CN108508461B - GNSS carrier phase based high-precision positioning integrity monitoring method - Google Patents
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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
- G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
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- G01S19/20—Integrity monitoring, fault detection or fault isolation of space segment
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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
- G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/13—Receivers
- G01S19/24—Acquisition or tracking or demodulation of signals transmitted by the system
- G01S19/29—Acquisition or tracking or demodulation of signals transmitted by the system carrier including Doppler, related
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Abstract
The invention provides a GNSS carrier phase-based high-precision positioning integrity monitoring method, which comprises the following steps of 1, monitoring integrity in an integer ambiguity solving stage on the basis of a constructed positioning Kalman filter, verifying the distribution of statistic T, wherein the distribution of statistic T is double noncentral F distribution, if the verification is passed, replacing a real number solution with an integer solution, entering the step 2, and if not, directly entering the step 2; step 2, integrity monitoring in a high-precision positioning stage, extracting residual error information from a positioning algorithm, constructing a second set of statistic, carrying out fault detection, judging whether a fault exists, if so, carrying out fault identification and isolation, reconstructing a Kalman filter, solving integer ambiguity, and repeating the step 1; if not, calculating the protection level, and judging whether the protection level is greater than an alarm threshold, if so, alarming; and if not, outputting the level protection result and the integrity identification. The invention reduces the risk generated in the application of the satellite navigation positioning device.
Description
Technical Field
The invention relates to the technical field of navigation integrity monitoring, in particular to a GNSS carrier phase-based high-precision positioning integrity monitoring method.
Background
Integrity is the degree of confidence in the correctness of the navigation system output. The probability that the system cannot guarantee that the offered service (exceeding the alarm threshold) cannot give an alarm within a specified Time (Time to Alert) should be less than the integrity risk specified value. A satellite navigation system positioning device (receiver) needs to have a set of mechanisms to provide reliability (integrity) for positioning results, and in the field of aviation, in order to ensure flight safety, Receiver Autonomous Integrity Monitoring (RAIM) is usually adopted to determine whether the receiver results can provide navigation information for an aircraft. The positioning accuracy of the receiver used by the airplane is in the meter level, and the positioning cannot be called high-accuracy positioning.
The high-precision satellite navigation positioning device receives radio navigation information sent by a satellite, and extracts position time information of the satellite and a distance between the positioning device and the satellite from a navigation signal. The distance may be obtained by processing a ranging code or signal carrier in the navigation signal. The distance obtained by the ranging code has relatively poor precision but is simple, so that the method is widely applied to the aviation field, and the integrity monitoring method is relatively mature. The distance obtained through the carrier wave is complex, the whole cycle (ambiguity) of the phase between the satellite and the positioning device needs to be obtained, but the distance measurement precision is high, and the integrity monitoring of high-precision satellite navigation positioning still has many challenging problems.
The carrier wave is an electromagnetic wave that can be modulated to transmit a navigation signal, the phase of the carrier wave is a measure describing the variation of the waveform of the signal, usually in degrees, and when the waveform of the signal varies in a periodic manner, the cycle of the waveform is 360 °. High precision GNSS (global navigation satellite system) positioning, carrier phase observations must be employed. The phase observation given by the receiver is only the phase of the signal after it is acquired, and the initial whole-cycle part, i.e. the integer number of the distance between the initial observation epoch satellite and the observation station relative to the carrier wavelength, is unknown. High-precision positioning can be implemented only after the initial value of the ambiguity is obtained.
Since the unknown positions are real numbers and the integer ambiguities are integers (integer unknowns corresponding to the first observed values of phase difference between the carrier phase and the reference phase), the two are coupled together. The solving method adopts a mixed integer and real least square method, namely the following expression:
where x ∈ R is a real unknown vector, Z ∈ Z is an integer unknown vector, A, B, y is a real known quantity, | | | | | calving 2 Representing a norm.
The hybrid least squares can be transformed into:
wherein the content of the first and second substances,
is orthogonal, R A A nonsingular upper triangular matrix, the superscript T being the transposition operation, equation (1) can be rewritten as:
thus, in the above formula
Becomes an integer least squares problem.
For the integer least squares problem, it is common to first process as a real least squares problem and then search for the most appropriate integer within a certain range around the real solution. To reduce the search space, the method of Least-squares AMBiguity decorationAdjustment (LAMBDA) is usually used.
The positioning algorithm may also use kalman filtering instead of least squares, so that the LAMBDA method and kalman filtering are fused together. The LAMBDA method, while reducing the search space, has significant problems in deciding which integers to choose. The current common method is to use the ambiguity residual
Wherein, the first and the second end of the pipe are connected with each other,
is an estimate of the real number of ambiguities,
is an ambiguity integer candidate (search value), i is an ambiguity number,
the ambiguity covariance.
The method usually adopted is to subject IR to i In order from small to large, i.e. IR i ＜IR i+1 i ∈ [1, m) m is the total number of ambiguities, which is then judged by the following statistics:
wherein T is d Is a threshold value. If T > T d Then accept IR 1 Is the correct integer ambiguity. The main problem with this method is that it is not possible to describe the statistics (T) of the pair with a reasonable distribution and therefore it is not possible to determine and to hook the threshold value for the decision, and it is currently used to use an empirical value T d Is 1.5, 2.0 or 3.0. Another method hooks threshold and confidence through monte carlo large sample simulation. These methods have problems that the former method is inaccurate and the latter method is time-consuming.
In summary, the prior art has the following disadvantages:
1) conventional Receiver Autonomous Integrity Monitoring (RAIM) is for a positioning apparatus based on code ranging (pseudorange) as an observed quantity, and cannot support integrity monitoring based on carrier phase high-precision positioning.
2) Existing integrity monitoring for high-accuracy positioning (patent application No. 201210286105.9) directly transplants conventional Receiver Autonomous Integrity Monitoring (RAIM) to the last stage in high-accuracy positioning using carrier phase, ignoring some key issues in carrier phase positioning, such as integrity in the whole-cycle ambiguity verification process.
Disclosure of Invention
The invention provides a GNSS carrier phase-based high-precision positioning integrity monitoring method, which solves the technical problem of determining whether a high-precision positioning result is credible (namely integrity), avoids misleading information output by a high-precision positioning device based on a satellite navigation system, and is an essential measure for ensuring the application of the high-precision satellite navigation positioning device in the risky field (such as safety).
The technical scheme adopted by the invention is as follows:
a GNSS carrier phase based high-precision positioning integrity monitoring method comprises the following steps on the basis of a constructed positioning Kalman filter:
step 1, integrity monitoring at an integer ambiguity solving stage, verifying distribution of statistic T, wherein the distribution of the statistic T is double-noncentral F distribution, if the verification is passed, replacing a real number solution with an integer solution, and entering step 2, otherwise, directly entering step 2;
step 2, integrity monitoring in a high-precision positioning stage, extracting residual error information from a positioning algorithm, constructing a second set of statistic, carrying out fault detection, judging whether a fault exists, if so, carrying out fault identification and isolation, constructing a Kalman filter, solving the ambiguity of the whole cycle, and repeating the step 1; if not, calculating the protection level, and judging whether the protection level is greater than an alarm threshold, if so, alarming; and if not, outputting the level protection result and the integrity identification.
Further, the distribution of the statistical quantity T in the step 1 is:
T～F(m 2 ，m 1 ，δ 2 ，δ 1 )
wherein m is 2 ，m 1 Is the number of integer ambiguities, δ 2 ，δ 1 Is a non-central parameter.
Further, δ 2 ，δ 1 And false alarm rate p FA And rate of missed detection p MD The correlation is obtained by the following equation:
where i is 1, 2, m is the total number of ambiguities, m is m 1 ＝m 2 。
Further, statisticsTdesired threshold T d And a degree of confidence p c The relationship of (a) to (b) is as follows:
wherein Γ () is a gamma function,
u＝m 2 /(m 2 k+m 1 k)，0≤u≤1，a＞0，b＞0。
further, the fault detection in step 2 is performed by means of sharing the full set residuals and the subset residuals:
the full set residual integrates a pseudo range residual, a wide lane residual and an L1 basic carrier phase residual for fault detection, wherein L1 is a first frequency of a GPS;
and the sub-set residual detection carries out single fault detection on the pseudo-range residual, the wide-lane residual and the L1 basic carrier phase residual respectively.
Further, the protection level calculation in step 2 is calculated by two protection level calculation methods, and then the maximum value is taken, specifically as follows:
the first protection level calculation method comprises the steps of converting elements related to positions in a covariance matrix in Kalman filtering to obtain a local horizontal coordinate system and combining integrity risks to obtain a first horizontal protection level and a first vertical protection level;
in the second protection level calculation method, the error of the observed quantity is mapped into a position error to obtain a second protection level in the horizontal direction and a second protection level in the vertical direction.
Further, the first horizontal direction protects the horizontal HPL 1 The following were used:
HPL 1 ＝k H σ H
first kind is perpendicularHorizontal VPL of direction protection 1 The following were used:
VPL 1 ＝k V σ V
wherein, the first and the second end of the pipe are connected with each other,
p is a Kalman filter covariance matrix converted into a horizontal coordinate system, k H And k V Respectively, are factors related to horizontal and vertical integrity risk probabilities.
Further, a second horizontal direction protection horizontal HPL 2 The following:
second vertical protection horizontal VPL 1 The following:
where K is the Kalman filter gain matrix, S ═ I-HK) T (I-HK), H is a design matrix, I is an identity matrix, b is a minimum detectable deviation, and the minimum detectable deviation is obtained by mapping the observation accuracy.
Further, the output protection level result takes the maximum of the two protection levels, which is specifically as follows:
HPL＝max(HPL 1 ，HPL 2 )
VPL＝max(VPL 1 ，VPL 2 )。
the method has the advantages of ensuring the integrity of the high-precision positioning result and avoiding the output of misleading information of the high-precision positioning device based on the satellite navigation system, thereby reducing the risk generated in the key application of the high-precision satellite navigation positioning device and avoiding the occurrence of safety accidents or legal liability and the like.
Drawings
FIG. 1 is a flow chart of the algorithm of the present invention.
Detailed Description
The invention can be used for monitoring the risk (for example, less than 10) borne by the integrity monitoring method according to the actual application requirement -7 ) As the input of the algorithm, whether the output information of the high-precision positioning device is credible or not is judged by a two-stage integrity monitoring method, and if the output information is not credible, an alarm is given in time. The invention is further illustrated below with reference to the figures and examples.
Fig. 1 is a flowchart of a GNSS carrier phase-based high-precision positioning integrity monitoring method of the present invention, which includes an integrity monitoring method at an integer ambiguity resolution stage and an integrity monitoring method at a high-precision positioning stage, and the following is specifically set forth:
1) integrity monitoring method for integer ambiguity solving stage
The distribution of the statistic T in the invention is a double noncentral F distribution, i.e. a distribution
T～F(m 2 ，m 1 ，δ 2 ，δ 1 ) (6)
Wherein m is 2 ，m 1 Is the amount of integer ambiguity, and IR 1 And IR 2 Are of the same dimension (are all m) 2 ＝m 1 ＝m)。δ 2 ，δ 1 Non-central parameters, they and false alarm rate p FA And rate of missed detection p MD Related, as shown in the following formula:
where i is 1, 2, δ can be obtained based on the above formula 2 And delta 1 . Therefore, the threshold T required by equation (6) can be further determined d And a degree of confidence p c When the two are connected together, the following steps are carried out:
the above formula can be rewritten as:
where Γ () is a gamma function,
u＝m 2 /(m 2 k+m 1 k) u is more than or equal to 0 and less than or equal to 1, a is more than 0, and b is more than 0. In actual operation, higher order terms may be discarded.
2) Integrity monitoring method for high-precision positioning stage
The high precision positioning may employ RTK or PPP modes. Rtk (real time kinematic) is a differential method for processing carrier phase observations of two measurement stations in real time by using a carrier phase differential technique, and sends carrier phases acquired by a reference station to a user receiver for difference solving. Ppp (close Point location) refers to a method for positioning and resolving phase and pseudo-range observed values acquired by a single GPS receiver by using precise satellite orbits, satellite clock errors and ionosphere errors calculated by using GPS observed data of a plurality of global ground tracking stations. The present invention is directed to an RTK mode in which dual frequency signals are typically used to double-differenced the observations of the user receiver and the reference station receiver, which causes correlation (non-independence) between the observations, i.e., the off-diagonal elements of the observation matrix are not all zero.
Wherein σ 2 The variance of the non-differential observations, the dimension of this matrix is (n-1) x (n-1), n being the number of available observations.
The formula (9) is used as a weighting matrix in a least square positioning algorithm, plays an important role in a weighting matrix in a Kalman filtering algorithm, and is used for decoupling the correlation observed quantity in an inverse matrix mode of the correlation matrix.
Taking L1, i.e., the GPS first frequency pseudorange, the carrier phase observed quantity, and the L2 second frequency pseudorange, the carrier phase observed quantity as an example, the combination of the wide lane is (widelane L1-L2), and the high-precision positioning observation vector is:
wherein the content of the first and second substances,
is the L1 pseudorange double difference observations;
carrier phase wide lane observations;
is an L1 carrier phase observation. The corresponding covariance matrix is:
wherein R is an observation noise covariance matrix; r p A pseudo-range observation noise covariance matrix; r is L1 Observing a noise covariance matrix for the L1 carrier phase; r is L2 The noise covariance matrix is observed for the L2 carrier phase.
In the invention, the integrity monitoring of the high-precision positioning stage is divided into two parts of fault detection and protection level calculation. The fault detection part is carried out by sharing the full set residual error and the subset residual error:
(1) and the full set residual integrates the pseudo range residual, the wide lane residual and the L1 basic carrier phase residual for fault detection.
(2) Sub-set residual detection for individual fault detection of pseudorange residual, wide-lane residual and L1 basic carrier phase residual
The fault detection method has the advantages that the fault can be found and timely identified so as to isolate the fault in time.
The level of protection is calculated in the present invention by two different methods and then taking the maximum value. The first method is to use the covariance matrix and position-related elements in kalman filtering, and obtain a first set of horizontal Protection level hpl (horizontal Protection level) and vertical Protection level vpl (vertical Protection level) by converting these elements to the local horizontal coordinate system (east-north-day) and combining the integrity risk as follows:
HPL 1 ＝k H σ H (14)
VPL 1 ＝k V σ V (15)
wherein the content of the first and second substances,
p is a Kalman filter covariance matrix k converted into a horizontal coordinate system H And k V Respectively, a factor relating to the horizontal and vertical integrity risk probabilities.
The second protection level calculation method maps the error of the observed quantity into a position error, and the expression is as follows:
where K is the Kalman filter gain matrix, S ═ I-HK) T (I-HK), H is a design matrix, I is an identity matrix, b is a minimum detectable deviation, and the minimum detectable deviation is obtained by mapping the observation accuracy.
After obtaining two sets of protection levels, the protection scheme takes the maximum value as the final protection level result, and the method specifically comprises the following steps:
HPL＝max(HPL 1 ，HPL 2 ) (18)
VPL＝max(VPL 1 ，VPL 2 ) (19)
although the present invention has been described with reference to the preferred embodiments, it is not intended to limit the present invention, and those skilled in the art can make variations and modifications of the present invention without departing from the spirit and scope of the present invention by using the method and technical content disclosed above, and therefore, any simple modifications, equivalent changes and modifications of the above embodiments according to the technical essence of the present invention shall fall within the protection scope of the present invention.
Claims (8)
1. A GNSS carrier phase based high-precision positioning integrity monitoring method is characterized by comprising the following steps of, based on a constructed positioning Kalman filter:
step 1, monitoring the integrity of an integer ambiguity solving stage, verifying the distribution of statistic T, wherein the distribution of statistic T is double noncentral F distribution, if the verification is passed, replacing a real number solution with an integer solution, entering step 2, otherwise, directly entering step 2;
step 2, integrity monitoring at a high-precision positioning stage, extracting residual error information from a positioning algorithm, constructing a second set of statistic, performing fault detection, judging whether a fault exists, if so, performing fault identification and isolation, reconstructing a Kalman filter, solving integer ambiguity, and repeating the step 1; if not, calculating the protection level, and judging whether the protection level is greater than an alarm threshold, if so, alarming; if not, outputting a horizontal protection result and integrity identification;
the fault detection in the step 2 is carried out in a mode of sharing the full set residual error and the subset residual error:
the full set residual integrates the pseudo-range residual, the wide lane residual and the L1 basic carrier phase residual for fault detection, wherein L1 is a first frequency of a GPS;
and (4) performing single fault detection on the pseudo-range residual, the wide-lane residual and the L1 basic carrier phase residual by using subset residual detection.
2. The GNSS carrier phase-based high-precision positioning integrity monitoring method according to claim 1, wherein the distribution of the statistical metric T in step 1 is:
T～F(m 2 ，m 1 ，δ 2 ，δ 1 )
wherein m is 2 ，m 1 Is the number of integer ambiguities, δ 2 ，δ 1 Is a non-central parameter.
3. The GNSS carrier phase based high-precision positioning integrity monitoring method as claimed in claim 2, wherein δ 2 ，δ 1 And false alarm rate p FA And rate of missed detection p MD The correlation is obtained by the following equation:
wherein, i is 1, 2, m is the total number of ambiguities, m is m 1 ＝m 2 。
4. The GNSS carrier phase based high-precision positioning integrity monitoring method as claimed in claim 2, wherein the statistic Tdesired threshold T d And a degree of confidence p c The relationship of (a) to (b) is as follows:
where Γ () is a gamma function,
u＝m 2 /(m 2 k+m 1 k)，0≤u≤1，a>0，b>0。
5. the GNSS carrier phase-based high-precision positioning integrity monitoring method according to claim 1, wherein the protection level calculation in step 2 is calculated by two protection level calculation methods, and then a maximum value is taken, specifically as follows:
the first protection level calculation method comprises the steps of converting elements related to positions in a covariance matrix in Kalman filtering to obtain a local horizontal coordinate system and combining integrity risks to obtain a first horizontal protection level and a first vertical protection level;
and the second protection level calculation method maps the error of the observed quantity into a position error to obtain a second protection level in the horizontal direction and a second protection level in the vertical direction.
6. The GNSS carrier phase based high-precision positioning integrity monitoring method as claimed in claim 5, wherein the first horizontal direction protection level HPL 1 The following were used:
HPL 1 ＝k H σ H
first vertical direction protection horizontal VPL 1 The following were used:
VPL 1 ＝k V σ V
wherein, the first and the second end of the pipe are connected with each other,
p is a Kalman filter covariance matrix converted into a horizontal coordinate system, k H And k V Respectively, are factors related to horizontal and vertical integrity risk probabilities.
7. The GNSS carrier phase based high-precision positioning integrity monitoring method as claimed in claim 6, wherein the second horizontal direction protection level HPL 2 The following were used:
second vertical protection horizontal VPL 1 The following were used:
where K is the Kalman filter gain matrix, S ═ I-HK) T (I-HK), H is a design matrix, I is an identity matrix, b is a minimum detectable deviation, and the minimum detectable deviation is obtained by mapping the accuracy of the observed quantity.
8. The GNSS carrier phase-based high-precision positioning integrity monitoring method of claim 7, wherein the output protection level result takes a maximum of two protection levels, specifically as follows:
HPL＝max(HPL 1 ,HPL 2 )
VPL＝max(VPL 1 ,VPL 2 )。
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