n,j) Wherein:
Figure BDA0003388912800000112
∑nthe error covariance matrix, which represents the location from the position of the ranging source, is related to the position uncertainty of the ranging source itself, reflecting the accuracy of the range measurements made from the ranging source signal. Since the onboard distance measuring source is throughThe positioning accuracy of the Multi-DME realized positioning can be expressed as:
Figure BDA0003388912800000113
where H denotes the direction cosine matrix between the ranging source and its plurality of DME stations, then,
Figure BDA0003388912800000114
then, the variance of the ranging error is expressed as:
Figure BDA0003388912800000115
position solution is carried out by a weighted minimization residual error method by using two equations (10) and (11):
δxi＝(GTWG)-1GTWδri (16)；
wherein G is a geometric matrix composed of line-of-sight unit vectors and related to the geometric positions of the ranging sources relative to the user, and W is a weighting matrix reflecting the ranging errors caused by the ranging sources and the diagonal elements of the weighting matrix
Figure BDA0003388912800000121
δriFor the distance measurement correction obtained in the iterative process, when | | | xi+1-xi||≤ε,ε>At 0, the user position converges on
Figure BDA0003388912800000122
The positioning error follows a multivariate Gaussian distribution N (0, sigma), and the covariance matrix sigma (G)TWG)-1。
(2) Empty to empty cooperative localization integrity monitoring based on least square residual method specifically includes:
calculating a detection threshold value of the fault according to the false detection probability of the system; calculating a minimum detectable fault according to the detection threshold and the missed detection probability; calculating a horizontal precision factor of the system; calculating a horizontal protection level of the system from the minimum detectable fault and the horizontal precision factor; based on the horizontal protection level, the integrity monitoring of the air-to-air positioning is completed, and the detailed process comprises the following steps:
the air-to-air co-location can achieve integrity monitoring through a least square residual error method.
The linearized pseudorange observation equation is as follows:
Y＝GX+ε (17)；
the position estimate that minimizes the sum of squared range errors is obtained by the least squares method:
Figure BDA0003388912800000123
the ranging residual vector is represented as:
Figure BDA0003388912800000124
wherein Q isνIs a co-factor matrix of the pseudorange residual vectors. Under fault-free conditions, the weighted norm of the residual vector obeys the center χ with degree of freedom N-22Distribution:
Figure BDA0003388912800000125
air-to-air co-location introduces a new failure mode, which may lead to new potential integrity risks. Similar to ephemeris failure in satellite navigation, in air-to-air cooperative positioning, the position broadcast of the airborne ranging source may have a failure Δ x, which will be reflected in the ranging error by the line-of-sight vector:
r(n)＝(xu-(x(n)+Δx))·1(n)+c·(dt(n)-dtu)+ε(n) (21)；
let Δ r be Δ x · 1(n)Then ranging expression under this faultComprises the following steps:
r(n)＝(xu-x(n))·1(n)+Δr(n)+c·(dt(n)-dtu)+ε(n) (22)；
when a fault occurs, the error delta r caused by the ranging fault causes the change of the pseudo-range residual vector, and the mean value of the ranging error corresponding to the position of the fault ranging source in the vector is not zero any more, so that the norm of the pseudo-range residual vector obeys non-center x2Distribution, non-central parameter Δ r2：
Figure BDA0003388912800000131
To evaluate the minimum detectable failure of the system, i.e., the maximum possible failure with a missed detection probability equal to the specified integrity risk. First passing the false detection probability P of the systemfdCalculating a detection threshold T for a faultD：
Figure BDA0003388912800000132
Calculating a minimum detectable failure E based on a detection threshold and a missed detection probabilityr：
Figure BDA0003388912800000133
In an actual navigation process, even if no failure occurs, the integrity monitoring algorithm may be unavailable due to the suboptimal geometry of the visible ranging sources. In order to judge the availability of the algorithm, a level of protection needs to be calculated. The horizontal precision factor HDOP of the airborne ranging source geometric configuration and the horizontal precision factor HDOP after the ith ranging source is removediObtaining the variation delta HDOP of the horizontal precision factori：
Figure BDA0003388912800000134
Finally, from the minimum detectable fault ErAnd the HDOP (horizontal precision factor) of the system calculates the horizontal protection level of the system:
HPL＝δHDOPmax×σA×Er (27)。
the determining the position of the aircraft by using the combined positioning algorithm specifically includes:
calculating ranging errors obtained by bidirectional ranging of m DME stations and pseudo-range errors obtained by unidirectional measurement of n LDACS stations; constructing an observation equation of a ranging system based on the ranging error and the pseudo-range error; taking the air pressure height as an observed quantity, and introducing an air pressure lift height table into the system to obtain a height observation equation; constructing an observation model of the system based on the observation equation and the height observation equation; and solving the observation model by adopting a least square method to determine the position of the aircraft.
(1) Combined positioning algorithm
In case of unavailable GNSS, the DME/DME or LDACS based APNT algorithm can provide basic PNT functionality for users in different airspaces, in combination with the above integrity monitoring algorithm to provide the users with the required navigation performance.
To further meet the higher demands of the partial users on positioning accuracy and integrity, a plurality of positioning methods can be combined to improve the redundancy measurement, for example, the DME, the LDACS and the barometric altimeter are combined, and the positioning is performed based on a residual minimization algorithm, and the algorithm block diagram is shown in fig. 3. The DME provides bidirectional distance measurement, the LDACS provides unidirectional pseudo-range measurement, and the air pressure type altimeter provides altitude information through air pressure measurement. The measurement information of each system is combined to realize higher-precision positioning.
First, the DME and LDACS are calculated to realize the ranging error under positioning.
The ranging error obtained by bidirectional ranging of m DME stations is as follows:
Figure BDA0003388912800000141
where ρ isiDenotes the distance, s, measured by the i-th DME stationiTo be the location of the ith DME station,
Figure BDA0003388912800000142
is the user location.
The pseudo range errors obtained by unidirectional measurement of n LDACS stations are as follows:
Figure BDA0003388912800000143
where ρ isLjRepresenting pseudoranges, s measured by the jth LDACS stationLjFor the location of the jth LDACS station,
Figure BDA0003388912800000151
dt is the clock bias for the user position.
Combining the two to obtain an observation equation of the ranging system:
Figure BDA0003388912800000152
wherein y is an observed quantity, i.e., a difference between the measured quantity and the approximated calculated distance; g is an observation matrix, ai,jAre the coefficients of the observation matrix; x is a state quantity to be estimated which is formed by 3 position errors (delta x, delta y and delta z) and a receiver clock deviation dt under the terrestrial coordinate system; epsilonDIs a vector of order mx 1, ∈LIs an n x 1 order vector, respectively represents the ranging deviation vector caused by propagation uncertainty and receiver noise in DME and LDACS ranging processes, and has standard deviation of sigmaDAnd σL。
In order to introduce the observation information of the air pressure type altimeter into the observation equation, the state quantity needs to be projected to a geographic coordinate system, and the coordinate conversion formula is as follows:
Figure BDA0003388912800000153
Figure BDA0003388912800000154
Figure BDA0003388912800000155
wherein the content of the first and second substances,
Figure BDA0003388912800000156
a is the major radius of the reference ellipsoid, and e is the ellipsoidal oblate rate.
From this iteration, the range error in the geographic coordinate system can be obtained, which is expressed as:
Figure BDA0003388912800000157
where φ, λ, and h denote latitude, longitude, and altitude, respectively, and A denotes a coordinate transformation matrix.
Taking the air pressure height as an observed quantity, introducing an air pressure lift height table into the system, and obtaining a height observation equation:
Figure BDA0003388912800000161
wherein HBIs the height of the air pressure,
Figure BDA0003388912800000162
for estimated height of user, epsilonBThe measurement error of the air pressure type altimeter is expressed, the zero mean value Gaussian distribution is obeyed, and the standard deviation is sigmaB。
Combining the observed quantities to obtain a new observation equation:
Figure BDA0003388912800000163
wherein Z represents observation information including observed quantities of DME, LDACS and the air pressure altimeter; h represents an observation matrix; x represents a state quantity, including three position errors in a geographic coordinate system and a distance measurement error equivalent to a receiver clock error; v is a measured noise matrix with a mean of 0 and a variance matrix of
Figure BDA0003388912800000164
AG is an n multiplied by 4 order matrix and represents a navigation system observation matrix obtained after coordinate transformation of the observation matrix G.
According to the system model, the positioning solution can be solved through a least square method. When the number of sites for DME and LDACS exceeds 3, equation (32) has a unique solution: delta phi1,Δλ1,Δh1Is superimposed on the initial position phi0,λ0,h0And obtaining the next approximate position, substituting the initial position into the equation (32) for iteration until delta phii,Δλi,ΔhiAnd when the required magnitude is reached, the least square solution of the user position under the geographic coordinate system can be obtained.
(2) The APNT integrity monitoring based on multi-solution separation specifically comprises the following steps:
calculating a state main estimate and a state sub-estimate based on an observation model of the system; calculating a difference covariance matrix based on the state main estimate and the state sub-estimate; constructing a horizontal position test statistic based on the difference covariance matrix; calculating a detection threshold value of the fault according to the false detection probability; determining whether there is a fault based on the test statistic and the detection threshold; if the fault exists, isolating the fault and calculating the protection level of the system; if no fault exists, directly calculating the protection level of the system; and completing the integrity monitoring of the combined positioning according to the protection level.
Fault detection
On the basis of establishing an observation model of a combined system, the integrity monitoring of the APNT is realized by adopting a multi-solution separation method. And defining the estimation obtained by using all the observed quantities as a main estimation, and the estimation obtained after excluding one observed quantity as a sub estimation. And setting a fault threshold, and comparing the difference value between different estimations with the set threshold to realize the monitoring and isolation of the APNT fault.
According to the observation equation, a state main estimation under the full observation quantity can be obtained:
X0＝Q0Z＝(HTWH)-1HTWZ (35)；
wherein W ═ R-1Is a positive definite weighting matrix, Q0The dimension is of order 4 × (m + n +1) for a least squares solution matrix under full observation conditions. Removing the ith distance observation quantity, and carrying out state solution by using the residual observation information to obtain a state sub-estimation:
Figure BDA0003388912800000171
of formula (II) to Q'iRepresents a 4 × (m + n) -th order least squares solution matrix under incomplete observation conditions after the ith distance observation is excluded, and Q 'is obtained by zero-filling the ith column for the convenience of subsequent calculation'iExpanded to a 4 (m + n +1) order matrix QiAnd obtaining a sub-estimation:
Xi＝QiZ(i＝1,2,Λ,m+n) (37)；
the covariance matrix of the difference between the main estimate and the sub estimate is:
Figure BDA0003388912800000172
from which horizontal position test statistics are constructed
Figure BDA0003388912800000173
According to the false detection probability PfdCalculating a detection threshold T for a faulti：
Figure BDA0003388912800000174
Wherein the content of the first and second substances,
Figure BDA0003388912800000175
represents dPiMaximum eigenvalue, erf, corresponding to the mid-horizontal position direction-1Is that
Figure BDA0003388912800000181
The inverse function of (c).
And carrying out fault judgment according to the m + n groups of test statistics and the fault detection threshold value according to the following steps:
(1) without fault H0: all test statistics satisfy di≤Ti；
(2) There is a fault H1: there is at least one set of test statistics satisfying di>Ti。
Fault isolation
After the fault is detected, the fault needs to be positioned and identified so as to realize fault isolation. By estimating XiAnd its sub-estimation Xi,jThe processing process is similar to the fault detection process, and the test statistic d needs to be calculated firsti,jAnd a detection threshold Ti,jThen, a decision is made, and the basis for judging that the nth ranging source has a fault is as follows: if there is and only one sub-estimate XnTest statistic X from all its estimatesn,jAre less than the fault detection threshold, then the nth ranging source needs to be isolated.
If all the sub-estimates and all the corresponding sub-estimates are larger than the fault detection threshold value, the fault of the multiple ranging sources is indicated, and the fault needs to be further analyzed by analogy with the method.
The multi-solution separation hierarchy is shown in FIG. 4.
Guard level computation
After the integrity monitoring is performed, the availability under the requirement of the integrity is judged, and a horizontal Protection Level (VPL) and a Vertical Protection Level (VPL) of the aircraft are calculated.
Corresponding to each sub-estimate XiHPL ofiIt consists of two parts: first, estimate XiAnd the main estimate X0Threshold for resolution, i.e. by false detection probability PfdCalculated derived fault detection thresholdTi(ii) a Secondly, estimating the self horizontal position error threshold aiNamely:
HPLi＝Ti+ai (40)；
definer estimate XiThe error covariance matrix of (a) is:
Figure BDA0003388912800000182
note the book
Figure BDA0003388912800000183
Is PiThe maximum characteristic value corresponding to the middle horizontal position direction gives the probability P of missed detectionmdThe following can be obtained:
Figure BDA0003388912800000184
and further calculating to obtain the horizontal protection level of the multi-solution separation method:
HPL＝max(HPLi)＝max(Ti+ai) (43)；
similarly, the vertical protection level of the multi-solution separation method can be calculated:
VPL＝max(VPLi)＝max(Di+ai) (44)；
wherein the content of the first and second substances,
Figure BDA0003388912800000191
Figure BDA0003388912800000192
example two
As shown in fig. 5, the present embodiment provides a system for locating and monitoring integrity of an APNT service, including:
a requirement determining module 501, configured to determine a requirement for positioning accuracy in a target scene.
A first positioning and integrity monitoring module 502, configured to determine a position of the aircraft by using a combined positioning algorithm and perform integrity monitoring on the combined positioning by using a multi-solution separation method when the positioning accuracy requirement is high-accuracy positioning.
A determining module 503, configured to determine whether the aircraft is a high-altitude user when the positioning accuracy requirement is low-accuracy positioning.
And a second positioning and integrity monitoring module 504, configured to determine, when the aircraft is a low-altitude user, a position of the aircraft by using an air-to-air positioning algorithm based on the LDACS for the high-altitude user and the low-altitude user, and perform integrity monitoring on the air-to-air positioning by using a least square residual method.
And a third positioning and integrity monitoring module 505 for determining a position of the aircraft using a DME/DME based positioning algorithm and performing integrity monitoring on the DME/DME based positioning algorithm when the aircraft is a high altitude user.
In the aspect of determining the position of the aircraft by using the air-to-air positioning algorithm based on the LDACS for the high-altitude users and the low-altitude users, the second positioning and integrity monitoring module specifically includes:
and the high-altitude user position information unit is used for determining the position information of the high-altitude users by adopting a Multi-DME positioning algorithm.
And the measurement distance determining unit is used for determining the measurement distance between the high-altitude user and the low-altitude user based on the two-way ranging function of the LDACS.
And the position determining unit is used for determining the position of the aircraft according to the measuring distance and the position information of the high-altitude user.
Compared with the prior art, the innovation part of the invention is as follows:
the invention provides a method for classifying according to the requirement of a user on positioning accuracy and actual application conditions, and provides three different APNT algorithms in consideration of various situation characteristics;
1. provides a method for realizing air-to-air relative cooperative positioning by utilizing the two-way distance measurement function of LDACSAn algorithm flow gives the position error of the airborne ranging source for realizing the positioning through the Multi-DME
Figure BDA0003388912800000201
Ranging error for positioning low-altitude user through LDACS
Figure BDA0003388912800000202
2. A special fault mode in the air-to-air cooperative positioning, namely the self position information fault of the airborne ranging source is analyzed and is similar to the ephemeris fault in the satellite navigation, and a ranging expression r in the fault mode is given(n)＝(xu-x(n))·1(n)+Δr(n)+c·(dt(n)-dtu)+ε(n)A method for carrying out fault detection by using chi-square detection and solving a detection threshold value is provided for the specific fault;
3. the horizontal protection level calculation method is suitable for the LDACS-based air-to-air cooperative positioning algorithm, and the HPL is delta HDOPmax×σA×ErFor judging the availability of the APNT system;
4. respectively providing ranging error expressions under positioning realized by using DME and LDACS, and providing an observation equation of a ranging system formed by combining m DME bidirectional ranging quantities and n LDACS pseudo-range measurements
Figure BDA0003388912800000203
5. The novel combined positioning method for realizing the APNT service by using the measurement information combination of the DME/LDACS/air pressure type altimeter is provided;
6. the observation equation obtained by combining DME/LDACS is converted into a geographic coordinate system through coordinates and is combined with the height observation quantity provided by the air pressure type altimeter to obtain a combined observation equation
Figure BDA0003388912800000211
The method (1) carries out positioning solution by a least square method;
7. according to DMThe characteristics of the E/LDACS/air pressure type altimeter combined positioning system provide a process for integrity monitoring by adopting a multi-solution separation algorithm: calculating a state primary estimate X from a state equation0＝Q0Z＝(HTWH)-1HTWZ and State sub-estimate Xi＝QiZ, constructing new horizontal position test statistic according to system characteristics
Figure BDA0003388912800000212
Calculating a detection threshold
Figure BDA0003388912800000213
Carrying out system fault judgment according to the test statistic and the fault detection threshold;
8. giving the estimation of X by calculating the state sub-estimate after the detection of a faultiSub-estimate X of sum sub-estimatei,jRealizing the process of fault isolation of the APNT ranging source;
9. a method for calculating APNT horizontal and vertical protection levels according to a covariance matrix of a main estimation difference value and a sub estimation difference value obtained by a DME/LDACS/pneumatic altimeter combined state equation and the false detection probability and the false alarm probability of a system is provided.
According to the scheme provided by the invention, the beneficial effects of the invention are as follows:
first, the present invention provides a number of APNT alternatives to aircraft, providing a solution to the positioning problem of aircraft where GNSS is not available;
secondly, the invention provides a relative positioning method for low-altitude users sheltered by terrain or buildings according to the two-way distance measurement function of LDACS;
thirdly, the invention provides a method for carrying out combined positioning by utilizing a DME/LDACS/air pressure type altimeter, and the positioning precision of the APNT is further improved;
fourthly, in order to realize integrity monitoring of APNT, the invention provides a fault detection algorithm suitable for each positioning algorithm, and the usability of the algorithm is proved by calculating the protection level;
fifthly, the method is helpful for improving the domestic attention degree of the APNT and promoting the popularization and application of the algorithm.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (10)

1. A method for location and integrity monitoring of APNT service, comprising:
determining the positioning precision requirement under a target scene;
when the positioning precision requirement is high-precision positioning, determining the position of the aircraft by adopting a combined positioning algorithm, and carrying out integrity monitoring on the combined positioning by adopting a multi-solution separation mode;
when the positioning precision requirement is low precision positioning, judging whether the aircraft is a high-altitude user;
if not, determining the position of the aircraft by adopting an air-to-air positioning algorithm of high-altitude users and low-altitude users based on LDACS, and carrying out integrity monitoring on the air-to-air positioning by adopting a least square residual method.
2. The method of claim 1, further comprising: when the aircraft is a high-altitude user, determining the position of the aircraft by adopting a DME/DME-based positioning algorithm, and carrying out integrity monitoring on the DME/DME-based positioning algorithm.
3. The method of claim 2, wherein the integrity monitoring of the DME/DME-based localization algorithm comprises:
calculating the position of the aircraft before the new measuring station is introduced and the position of the aircraft after the new measuring station is introduced;
calculating a protection level of the DME/DME-based positioning algorithm based on the position of the aircraft before the introduction of the new station and the position of the aircraft after the introduction of the new station;
the protection level is compared to a required level warning limit for the route to complete integrity monitoring of the DME/DME based positioning algorithm.
4. The method of claim 1, wherein the determining the position of the aircraft using the air-to-air positioning algorithm based on LDACS for high-altitude users and low-altitude users comprises:
determining the position information of the high-altitude user by using a Multi-DME positioning algorithm;
determining the measurement distance between the high-altitude user and the low-altitude user based on the two-way distance measurement function of the LDACS;
and determining the position of the low-altitude aircraft according to the measuring distance and the position information of the high-altitude user.
5. The method of claim 1, wherein the performing integrity monitoring on the null-to-null positioning by using the least-squares residual method specifically comprises:
calculating a detection threshold value of the fault according to the false detection probability of the system;
calculating a minimum detectable fault according to the detection threshold and the missed detection probability;
calculating a horizontal precision factor of the system;
calculating a horizontal protection level of the system from the minimum detectable fault and the horizontal precision factor;
and completing the integrity monitoring of the air-to-air positioning based on the horizontal protection level.
6. The method for location and integrity monitoring of APNT services as claimed in claim 1, wherein said determining the location of the aircraft using a combined location algorithm specifically comprises:
calculating ranging errors obtained by bidirectional ranging of m DME stations and pseudo-range errors obtained by unidirectional measurement of n LDACS stations;
constructing an observation equation of a ranging system based on the ranging error and the pseudo-range error;
taking the air pressure height as an observed quantity, and introducing an air pressure lift height table into the system to obtain a height observation equation;
constructing an observation model of the system based on the observation equation and the height observation equation;
and solving the observation model by adopting a least square method to determine the position of the aircraft.
7. The method of claim 6, wherein the integrity monitoring of the position and integrity of the APNT service by using the multi-solution separation method specifically comprises:
calculating a state main estimate and a state sub-estimate based on an observation model of the system;
calculating a difference covariance matrix based on the state main estimate and the state sub-estimate;
constructing a horizontal position test statistic based on the difference covariance matrix;
calculating a detection threshold value of the fault according to the false detection probability;
determining whether there is a fault based on the test statistic and the detection threshold;
if the fault exists, isolating the fault and calculating the protection level of the system;
if no fault exists, directly calculating the protection level of the system;
and completing the integrity monitoring of the combined positioning according to the protection level.
8. A system for location and integrity monitoring of an APNT service, comprising:
the requirement determining module is used for determining the positioning precision requirement in the target scene;
the first positioning and integrity monitoring module is used for determining the position of the aircraft by adopting a combined positioning algorithm and monitoring the integrity of the combined positioning by adopting a multi-solution separation mode when the positioning precision requirement is high-precision positioning;
the judging module is used for judging whether the aircraft is a high-altitude user or not when the positioning precision requirement is low-precision positioning;
and the second positioning and integrity monitoring module is used for determining the position of the aircraft by adopting an air-to-air positioning algorithm of high-altitude users and low-altitude users based on LDACS when the aircraft is a low-altitude user, and monitoring the integrity of the air-to-air positioning by adopting a least square residual method.
9. The system of claim 8, further comprising: and the third positioning and integrity monitoring module is used for determining the position of the aircraft by adopting a DME/DME-based positioning algorithm and carrying out integrity monitoring on the DME/DME-based positioning algorithm when the aircraft is a high-altitude user.
10. The system of claim 8, wherein the second location and integrity monitoring module, in determining the position of the aircraft using the air-to-air location algorithm with LDACS-based high altitude users and low altitude users, comprises:
the high-altitude user position information unit is used for determining the position information of the high-altitude users by adopting a Multi-DME positioning algorithm;
the measuring distance determining unit is used for determining the measuring distance between the high-altitude user and the low-altitude user based on the two-way distance measuring function of the LDACS;
and the position determining unit is used for determining the position of the low-altitude aircraft according to the measuring distance and the position information of the high-altitude user.
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