CN110646821A - Train integrity detection method based on moving baseline calculation - Google Patents

Train integrity detection method based on moving baseline calculation Download PDF

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CN110646821A
CN110646821A CN201910918263.3A CN201910918263A CN110646821A CN 110646821 A CN110646821 A CN 110646821A CN 201910918263 A CN201910918263 A CN 201910918263A CN 110646821 A CN110646821 A CN 110646821A
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satellite
difference
antenna
train
tail
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姜维
刘永强
王剑
蔡伯根
刘丹
上官伟
陆德彪
刘江
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Beijing Jiaotong University
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Beijing Jiaotong University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/42—Determining position
    • G01S19/43—Determining position using carrier phase measurements, e.g. kinematic positioning; using long or short baseline interferometry
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B61—RAILWAYS
    • B61L—GUIDING RAILWAY TRAFFIC; ENSURING THE SAFETY OF RAILWAY TRAFFIC
    • B61L23/00—Control, warning, or like safety means along the route or between vehicles or vehicle trains
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B61—RAILWAYS
    • B61L—GUIDING RAILWAY TRAFFIC; ENSURING THE SAFETY OF RAILWAY TRAFFIC
    • B61L25/00—Recording or indicating positions or identities of vehicles or vehicle trains or setting of track apparatus
    • B61L25/02—Indicating or recording positions or identities of vehicles or vehicle trains
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/40—Correcting position, velocity or attitude
    • G01S19/41—Differential correction, e.g. DGPS [differential GPS]
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/42—Determining position
    • G01S19/51—Relative positioning

Abstract

The invention provides a train integrity detection method based on moving baseline calculation. The method comprises the following steps: eliminating clock errors of a satellite and a receiver and ionosphere and troposphere delay errors related to a propagation path by adopting a double-difference carrier phase method, and estimating relative position coordinates between the two antennas at the head and the tail of the column by using Kalman filtering so as to obtain the length of a base line between the two antennas at the head and the tail of the column; and then comparing the calculated baseline length with a preset reference baseline length, and judging whether the difference value of the two is within the threshold range. If the train integrity state is within the threshold value range, the train integrity state is normal, otherwise, the train integrity state is abnormal, and a unhooking condition may exist. The method is based on the resolved length of the mobile base line, compares the calculated length with the reference length, further obtains the real-time integrity state information of the train, has the characteristics of good continuity and high reliability, and can effectively reduce the probability of false alarm and false alarm of the integrity of the train.

Description

Train integrity detection method based on moving baseline calculation
Technical Field
The invention relates to the technical field of train integrity detection, in particular to a train integrity detection method based on moving baseline calculation.
Background
The carriages of the train are physically connected together through the couplers, frequent acceleration and braking are needed in the running process of the train, the couplers are damaged under the action of a long time, and therefore the risk of uncoupling exists between the carriages. Once the train is unhooked, the train integrity detection system should be able to give alarm information immediately to avoid accidents such as train derailment or collision with a rear train. In fact, before the train enters the block, it must be ensured that the block has been completely cleared and that the previous train has no cars left in the block. Therefore, the train integrity detection is an important part of a train operation control system, and has important significance for ensuring the train integrity and avoiding rear-end collision and even derailment accidents.
At present, there are three main methods for detecting the integrity of a train in the prior art:
1. the method for detecting the occupancy of the train through the track circuit mainly comprises the following steps: when the train wheels press the steel rails, the current and voltage on the rails are influenced, the state of the relay is changed, and the rail occupation inspection is realized according to the state of the inspection relay. And the remaining carriages after the train coupler is separated can be detected through the track occupation state.
The disadvantages of this method are: the detection method based on the track circuit needs to lay a large amount of ground equipment on an operation line, and the problems of high construction and maintenance cost and the like are faced.
2. The abnormal method for judging the complete state of the train by the pressure of the braking air pipe mainly comprises the following steps: because the brake pipe of train air braking runs through all carriages of the train, the carriage separation accident can cause the wind pressure pipe fracture and leak air, and then lead to the train brake trachea the wind pressure can drop sharply. The tail of the train sends the pressure of a tail air pipe, tail positioning information and the like to the locomotive through a special digital radio station, and the on-board computer compares the received tail air pressure with a standard air pressure value to determine the integrity of the train.
The disadvantages of this method are: the method generally carries out one-time automatic query for two minutes, and cannot ensure the real-time performance of train integrity detection; in addition, the method needs a common communication channel, and communication interference and collision are easily caused, so that the stability of communication is not high.
3. The train integrity detection method based on satellite navigation positioning mainly comprises the following steps: satellite navigation (including GPS, Beidou, GLONASS and the like) antennas are respectively arranged in the top of a head carriage (head) and the top of a tail carriage (tail) of the train, the positions of the head carriage and the tail carriage are calculated in real time, the length of the train is estimated through the position difference of the head carriage and the tail carriage, and the calculation result is compared with the actual length of the train, so that the integrity of the train is detected.
The disadvantages of this method are: when the deviation of the positioning result is large, the calculated positions of the vehicle head and the vehicle tail are inaccurate, and at the moment, the estimated vehicle length error is large, and the false alarm or false alarm probability is large. The error of the method is about 10 meters, the precision is not high enough, not only the potential safety hazards of false alarm and false alarm are existed, but also the improvement of the railway transportation efficiency is not facilitated.
Disclosure of Invention
The embodiment of the invention provides a train integrity detection method based on moving baseline calculation, which aims to overcome the problems in the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme.
A train integrity detection method based on moving baseline calculation comprises the following steps:
step S1, respectively establishing carrier phase observation equations of a train head and a train tail of the train according to the propagation process of the carrier signals, performing single difference on the carrier phase observation equations of the train head and the train tail to obtain a single difference equation of carrier phases, and performing single difference on the single difference equations of the carrier phases corresponding to different satellites to obtain an observation equation of double-difference carrier phases;
s2, establishing a system equation and a measurement equation of a Kalman filtering model according to the observation equation after the double-difference carrier phase, estimating a state vector of the train at each moment according to the Kalman filtering model, and calculating the length of a moving baseline according to the relative positions of two antennas at the head and the tail of the train in the state vector;
step S3, calculating the difference between the length of the moving baseline and a given reference length, judging whether the difference is smaller than a given threshold value, and if so, judging that the integrity state of the train is normal; otherwise, judging that the integrity of the train is abnormal.
Preferably, the step S1 specifically includes:
s11: obtaining a carrier phase observation equation of the two antennae at the head and the tail of the vehicle according to the positioning error of the carrier phase as follows;
Figure BDA0002216739960000032
where φ represents a carrier phase measurement; λ is the wavelength of the carrier signal; ρ is the true distance from the satellite to the antenna; i is the ionospheric delay error; t is the tropospheric delay error; f is the frequency of the carrier wave; δ t is the clock difference of the antenna; dt is the clock error of the satellite; n is the integer ambiguity; epsilon is the sum of errors that are difficult to describe quantitatively, including antenna noise, etc.; i represents the ith satellite; b, r respectively represents a reference station of the vehicle head and an auxiliary station of the vehicle tail;
s12: time alignment processing is carried out on the carrier phase between the two antennas at the head and the tail of the vehicle, and if the time alignment of the carrier phase at the head and the tail of the vehicle is successful, the step S13 is carried out; otherwise, continuing to S12 to enter the next time alignment;
s13: and (3) successfully aligning the time of the carrier phase observed quantity of the locomotive tail, performing double-difference carrier phase error elimination processing, and taking the processed result as the input of S3 moving baseline calculation:
Figure BDA0002216739960000033
s14: according to S13, the part related to the antenna position is
Figure BDA0002216739960000034
From the above derivation, the true double difference distance
Figure BDA0002216739960000035
Can be written as:
Figure BDA0002216739960000041
s15: a reference antenna and an auxiliary antenna are selected, assuming that the reference antenna has coordinates of (x)b,yb,zb) The auxiliary antenna has a rough coordinate of
Figure BDA0002216739960000042
Using the position of the reference antenna b as the approximate position of the antenna r, and performing first-order Taylor expansion on the distance from the auxiliary antenna r to the satellite at the approximate position to obtain:
Figure BDA0002216739960000044
in the formula, the deviation between the actual coordinates and the approximate coordinates of the antennas is expressed as (Δ x, Δ y, Δ z), that is, the relative position between the two antennas;
the coefficients of the first-order taylor expansion represent cosine parameters of the direction of the reference antenna pointing to the satellite, and the cosine parameters defining the directions of the three axes are (l, m, q), then:
Figure BDA0002216739960000045
s＝i,j
s16: substituting the above equation into S14 yields:
Figure BDA0002216739960000046
subjecting the obtained
Figure BDA0002216739960000047
Substituting the expansion of (a) into S13 can result in:
s17: assuming that the number of satellites observed by two antennas simultaneously in the current epoch is n, selecting a reference satellite can obtain (n-1) double-difference equations, and simultaneously establishing the equations and writing the equations into a matrix form to obtain a double-difference observation equation of the carrier phase:
-λφ＝HX-λΝ
wherein, the phi vector is obtained by subtracting the observed value of the carrier phase measured by the antenna twice; solving the H matrix requires the position of the satellite and the approximate position of the reference antenna, the position of the satellite is resolved by satellite ephemeris output by the antenna, and the approximate position of the auxiliary antenna adopts the position of the reference antenna; x is the baseline vector to be solved; Ν consists of (n-1) double-difference integer ambiguities.
Preferably, the double-difference carrier phase error elimination in step S13 includes the following steps:
s131: taking a head antenna as a reference station and a tail antenna as a mobile station, and performing inter-station difference between the reference station and the mobile station to eliminate errors related to a satellite and a propagation path, wherein the errors comprise clock error of the satellite, and delay errors of an ionosphere and a troposphere;
Figure BDA0002216739960000051
in the formula, the subscript br denotes a value of a difference between two antennas;
the antenna simultaneously tracks signals of a plurality of satellites, and supposing that the two antennas observe another satellite j at the same moment, a single difference equation of a carrier phase corresponding to the satellite j is obtained:
Figure BDA0002216739960000052
s132: difference between stars: on the basis of the difference between the S131 stations, selecting a satellite with the best altitude angle as a reference satellite, and making a difference between carrier phases corresponding to other satellites and carrier phases of the reference satellite to obtain:
Figure BDA0002216739960000053
in the formula, the superscript ij indicates that the difference is made between the ith star and the jth star.
Preferably, one satellite with the largest altitude angle is selected as the reference satellite, and the method for calculating the altitude angle of the satellite comprises the following steps:
and calculating the coordinates of the satellite under a carrier coordinate system at the antenna of the locomotive, wherein the conversion relation is as follows:
Figure BDA0002216739960000054
and then calculating the altitude angle of the satellite at the antenna of the locomotive:
θ＝arctan(U2/(E2+N2))
in the formula (X)s,Ys,Zs) Is the position coordinate of the satellite in the earth center earth fixation coordinate system; (E, N, U) are position coordinates of the satellite under a carrier coordinate system with the vehicle head antenna as the center; l and B are respectively the longitude and latitude of the head antenna; θ represents the altitude of the satellite.
Preferably, the position of the reference antenna in S15 is obtained by a single-point positioning method based on the least square principle.
Preferably, the step S2 of establishing the system equation and the measurement equation of the kalman filter model according to the measurement equation of the double-difference carrier phase includes:
the system equation of the Kalman filtering model is as follows:
Xk＝AXk-1+Qk
in the formula, XkIs the state vector of the system; a is a state transition matrix; qkIs the process noise of the system;
the dimension of the state of the system is 6+ (n-1), and comprises the relative position, the relative speed and the double-difference integer ambiguity of three coordinate axis directions under the geocentric geostationary coordinate system:
Figure BDA0002216739960000061
in the formula (I), the compound is shown in the specification,representing the relative velocities in three directions and assuming that they follow a first order markov distribution;
Figure BDA0002216739960000063
is a matrix of double difference integer ambiguities;
state transition matrix:
wherein the time interval Δ T is 0.1 s;
the noise matrix of the system is:
Figure BDA0002216739960000065
wherein τ is the correlation time;
measurement model of the system:
Zk＝HkXk+Vk
in the formula ZkIs the observation vector of the system; hkIs a measurement matrix; vkIs the measurement noise, which is assumed to be white gaussian noise, whose covariance matrix is R.
Systematic observation vector:
Figure BDA0002216739960000071
measurement matrix of the system:
Hk＝[l(n-1)×1 m(n-1)×1 q(n-1)×1 0(n-1)×3 -λ·I(n-1)×(n-1)]
where (l, m, q) is a matrix consisting of the difference of (n-1) cosine parameters (l, m, q).
Noise covariance matrix:
Figure BDA0002216739960000072
in the formula, the parameter σ is a standard deviation of L1 carrier noise, and its value is 0.0008 m.
Preferably, the estimating a state vector of the train at each moment according to a kalman filter model, and calculating the length of the moving baseline according to the relative positions of the two antennas at the head and the tail of the train in the state vector, includes:
setting the relative positions of the two antennas at the head and the tail of the vehicle in the state vector X estimated by Kalman filtering as (delta X, delta y and delta z), and then calculating the length L of the moving base line by the formula;
Figure BDA0002216739960000073
preferably, the step S2 of establishing a system equation and a measurement equation of a kalman filter model according to the measurement equation of the double-difference carrier phase further includes:
1) and when the visible satellite at the current moment is reduced compared with the previous moment, obtaining the PRN number of the unlocked satellite, removing the value corresponding to the unlocked satellite from the state matrix and the covariance matrix of the Kalman filtering model, and then carrying out filtering calculation.
2) When the visible satellites at the current moment are increased compared with the previous moment;
step 1: firstly, obtaining the relative positions (delta x, delta y and delta z) of a head antenna and a tail antenna at the current moment according to the corresponding matrix filtering of the visible satellite at the previous moment;
step 2: using the relative positions (delta x, delta y, delta z) of the two antennae at the head and the tail of the vehicle at the current time to reversely solve the double-difference integer ambiguity corresponding to the increased satellite
Figure BDA0002216739960000081
And step 3: using the double difference integer ambiguity calculated in step 2
Figure BDA0002216739960000082
Updating the state matrix X; the covariance matrix P reserves the corresponding position and speed part, and the rest part is initialized completely;
and 4, step 4: and filtering the updated matrixes X and P once, smoothing and then filtering for the next moment.
According to the technical scheme provided by the embodiment of the invention, the train integrity detection method based on the mobile baseline solution eliminates errors such as clock errors of satellites and antennas, delays of an ionosphere and a troposphere and the like through twice difference of the carrier phase observation equation, and establishes the Kalman filtering observation equation. And dynamically estimating the relative position between the two antennas through a Kalman filtering algorithm, and further calculating to obtain the length of the moving baseline. The calculated moving base line has high precision, and compared with the traditional train integrity detection method, the reliability of train integrity detection is improved, and the probability of false alarm and false alarm is reduced.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced 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 based on these drawings without creative efforts.
Fig. 1 is a processing flow chart of a train integrity detection method based on moving baseline solution according to an embodiment of the present invention;
FIG. 2 is a flow chart of a method for mobile baseline resolution according to an embodiment of the present invention;
fig. 3 is a schematic diagram of a vehicle head antenna as a reference station and a vehicle tail antenna as a mobile station according to an embodiment of the present invention;
fig. 4 is a length of a moving baseline corresponding to two cases, namely normal and abnormal, of the integrity of a train according to an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
As used herein, the singular forms "a", "an", "the" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. It will be understood that when an element is referred to as being "connected" or "coupled" to another element, it can be directly connected or coupled to the other element or intervening elements may also be present. Further, "connected" or "coupled" as used herein may include wirelessly connected or coupled. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.
It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
For the convenience of understanding the embodiments of the present invention, the following description will be further explained by taking several specific embodiments as examples in conjunction with the drawings, and the embodiments are not to be construed as limiting the embodiments of the present invention.
In order to further reduce the error of resolving the train length, the embodiment of the invention provides a train integrity detection method based on moving baseline resolution, and the processing flow of the method is shown in fig. 1 and comprises the following processing steps:
s1, eliminating clock errors of the satellite and the antenna and errors of a troposphere and an ionosphere by adopting a carrier phase based on double differences to obtain an observation equation of the carrier phase based on the double differences;
s2, establishing a system equation and a measurement equation of a Kalman filtering model according to an observation equation after double-difference carrier phases; estimating a state vector at each moment according to a Kalman filtering model, and calculating the length of a moving baseline according to the relative positions of two antennas in the state vector
Step S3, the calculated length of the moving baseline is compared with a given reference length, and the difference between the two lengths is compared with a given threshold. If the train integrity state is within the threshold range, the train integrity state is considered to be normal; and otherwise, if the difference value between the length of the calculated moving baseline and the reference length exceeds the threshold range, the integrity of the train is considered to be abnormal.
Further, the specific processing procedure of step S1 includes:
fig. 2 is a flowchart of moving baseline solution according to an embodiment of the present invention. The propagation of the carrier signal is affected by error sources such as satellite clock error, antenna clock error, ionosphere delay error, troposphere delay error, and the like. According to the propagation process of the carrier signal, the carrier phase observation equation of the two antennae at the head and the tail of the vehicle can be written
Figure BDA0002216739960000101
And
Figure BDA0002216739960000102
Figure BDA0002216739960000103
Figure BDA0002216739960000104
where φ represents a carrier phase measurement; λ is the wavelength of the carrier signal; ρ is the true distance from the satellite to the antenna; i is the ionospheric delay error; t is the tropospheric delay error; f is the frequency of the carrier wave; δ t is the clock difference of the antenna; dt is the clock error of the satellite; n is the integer ambiguity; epsilon is the sum of errors that are difficult to describe quantitatively, including antenna noise, etc.; i represents the ith satellite; b and r respectively represent a reference station at the head of the vehicle and an auxiliary station at the tail of the vehicle.
Difference between stations: as shown in fig. 3, the length between two antennas (train) is about 200m and is much shorter than the distance between the satellite and two observation stations (about 20200km) by using the head antenna as a reference station and the tail antenna as a mobile station, so that it can be considered that the propagation paths between the satellite and the two antennas are the same, and the carrier signals arriving at the two antennas pass through the ionosphere and the troposphere delay error are the same. The errors related to the satellite and the propagation path can be eliminated by carrying out inter-station difference between the reference station and the mobile station, wherein the errors comprise clock error of the satellite, and delay errors of an ionosphere and a troposphere;
performing one-time single difference between the two antennas at the head and the tail of the vehicle to obtain a single difference equation of the carrier phase:
Figure BDA0002216739960000111
in the formula, the subscript br denotes a single difference between the two antennas,
Figure BDA0002216739960000112
the inter-station difference of the carrier phase between the two antennas at the head and the tail of the vehicle.
The antenna can track signals of a plurality of satellites at the same time, and if two antennas observe another satellite j at the same time, a single difference equation of a carrier phase corresponding to the satellite j can be obtained:
Figure BDA0002216739960000113
difference between stars: the antenna itself is unchanged and the clock offset of the antenna can be eliminated after making the difference between the satellites again. On the basis of the difference between stations, one satellite with the best altitude angle is selected as a reference satellite, and the carrier phases corresponding to other satellites are differentiated from the carrier phase of the reference satellite, so that errors related to the antenna, such as antenna clock error, can be eliminated.
Figure BDA0002216739960000114
In the formula, the superscript ij indicates that the difference is made between the ith star and the jth star.
The part of the above formula related to the position of the antenna is
Figure BDA0002216739960000121
From the above derivation, the true double difference distance
Figure BDA0002216739960000122
Can be written as:
Figure BDA0002216739960000123
locating the distance from the secondary antenna to the satellite at a reference antenna position coordinate (x)b,yb,zb) And performing first-order Taylor series expansion on the vicinity to obtain:
Figure BDA0002216739960000124
Figure BDA0002216739960000125
in the equation, the deviation from the actual coordinates of the antenna and the approximate coordinates is expressed as (Δ x, Δ y, Δ z), that is, the relative position between the two antennas.
The coefficients of the first-order taylor expansion represent cosine parameters of the direction of the reference antenna pointing to the satellite, and the cosine parameters defining the directions of the three axes are (l, m, q), then:
Figure BDA0002216739960000126
double differential distance
Figure BDA0002216739960000127
Can be further written as:
Figure BDA0002216739960000128
the observation equation for double-differenced carrier phase can be written as:
Figure BDA0002216739960000129
in the current epoch, the number of satellites observed by two antennas simultaneously is n, and if a reference satellite is selected, (n-1) double-difference equations can be obtained, and the equations are combined and written into a matrix form:
-λφ＝HX-λΝ
the phi vector at the left end of the equation can be obtained by directly making two differences on the observed value of the carrier phase measured by the antenna; the solving of the H matrix requires the position of the satellite and the approximate position of the reference antenna, the position of the satellite can be solved by satellite ephemeris output by the antenna, and the approximate position of the auxiliary antenna adopts the position of the reference antenna; x is the baseline vector to be solved; Ν consists of (n-1) double-difference integer ambiguities.
The method for calculating the satellite altitude angle comprises the following steps:
and calculating the coordinates of the satellite under a carrier coordinate system at the antenna of the locomotive, wherein the conversion relation is as follows:
Figure BDA0002216739960000131
and then calculating the altitude angle of the satellite at the antenna of the locomotive:
θ＝arctan(U2/(E2+N2))
in the formula (X)s,Ys,Zs) Is the position coordinate of the satellite in the earth center earth fixation coordinate system; (E, N, U) are position coordinates of the satellite under a carrier coordinate system with the vehicle head antenna as the center; l and B are respectively the longitude and latitude of the head antenna; θ represents the altitude of the satellite.
Further, the specific processing procedure of step S2 includes:
the Kalman filtering comprises two processes of time updating and state updating. The state matrix of the system is 6+ (n-1) dimensional and comprises relative positions, relative speeds and double-difference integer ambiguity of (n-1) dimension of three coordinate axis directions under the geocentric coordinate system. Then the system state vector X is:
wherein, (Δ x, Δ y, Δ z) represents the relative position of the geocentric geostationary coordinate system in three directions;
Figure BDA0002216739960000133
representing the relative velocities in three directions and assuming that they follow a first order markov distribution;
Figure BDA0002216739960000134
indicating the integer ambiguity for the double-differenced carrier phase.
The measurement vector Z of the system is:
Figure BDA0002216739960000135
wherein:
Figure BDA0002216739960000141
the value obtained by subtracting the carrier phase twice after the inter-station difference and the inter-satellite difference are performed is shown.
Under the condition that the satellite is in a good condition and can be positioned, the double difference of the carrier phases is used as measurement input, the relative position and the relative speed between the head antenna and the tail antenna are estimated through Kalman filtering processing, and then the length of the moving base line is calculated through the relative position.
Kalman filtering includes two main information update processes: time updates and measurement updates.
The time updating comprises the calculation of state one-step prediction and one-step prediction mean square error, and the calculation formulas are respectively as follows:
wherein A represents a state transition matrix, Xk-1Representing the estimated state at time k-1,
Figure BDA0002216739960000143
representing a one-step predicted state at time k, QkRepresenting the noise covariance matrix, Pk -A covariance matrix representing the estimated state error at time k-1.
State transition matrix:
Figure BDA0002216739960000144
wherein the time interval Δ T is 0.1 s.
The noise matrix can be written as:
Figure BDA0002216739960000145
where τ is the correlation time.
Observation matrix:
Figure BDA0002216739960000146
measurement matrix of the system:
Hk＝[l(n-1)×1 m(n-1)×1 q(n-1)×1 0(n-1)×3 -λgI(n-1)×(n-1)]
where (l, m, q) is a matrix consisting of the difference of (n-1) cosine parameters (l, m, q).
Noise covariance matrix:
Figure BDA0002216739960000151
in the formula, the parameter σ is a standard deviation of L1 carrier noise, and its value is 0.0008 m.
The measurement updating comprises the calculation of filter gain, state estimation and estimation mean square error, and the calculation formulas are respectively as follows:
Figure BDA0002216739960000152
wherein H represents a measurement matrix of the system, R represents a covariance matrix of system measurement noise, and KkRepresenting the filter gain, Z representing the observation matrix of the system, PkMean square error, X, representing state estimationkAnd the state of the estimation is represented and consists of two parts of state prediction and state measurement and update, wherein the two parts of state measurement and update comprise the relative position, the relative speed and the double-difference integer ambiguity between the two antennae at the head and the tail of the vehicle.
The measurement matrix H of the system is:
Hk＝[l(n-1)×1 m(n-1)×1 q(n-1)×1 0(n-1)×3 -λ·I(n-1)×(n-1)]
where (l, m, q) is a matrix consisting of the difference of the cosine parameters of the direction of the satellite to the reference station (l, m, q). 0(n-1)×3Is a zero matrix of n-1 rows and 3 columns, I(n-1)×(n-1)An identity matrix of order n-1 is shown, and λ is the wavelength of the carrier signal.
Noise covariance matrix:
Figure BDA0002216739960000161
in the formula, the parameter σ is a standard deviation of the carrier noise, and the value corresponding to the L1 band is 0.0008 m.
And selecting the reference satellite according to the altitude angle of the satellite, and taking the satellite with the best altitude angle as the reference satellite.
The calculation of the satellite altitude angle firstly calculates the coordinates of the satellite under a carrier coordinate system at the antenna of the vehicle head, and the conversion relation is as follows:
Figure BDA0002216739960000162
and then calculating the altitude angle of the satellite at the antenna of the locomotive:
θ＝arctan(U2/(E2+N2))
in the formula (X)s,Ys,Zs) Is the position coordinate of the satellite in the earth center earth fixation coordinate system; (E, N, U) are position coordinates of the satellite under a carrier coordinate system with the vehicle head antenna as the center; l and B are respectively the longitude and latitude of the head antenna; θ represents the altitude of the satellite.
The calculation of the satellite position is to calculate the satellite position according to the broadcast ephemeris, and comprises the following steps:
(1) the average angular velocity n of the satellite motion is calculated.
Firstly, according to the parameters given in the broadcast ephemeris
Figure BDA0002216739960000163
Calculating the average angular velocity n of the reference time TOE0：
Figure BDA0002216739960000164
Wherein GM is the product of gravitational constant G and total mass M of the earth.
Then, calculating the average angular velocity n of the satellite at the observation time according to perturbation parameters delta n given in the broadcast ephemeris:
n＝n0+Δn
(2) calculating mean and near point angle M of observation instantaneous satellite
M＝M0+n(t-TOE)
In the formula, M0The mean anomaly at the reference time TOE is given by the broadcast ephemeris.
(3) Calculating the angle of approach E
E＝M+e sin E
This equation can be solved iteratively or by differential equation correction.
(4) Calculating true proximal angle f
Figure BDA0002216739960000171
Where e is the eccentricity of the satellite orbit, given by the broadcast ephemeris.
(5) Calculating liter intersection distance angle u'
u′＝ω+f
Where ω -is the angular distance to the near location, given by the broadcast ephemeris.
(6) Calculating perturbation correction term deltau,δr,δi
The following 6 perturbation parameters are given in the broadcast ephemeris: cuc,Cus,Crc,Crs,Cic,CisFrom this, the factor J can be obtained2Perturbation correction term delta of ascending angle u caused by termuPerturbation correction term delta of satellite vector ruPerturbation correction of satellite orbit inclination angle iTerm δi. The calculation formula is as follows:
Figure BDA0002216739960000172
(7) calculating u ', r', i0Performing perturbation correction
Figure BDA0002216739960000181
In the formula: a-is the long radius of the satellite orbit,
Figure BDA0002216739960000182
i0-orbit tilt at time TOE, given by kepler parameters in the broadcast ephemeris;
Figure BDA0002216739960000183
the rate of change for i is given by the perturbation parameters in the broadcast ephemeris.
(8) Calculating the position of the satellite in the orbital plane coordinate system
In the orbital plane rectangular coordinate system (the origin of coordinates is located at the earth center, and the X-axis points to the elevation intersection point), the plane rectangular coordinates of the satellite are:
Figure BDA0002216739960000184
(9) calculating the longitude L of the ascending point at the observation moment
Right ascension at the rising intersection at the reference time TOE is ΩTOERate of change of point of intersection to time
Figure BDA0002216739960000185
Then the rising point right ascension Ω at the observation instant t should be:
Figure BDA0002216739960000186
wherein
Figure BDA0002216739960000187
Can be given from perturbation parameters of broadcast ephemeris。
Let the start time of the week (0 time of Sunday) Greenwich mean time be GASTweekThen, the observation of the instantaneous greenish-fixed star time is:
GAST＝GASTweek+ωet
in the formula: omegae-is the earth rotation angular velocity; t-is the time(s) in the week.
Thus, the longitude value of the observation instant ascending and crossing point can be obtained as follows:
Figure BDA0002216739960000188
let omega0＝ΩTOE-GASTweekThen, there are:
Figure BDA0002216739960000189
(10) computing the position of a satellite in a transient global coordinate system
Knowing the geodetic longitude L of the elevation point and the inclination i of the orbital plane, the position of the satellite in the earth-fixed coordinate system can be conveniently found by two rotations:
Figure BDA0002216739960000191
further calculating the length L of the moving base line according to the relative positions (delta X, delta y, delta z) of the two antennae in the state vector X estimated by Kalman filtering;
Figure BDA0002216739960000192
further, the specific processing procedure of step S3 includes:
estimating the real-time length of the baseline, and presetting a reference length and a threshold value according to practical experience, wherein the given reference length is S and the threshold value is eta.
If the solved base length L meets the condition that | L-S | is less than or equal to η, the integrity state of the train is considered to be normal; on the contrary, if the length L of the base line meets the condition that | L-S | is more than or equal to η, the integrity state of the train is considered to be abnormal, and an alarm is given in time.
Fig. 3 is a schematic relationship between train integrity and a moving baseline according to an embodiment of the present invention.
In the case of normal train integrity, as shown in the diagram (a), the length of the moving baseline should satisfy: reference length-threshold ≦ length of moving baseline ≦ reference length + threshold.
In the case of an abnormal train integrity, as shown in the diagram (b), the length of the moving baseline is beyond the range of the "reference length ± threshold".
And after the filtering at the current moment is finished, sequentially performing filtering calculation and baseline calculation at the next moment.
The tracked visible satellites are constantly changing during the actual operation of the train. The state matrix X of the kalman filter includes double-difference ambiguity of the satellite, and the error covariance matrix P includes error information of each satellite, so that when an observed satellite changes, the state matrix X and the error covariance matrix P of the kalman filter correspondingly change.
The change of the satellite can be divided into the following three cases, which are considered respectively:
1) reduction of satellites
And (4) reducing the visible satellites at the moment compared with the previous moment, obtaining the PRN (pseudo random number) of the unlocked satellite, removing the value corresponding to the unlocked satellite from the state matrix and the covariance matrix, and then carrying out filtering calculation.
2) Augmentation of satellites
Step 1: firstly, obtaining the relative positions (delta x, delta y and delta z) of two antennas at the current moment according to the corresponding matrix filtering of the visible satellite at the previous moment;
step 2: according to the formula (11), the double difference integer ambiguity corresponding to the increased satellite is solved by using the relative position of the current time
Figure BDA0002216739960000201
And step 3: double differences calculated in Step 2Integer ambiguityUpdating the state matrix X; the covariance matrix P reserves the corresponding position and speed part, and the rest part is initialized completely;
and 4, step 4: and filtering the updated matrixes X and P once, smoothing and then filtering for the next moment.
3) Satellite reduction with other satellite additions
Firstly, performing satellite reduction treatment according to 1), and then performing satellite addition treatment according to 2).
In summary, in the train integrity detection method based on mobile baseline solution according to the embodiment of the present invention, the clock error of the satellite and the antenna, the delay of the ionosphere and the troposphere, and other errors are eliminated by performing the subtraction twice on the carrier phase observation equation, and the kalman filter observation equation is established. And dynamically estimating the relative position between the two antennas through a Kalman filtering algorithm, and further calculating to obtain the length of the moving baseline. The calculated moving base line has high precision, and compared with the traditional train integrity detection method, the reliability of train integrity detection is improved, and the probability of false alarm and false alarm is reduced.
The method is based on the resolved length of the mobile base line, compares the calculated length with the reference length, further obtains the real-time integrity state information of the train, has the characteristics of good continuity and high reliability, and can effectively reduce the probability of false alarm and false alarm of the integrity of the train.
Those of ordinary skill in the art will understand that: the figures are merely schematic representations of one embodiment, and the blocks or flow diagrams in the figures are not necessarily required to practice the present invention.
From the above description of the embodiments, it is clear to those skilled in the art that the present invention can be implemented by software plus necessary general hardware platform. Based on such understanding, the technical solutions of the present invention may be embodied in the form of a software product, which may be stored in a storage medium, such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method according to the embodiments or some parts of the embodiments.
The embodiments in the present specification are described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, for apparatus or system embodiments, since they are substantially similar to method embodiments, they are described in relative terms, as long as they are described in partial descriptions of method embodiments. The above-described embodiments of the apparatus and system are merely illustrative, and the units described as separate parts may or may not be physically separate, and the parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (8)

1. A train integrity detection method based on moving baseline calculation is characterized by comprising the following steps:
step S1, respectively establishing carrier phase observation equations of a train head and a train tail of the train according to the propagation process of the carrier signals, performing single difference on the carrier phase observation equations of the train head and the train tail to obtain a single difference equation of carrier phases, and performing single difference on the single difference equations of the carrier phases corresponding to different satellites to obtain an observation equation of double-difference carrier phases;
s2, establishing a system equation and a measurement equation of a Kalman filtering model according to the observation equation after the double-difference carrier phase, estimating a state vector of the train at each moment according to the Kalman filtering model, and calculating the length of a moving baseline according to the relative positions of two antennas at the head and the tail of the train in the state vector;
step S3, calculating the difference between the length of the moving baseline and a given reference length, judging whether the difference is smaller than a given threshold value, and if so, judging that the integrity state of the train is normal; otherwise, judging that the integrity of the train is abnormal.
2. The method according to claim 1, wherein the step S1 specifically includes:
s11: obtaining a carrier phase observation equation of the two antennae at the head and the tail of the vehicle according to the positioning error of the carrier phase as follows;
Figure FDA0002216739950000011
where φ represents a carrier phase measurement; λ is the wavelength of the carrier signal; ρ is the true distance from the satellite to the antenna; i is the ionospheric delay error; t is the tropospheric delay error; f is the frequency of the carrier wave; δ t is the clock difference of the antenna; dt is the clock error of the satellite; n is the integer ambiguity; epsilon is the sum of errors that are difficult to describe quantitatively, including antenna noise, etc.; i represents the ith satellite; b, r respectively represents a reference station of the vehicle head and an auxiliary station of the vehicle tail;
s12: time alignment processing is carried out on the carrier phase between the two antennas at the head and the tail of the vehicle, and if the time alignment of the carrier phase at the head and the tail of the vehicle is successful, the step S13 is carried out; otherwise, continuing to S12 to enter the next time alignment;
s13: and (3) successfully aligning the time of the carrier phase observed quantity of the locomotive tail, performing double-difference carrier phase error elimination processing, and taking the processed result as the input of S3 moving baseline calculation:
Figure FDA0002216739950000021
s14: according to S13, the part related to the antenna position is
Figure FDA0002216739950000022
From the above derivation, the true double difference distance
Figure FDA0002216739950000023
Can be written as:
Figure FDA0002216739950000024
s15: a reference antenna and an auxiliary antenna are selected, assuming that the reference antenna has coordinates of (x)b,yb,zb) The auxiliary antenna has a rough coordinate of
Figure FDA0002216739950000025
Using the position of the reference antenna b as the approximate position of the antenna r, and performing first-order Taylor expansion on the distance from the auxiliary antenna r to the satellite at the approximate position to obtain:
Figure FDA0002216739950000026
Figure FDA0002216739950000027
in the formula, the deviation between the actual coordinates and the approximate coordinates of the antennas is expressed as (Δ x, Δ y, Δ z), that is, the relative position between the two antennas;
the coefficients of the first-order taylor expansion represent cosine parameters of the direction of the reference antenna pointing to the satellite, and the cosine parameters defining the directions of the three axes are (l, m, q), then:
s16: substituting the above equation into S14 yields:
Figure FDA0002216739950000029
subjecting the obtained
Figure FDA00022167399500000210
Substituting the expansion of (a) into S13 can result in:
Figure FDA0002216739950000031
s17: assuming that the number of satellites observed by two antennas simultaneously in the current epoch is n, selecting a reference satellite can obtain (n-1) double-difference equations, and simultaneously establishing the equations and writing the equations into a matrix form to obtain a double-difference observation equation of the carrier phase:
-λφ＝HX-λΝ
wherein, the phi vector is obtained by subtracting the observed value of the carrier phase measured by the antenna twice; solving the H matrix requires the position of the satellite and the approximate position of the reference antenna, the position of the satellite is resolved by satellite ephemeris output by the antenna, and the approximate position of the auxiliary antenna adopts the position of the reference antenna; x is the baseline vector to be solved; Ν consists of (n-1) double-difference integer ambiguities.
3. The method according to claim 2, wherein the double difference carrier phase error elimination in step S13 comprises the following steps:
s131: taking a head antenna as a reference station and a tail antenna as a mobile station, and performing inter-station difference between the reference station and the mobile station to eliminate errors related to a satellite and a propagation path, wherein the errors comprise clock error of the satellite, and delay errors of an ionosphere and a troposphere;
Figure FDA0002216739950000032
in the formula, the subscript br denotes a value of a difference between two antennas;
the antenna simultaneously tracks signals of a plurality of satellites, and supposing that the two antennas observe another satellite j at the same moment, a single difference equation of a carrier phase corresponding to the satellite j is obtained:
s132: difference between stars: on the basis of the difference between the S131 stations, selecting a satellite with the best altitude angle as a reference satellite, and making a difference between carrier phases corresponding to other satellites and carrier phases of the reference satellite to obtain:
Figure FDA0002216739950000034
in the formula, the superscript ij indicates that the difference is made between the ith star and the jth star.
4. The method of claim 3, wherein the satellite with the largest altitude angle is selected as the reference satellite, and the method for calculating the altitude angle of the satellite comprises:
and calculating the coordinates of the satellite under a carrier coordinate system at the antenna of the locomotive, wherein the conversion relation is as follows:
Figure FDA0002216739950000041
and then calculating the altitude angle of the satellite at the antenna of the locomotive:
θ＝arctan(U2/(E2+N2))
in the formula (X)s,Ys,Zs) Is the position coordinate of the satellite in the earth center earth fixation coordinate system; (E, N, U) are position coordinates of the satellite under a carrier coordinate system with the vehicle head antenna as the center; l and B are respectively the longitude and latitude of the head antenna; theta represents the altitude of the satelliteAnd (4) an angle.
5. The method of claim 3, wherein the position of the reference antenna in S15 is determined by a single-point positioning method based on least squares.
6. The method according to claim 3, 4 or 5, wherein the step S2 of establishing the system equation and the measurement equation of the kalman filter model according to the measurement equation of the double-difference carrier phase includes:
the system equation of the Kalman filtering model is as follows:
Xk＝AXk-1+Qk
in the formula, XkIs the state vector of the system; a is a state transition matrix; qkIs the process noise of the system;
the dimension of the state of the system is 6+ (n-1), and comprises the relative position, the relative speed and the double-difference integer ambiguity of three coordinate axis directions under the geocentric geostationary coordinate system:
Figure FDA0002216739950000042
in the formula (I), the compound is shown in the specification,
Figure FDA0002216739950000051
representing the relative velocities in three directions and assuming that they follow a first order markov distribution;
Figure FDA0002216739950000052
is a matrix of double difference integer ambiguities;
state transition matrix:
Figure FDA0002216739950000053
wherein the time interval Δ T is 0.1 s;
the noise matrix of the system is:
Figure FDA0002216739950000054
wherein τ is the correlation time;
measurement model of the system:
Zk＝HkXk+Vk
in the formula ZkIs the observation vector of the system; hkIs a measurement matrix; vkIs the measurement noise, which is assumed to be white gaussian noise, whose covariance matrix is R.
Systematic observation vector:
measurement matrix of the system:
Hk＝[l(n-1)×1 m(n-1)×1 q(n-1)×1 0(n-1)×3 -λI(n-1)×(n-1)]
where (l, m, q) is a matrix consisting of the difference of (n-1) cosine parameters (l, m, q).
Noise covariance matrix:
Figure FDA0002216739950000056
in the formula, the parameter σ is a standard deviation of L1 carrier noise, and its value is 0.0008 m.
7. The method of claim 1, wherein estimating the state vector of the train at each time according to the kalman filter model, and calculating the length of the moving baseline according to the relative positions of the two antennas at the head and the tail of the train in the state vector comprises:
setting the relative positions of the two antennas at the head and the tail of the vehicle in the state vector X estimated by Kalman filtering as (delta X, delta y and delta z), and then calculating the length L of the moving base line by the formula;
Figure FDA0002216739950000061
8. the method of claim 6, wherein the step S2 of establishing the system equation and the measurement equation of the kalman filter model according to the measurement equation of the double-difference carrier phase further comprises:
1) and when the visible satellite at the current moment is reduced compared with the previous moment, obtaining the PRN number of the unlocked satellite, removing the value corresponding to the unlocked satellite from the state matrix and the covariance matrix of the Kalman filtering model, and then carrying out filtering calculation.
2) When the visible satellites at the current moment are increased compared with the previous moment;
step 1: firstly, obtaining the relative positions (delta x, delta y and delta z) of a head antenna and a tail antenna at the current moment according to the corresponding matrix filtering of the visible satellite at the previous moment;
step 2: using the relative positions (delta x, delta y, delta z) of the two antennae at the head and the tail of the vehicle at the current time to reversely solve the double-difference integer ambiguity corresponding to the increased satellite
And step 3: using the double difference integer ambiguity calculated in step 2
Figure FDA0002216739950000063
Updating the state matrix X; the covariance matrix P reserves the corresponding position and speed part, and the rest part is initialized completely;
and 4, step 4: and filtering the updated matrixes X and P once, smoothing and then filtering for the next moment.
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