CN109061684A - The real-time enveloping method of civil aviaton's satellite navigation integrity enhancing systematic error - Google Patents
The real-time enveloping method of civil aviaton's satellite navigation integrity enhancing systematic error Download PDFInfo
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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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Abstract
The invention discloses a kind of real-time enveloping methods of civil aviaton's satellite navigation integrity enhancing systematic error, it is analyzed using temporal correlation of the time series models to pseudorange error, be eliminated the thick tail error sample of temporal correlation, and using EC GARCH GARCH to envelope calculating is carried out after the processing of thick tail error samples normalization, to establish the stationary model of error with relation to time；It determines the confidence upper limit of pseudorange error standard deviation, and determines optimal pseudorange error sequence length, realize the uncertainty and the non-stationary processing of error to above-mentioned model.This method can't introduce additional integrity risk, due to envelope is tighter, the protected level calculated in real time be less than it is calculated using conventional method, to improve the availability of satellite navigation reinforcing system.
Description
Technical field
The present invention relates to satellite navigation reinforcing system technical fields more particularly to a kind of civil aviaton's satellite navigation integrity to enhance
The real-time enveloping method of systematic error.
Background technique
Satellite navigation foundation enhancing system GBAS (Ground Based Augmentation System) includes satellite
System, ground subsystem and On-Board Subsystem, airborne user's (being often referred to aircraft) is into mistake that is close and taking off in On-Board Subsystem
The monitoring station of Cheng Zhong, airborne user and ground subsystem is closer, and utilizes correlation of the position error on room and time
Property (thinking that the position error of airborne user and monitoring station in certain space and time range is essentially identical), airborne user can
To improve the precision of navigation and integrity monitoring ability is provided with the pseudo-range corrections value broadcast according to monitoring station and integrity information,
Wherein integrity refers to the ability that system failure alerts in time.Implement principle are as follows: each satellite of Satellite subsystem produces
Raw satellite navigation signals are simultaneously sent to ground subsystem and On-Board Subsystem；Each receiver in ground subsystem in monitoring station connects
Receive satellite navigation signals, measure each receiver to each satellite distance (distance be the Pseudo-range Observations containing measurement error),
The position of satellite is calculated according to satellite navigation signals simultaneously, and then combines the exact position of each receiver in known monitoring station
Calculate each receiver to each satellite actual distance, monitoring station by the Pseudo-range Observations of each receiver to each satellite and really away from
From being compared, the pseudo-range corrections value of each satellite is calculated, and obtains the integrity information of GBAS by integrity monitoring algorithm,
Ground subsystem is sent to On-Board Subsystem using pseudo-range corrections value and integrity information as enhancement information；In On-Board Subsystem
Airborne receiver user receives satellite navigation signals, the Pseudo-range Observations containing pseudo range measurement error is measured, further according to received
The enhancement information that ground subsystem is sent reduces airborne user's by vacant lot difference method using the correlation of position error
Position error is completed exact position and is resolved, and improves positioning accuracy and provides integrity monitoring ability.
Protected level (Protection Level, PL) rises in the integrity monitoring of satellite navigation foundation enhancing system GBAS
Important function.Protected level refers to the confidence upper limit of position error, by with given alarm limit (Alert Limit,
AL) it is compared the monitoring realized to integrity.The geometry moment of navigation satellite changes, and the characteristic of locator field error also can
It changes correspondingly.Therefore, statistical modeling analysis usually is carried out to error in pseudorange domain, satellite geometry structure at that time is recycled to throw
Shadow carries out the calculating of protected level to locator field.Vertical protected level (the Vertical of lower GBAS is assumed with fault-free (H0)
Protection Level, VPL) for, calculation formula is as follows:
Wherein, H0 assumes to indicate that failure is not present in ranging process, and S is the projection square projected from pseudorange domain to locator field
Battle array, KffmdIt is the amplification coefficient determined by fault-free false dismissal probability, σiIt is the pseudorange error standard deviation of i-th visible satellite.
It implies hypotheses: pseudorange error Gaussian distributed in above-mentioned protected level calculation formula, however defends
The pseudorange error of star navigation augmentation system has the characteristics that following 3:
Non-stationary: one of the main error source as GBAS, multipath error is related with satellite elevation angle, therefore pseudorange error
Statistical property can not be kept in the change procedure of satellite elevation angle stablize；
Temporal correlation: the presence due to Hatch filtering etc. in GBAS, pseudorange error sample have strong correlation
Property；
Thick tail distribution characteristic: actual error may disobey Gaussian Profile, also prove that error is obeyed without enough samples
Gaussian Profile, it is therefore necessary to consider the case where error is distributed thick tail to guarantee that calculated protected level is bigger than actual, from
And safeguards system operational safety.
To solve the problems, such as caused by above-mentioned pseudorange error feature, in traditional ground strengthening system protected level calculation method
In, for non-stationary, pseudorange error sample is grouped according to satellite elevation angle, and it is identical to assume that the error in each elevation angle group is obeyed
Distribution；The sampling interval is arranged to 200 seconds to remove temporal correlation simultaneously；And thick tail error envelope is proposed on this basis
Concept guarantees that protected level calculation formula is effective.In fact, so-called error envelope, i.e., use one during calculating protected level
A conservative Gaussian Profile substitutes true thick tail distribution, so that the protected level calculated is bigger than true.
Carry out pseudorange error envelope, it is necessary first to model, then recycle high to the true distribution of pseudorange error
Pseudorange error distributed model before this distribution envelope.Obviously, the foundation of pseudorange error distributed model is entire error envelope
Key, academia also accordingly propose many pseudorange error distributed models, such as Gaussian kernel exponential tail (Gaussian Core
Exponential Tail, GCET) model, the anti-Gauss of normal state (Normal Inverse Gaussian, NIG) model, Gaussian kernel
Gauss secondary lobe (Gaussian Core Gaussian Sidelobes, GCGS) model and mixed Gaussian (Mixed Gaussian)
Model etc..
The defect of the prior art: since conventional method is non-stationary to error and the processing of temporal correlation, cause not having
Enough independent samples verify the validity of above-mentioned model；Error envelope and protection level security to guarantee calculating simultaneously
Effectively, it is necessary to which model parameter is exceedingly amplified.
Summary of the invention
(1) goal of the invention
The object of the present invention is to provide a kind of real-time enveloping method of civil aviaton's satellite navigation integrity enhancing systematic error, solutions
Certainly processing non-stationary to pseudorange error and temporal correlation in the prior art, causes no enough independent samples to above-mentioned
The validity of model is verified；And the independent sample shortage for envelope to calculate causes error model parameters excessively to be amplified
Problem.
(2) technical solution
To solve the above problems, the first aspect of the present invention provides a kind of civil aviaton's satellite navigation integrity enhancing system mistake
The real-time enveloping method of difference, is analyzed using temporal correlation of the time series models to pseudorange error, is eliminated the time
The thick tail error sample of correlation, and using EC GARCH GARCH to thick tail error samples normalization
Envelope calculating is carried out after processing；It determines the confidence upper limit of pseudorange error standard deviation, and determines optimal pseudorange error sequence length, it is real
Pseudorange error envelope and protected level is calculated when real.
Further, the real-time enveloping method of a kind of civil aviaton's satellite navigation integrity enhancing systematic error, also sets up packet
The Real-time Error envelope Computational frame in cable architecture and offline structure is included, realize pseudorange error envelope and obtains protected level.
Further, the real-time enveloping method of a kind of civil aviaton's satellite navigation integrity enhancing systematic error, wherein described
The temporal correlation of pseudorange error is introduced by linear system G, temporal correlation error sequence { ytIt is that independent input pseudorange misses
Difference sequence { rtVia obtained by linear system G, linear system G is fitted using time series models, and symmetrical based on ball
Enveloping theory obtains linear system G input pseudorange error sequence { rtEnvelope and output temporal correlation error sequence { yt }
Envelope between relationship, finally obtain eliminate temporal correlation thick tail error sample.
Further, the real-time enveloping method of a kind of civil aviaton's satellite navigation integrity enhancing systematic error, further includes benefit
It is modeled with Conditional heterosedasticity of the GARCH model to thick tail distribution error sample, obtains pseudorange error sequence { rtCondition side
Difference and the normalization sample for being normalized to standardized normal distribution carry out Gaussian envelope calculating to normalization sample.
Further, the real-time enveloping method of a kind of civil aviaton's satellite navigation integrity enhancing systematic error, further includes benefit
The confidence upper limit of pseudorange error standard deviation is calculated with the parametric covariance and Gauss Cumulative Distribution Function of GARCH model, is determined most
The confidence upper limit of small pseudorange error standard deviation and optimal pseudorange error sequence length, wherein making the confidence of pseudorange error standard deviation
The smallest pseudorange error sequence length of the upper limit is optimal pseudorange error sequence length.
Further, the real-time enveloping method of a kind of civil aviaton's satellite navigation integrity enhancing systematic error, wherein determine
The confidence upper limit of the smallest pseudorange error standard deviation and optimal pseudorange error sequence length include:
Determine the maximum length L of pseudorange error sequence held stationarym；
Will held stationary longest pseudorange error sequence segment, wherein segment level be N, be able to maintain smoothly
Longest pseudorange error sequence is divided into 2 according to segment levelN-1A subsequence；
GARCH models fitting is carried out to all subsequences of each segment level, and calculates corresponding pseudorange error standard
Poor confidence upper limit obtains N standard deviation confidence upper limit sequence；It is selected in the smallest pseudorange error standard deviation confidence at each moment
Limit.
Further, the real-time enveloping method of a kind of civil aviaton's satellite navigation integrity enhancing systematic error, wherein establish
Including the Real-time Error envelope Computational frame in cable architecture and offline structure, realizes pseudorange error envelope and obtain protected level, institute
It states and is analyzed in cable architecture realization using temporal correlation of the time series models to pseudorange error, be eliminated time correlation
Property thick tail error sample, and using EC GARCH GARCH to thick tail error samples normalization.
The offline structure carries out Gaussian envelope calculating to normalized thick tail error sample；
The confidence upper limit that pseudorange error standard deviation is also determined in cable architecture, and determine that optimal pseudorange error sequence is long
Degree, obtains real-time pseudorange error envelope in conjunction with the Gaussian envelope that offline structure obtains, and is calculated and is protected using the Real-time Error envelope
Grade.
A kind of real-time enveloping method of civil aviaton's satellite navigation integrity enhancing systematic error of the present invention, by utilizing time sequence
Column model analyzes the temporal correlation of pseudorange error, the thick tail error sample for the temporal correlation that is eliminated, and utilizes
EC GARCH GARCH is to envelope calculating is carried out after the processing of thick tail error samples normalization, to establish
The stationary model of error with relation to time；It determines the confidence upper limit of pseudorange error standard deviation, and determines optimal pseudorange error sequence
Length realizes uncertainty and the non-stationary processing of error to above-mentioned model；Foundation is included in cable architecture and offline knot
The Real-time Error envelope Computational frame of structure, and protected level is obtained, it realizes the error envelope for having online+offline structure and counts in real time
It calculates.
(3) beneficial effect
Above-mentioned technology disclosed in a kind of real-time enveloping method of civil aviaton's satellite navigation integrity enhancing systematic error of the present invention
Scheme has following beneficial technical effect: can't be introduced using Real-time Error envelope and protected level calculation method of the invention
Additional integrity risk.Simultaneously as the reason that envelope is tighter, is less than utilization using the protected level that this method calculates in real time
Conventional method is calculated, to improve the availability of satellite navigation reinforcing system.
Detailed description of the invention
Fig. 1 is the real-time enveloping method for illustrating civil aviaton's satellite navigation integrity enhancing systematic error according to the present invention
Flow diagram；
Fig. 2 is the flow chart for illustrating the stationary model of settling time correlated error according to the present invention；
Fig. 3 is illustrated according to the present invention for modeling statistics uncertainty and the non-stationary process flow of error
Figure；
Fig. 4 be illustrate according to the present invention will held stationary longest pseudorange error sequence segment signal
Figure；
Fig. 5 is to illustrate the Real-time Error envelope Computational frame having in cable architecture and offline structure according to the present invention
Figure.
Specific embodiment
In order to make the objectives, technical solutions and advantages of the present invention clearer, With reference to embodiment and join
According to attached drawing, the present invention is described in more detail.It should be understood that these descriptions are merely illustrative, and it is not intended to limit this hair
Bright range.In addition, in the following description, descriptions of well-known structures and technologies are omitted, to avoid this is unnecessarily obscured
The concept of invention.
The pseudorange error of satellite navigation reinforcing system has the characteristics that following 3:
1, non-stationary: one of the main error source as GBAS, multipath error is related with satellite elevation angle, therefore pseudorange misses
The statistical property of difference can not keep stablizing in the change procedure of satellite elevation angle；
2, temporal correlation: the presence due to Hatch filtering etc. in GBAS, pseudorange error sample have strong phase
Guan Xing；
3, thick tail distribution characteristic: actual error may disobey Gaussian Profile, also prove error clothes without enough samples
From Gaussian Profile, it is therefore necessary to consider the case where error is distributed thick tail to guarantee that calculated protected level is bigger than actual,
To safeguards system operational safety.
To solve the problems, such as that above-mentioned pseudorange error exists, in traditional protected level calculation method, for non-stationary, puppet
It is grouped away from error sample according to satellite elevation angle, and assumes that the error in each elevation angle group obeys same distribution；Sampling interval simultaneously
It is arranged to 200 seconds to remove temporal correlation；And the concept of thick tail error envelope is proposed on this basis, guarantee protected level meter
It is effective to calculate formula.In fact, so-called error envelope, i.e., come during calculating protected level using a conservative Gaussian Profile
True thick tail distribution is substituted, so that the protected level calculated is bigger than true.
Carry out error envelope, it is necessary first to model to the true distribution of pseudorange error, then recycle Gauss point
Pseudorange error distributed model before cloth envelope.Obviously, the foundation of pseudorange error distributed model is the key that entire error envelope,
Academia also accordingly proposes many pseudorange error distributed models, such as Gaussian kernel exponential tail (Gaussian Core
Exponential Tail, GCET) model, the anti-Gauss of normal state (Normal Inverse Gaussian, NIG) model, Gaussian kernel
Gauss secondary lobe (Gaussian Core Gaussian Sidelobes, GCGS) model and mixed Gaussian (Mixed Gaussian)
Model etc..
The defect of the prior art: since conventional method is non-stationary to error and the processing of temporal correlation, cause not having
Enough independent samples verify the validity of above-mentioned model；Error envelope and protection level security to guarantee calculating simultaneously
Effectively, it is necessary to which model parameter is exceedingly amplified.
Fig. 1 illustrates the real-time enveloping method flow diagram of civil aviaton's satellite navigation integrity enhancing systematic error,
In conjunction with Fig. 1, the real-time enveloping method of civil aviaton's satellite navigation integrity enhancing systematic error of the present invention initially sets up time correlation puppet
Stationary model away from error is analyzed using temporal correlation of the time series models to pseudorange error, is eliminated the time
The thick tail error sample of correlation, and using EC GARCH GARCH to thick tail error samples normalization
Envelope calculating is carried out after processing.
Secondly, the non-stationary of statistical uncertainty and error to above-mentioned model is handled, pseudorange error mark is determined
The confidence upper limit of quasi- difference, and determine optimal pseudorange error sequence length, according to disclosed two step, real-time pseudorange can be realized and miss
Poor envelope simultaneously calculates protected level.
The Computational frame of real-time enveloping method is constructed, i.e. foundation includes the Real-time Error envelope in cable architecture and offline structure
Computational frame, and obtain protected level.It is appreciated that establishing the Computational frame including method in real time is to make above-mentioned processing method
Has the online and offline processing mode combined；It can according to need and establish other above-mentioned real-time enveloping methods of realization
Computational frame.
Time series models: in production and scientific research, observing and measuring some or one group of variable x (t), will
It is arranged in a series of moment t1, t2 ..., tn (t is independent variable) according to chronological order, and for explanatory variable and correlation
Mathematic(al) representation.Time series analysis is the time series data obtained according to systematic observation, is estimated by curve matching and parameter
Meter carrys out the theory and method of founding mathematical models.
It is analyzed using temporal correlation of the time series models to pseudorange error, the thickness for the temporal correlation that is eliminated
Tail error sample, and carried out after being handled using EC GARCH GARCH thick tail error samples normalization
Envelope calculates；The temporal correlation of the pseudorange error is introduced by linear system G, temporal correlation error sequence { ytIt is independent
Input pseudorange error sequence { rtVia obtained by linear system G, linear system G is fitted using time series models,
And it is theoretical (Spherically Symmetric Overbounding Theorem, SSOT) based on ball symmetric envelope, obtain line
Property system G input pseudorange error sequence { rtEnvelope and output temporal correlation error sequence { ytEnvelope between relationship,
Finally obtain the thick tail error sample for eliminating temporal correlation.
As an example, Fig. 2 shows the flow charts of the stationary model of settling time correlated error, first to pseudorange error
Temporal correlation is analyzed, it is assumed that temporal correlation is introduced by a linear system, wherein temporal correlation error { ytBe
Independent input { rtVia linear system G gained, while this linear system is fitted using time series models.Base
Between ball symmetric envelope theory SSOT, the envelope that linear system is output and input there are following relationships:
Wherein " > " indicates envelope relationship, and g is the unit impulse response of linear system G, fyIt is ytDistribution, frobAnd fyob
It is r respectivelytAnd ytEnvelope.
In view of | | g | |2rtEnvelope be also { yt } envelope, therefore use | | g | |2rtAs elimination time phase
The thick tail distribution error sample of closing property.
Using the above method, the correlation in initial error on the one hand can be eliminated, on the other hand, statistical analysis discovery |
|g||2rtReflected Conditional heterosedasticity can also be used to estimate the conditional variance of each moment pseudorange error.
Secondly, to the processing of thick tail error samples normalization, it is different using condition of the GARCH model to thick tail distribution error sample
Scedasticity modeling, obtains pseudorange error sequence { rtConditional variance and be normalized to the normalization sample of standardized normal distribution
This, carries out Gaussian envelope calculating to normalization sample.
It normalizes and comes from standardized normal distribution on sample theory, therefore normalize thick tail after sample is normalized
The sample that characteristic disappears.
As an example, EC GARCH (Generalized can be used
Autoregressive Conditional Heteroscedasticity, GARCH) correlation of error variance is built
Mould, and then estimate the standard deviation of each moment error.GARCH model is defined as follows:
If rt indicates the observation of moment t:
It is above-mentioned to be referred to as GARCH (p, q) model, wherein parameter { ai> 0, i=0,1,2 ..., q } and { bj> 0, j=1,
2 ..., p } it is constant, For the error to standard deviation of t moment,To normalize error sample, etClothes
From standardized normal distribution.
It, can be with after being modeled using Conditional heterosedasticity of the EC GARCH GARCH to error
Obtain pseudorange error sequence { rtConditional variance, same to time seriesStandardized normal distribution is obeyed, the sequence is in the present invention
In be known as normalization error；Thick tail error sample is normalized to obey the sample (normalization sample) of standardized normal distribution, from
And the Gaussian error envelope calculated is capable of the tighter of envelope, calculated protected level also can be smaller.
Meanwhile after being normalized, the sample from different satellites and different elevations angle group all obeys identical standard normal
Distribution, therefore all normalization error samples can mix the calculating for carrying out envelope without grouping, hence it is evident that reduce
Amplify when calculating envelope for the model parameter of statistical uncertainty.
Above-mentioned example on the basis of assuming that error sequence is stable to the temporal correlation of error and thick tail distribution characteristic into
Row discusses and modeling.Increasing the sampling interval is a kind of method for eliminating temporal correlation, but will lead to the shortage of sample.The present invention
Then use another temporal correlation for assuming temporal correlation by linear system introducing without losing error sample number
Removing method.On this basis, due to lacking the theoretical support with data, all there is certain subjectivity in pseudorange error distributed model
Property, and the invention proposes a kind of methods for converting Gaussian Profile error for thick tail error, miss to avoid subjective selection
The process of poor distributed model.In conjunction with above-mentioned 2 kinds of methods, the thick tail error sample of time correlation, which is converted into, obeys standard normal point
The sample of cloth, it is tighter that this obtains error envelope, while calculated protected level is also smaller.
As shown in Figure 1, it is also necessary to which the non-stationary of statistical uncertainty and error to the model of above-mentioned foundation is located
Reason determines the confidence upper limit of pseudorange error standard deviation, and determines optimal pseudorange error sequence length；
Due to constantly changing etc. satellite elevation angle, pseudorange error sequence and non-stationary exist non-stationary.Therefore on
The method for stating error modeling and envelope needs to improve for non-stationary.When satellite elevation angle variation, the distribution of error is same
Step changes.This is non-stationary to cause above-mentioned GARCH model that can not use on longer error sequence.However, compared with
In the short period, it can be assumed that error sequence is stable.That is, to make GARCH model effective, error sequence is shorter
Better.On the other hand, error to standard deviation is estimated using GARCH model, it is therefore desirable to consider that the statistics of model parameter is not true
It is qualitative.In practice in order to reduce the amplification for statistical uncertainty as far as possible, pseudorange error sequence answers that the longer the better.
Indeed, it is difficult to the length of error sequence is determined in advance, and the present invention then propose it is a kind of based on the adaptive of data
Error sequence length is answered to be dynamically determined method.Envelope is carried out to statistical uncertainty first, then considers stationarity and system simultaneously
Meter is uncertain, provides the strategy of Select Error sequence length.
It is calculated in the confidence of pseudorange error standard deviation using the parametric covariance and Gauss Cumulative Distribution Function of GARCH model
Limit, determines the confidence upper limit and optimal pseudorange error sequence length of the smallest pseudorange error standard deviation, wherein making pseudorange error mark
The smallest pseudorange error sequence length of confidence upper limit of quasi- difference is optimal pseudorange error sequence length.
As shown in figure 3, illustrating for modeling statistics uncertainty and the non-stationary process flow diagram of error:
Envelope statistical uncertainty first:
As an example, the confidence upper limit of error to standard deviation is calculated using the parametric covariance of GARCH model.The Σ is enabled to be
Model parameter covariance matrix, l=(1, rt-1 2,…rt-q 2,ht-1,…,ht-p), then htConfidence level is that the confidence upper limit of 1- β is as follows
It is shown:
WhereinIt is Gauss cumulative distribution function (Cumulative
Distribution Function, CDF) inverse function, μ is mean value, and σ is standard deviation.
Confidence level is also referred to as reliability or confidence level, confidence coefficient, i.e., when sampling makes an estimate to population parameter,
Due to the randomness of sample, conclusion is always uncertain.Therefore, it is united using a kind of statement method of probability, that is, mathematics
Within the error range centainly allowed, corresponding probability has more for interval estimation method in meter, i.e. estimated value and population parameter
Greatly, this corresponding probability is referred to as confidence level.
Secondly, as shown in figure 3, also to handle non-stationary:
Regardless of pseudorange error sequence be it is too long or too short, the error to standard deviation of estimation all can because of it is non-stationary or statistics
Uncertain reason and excessively amplify.Based on this, so that the smallest error sequence length of pseudorange error standard deviation confidence upper limit
As optimal sequence length.
As an example, it obtains the smallest error to standard deviation confidence upper limit and optimal sequence length needs following 3 steps
It is rapid:
1) the maximum length L of pseudorange error sequence held stationary is determinedm；It is whether steady due to being difficult validation error sequence,
And GARCH model itself is stable, therefore assert that the sequence that can be fitted very well by GARCH model is stationary sequence；
2) as Fig. 4 provide will held stationary longest pseudorange error sequence segment schematic diagram, will keep flat
Steady longest pseudorange error sequence segment, wherein segment level is N, is able to maintain stable longest pseudorange error sequence root
It is divided into 2 according to segment levelN-1A equal long sub-sequences；Segment level position is more than or equal to 1 natural number.
3) GARCH models fitting is carried out to all subsequences of each segment level, and calculates corresponding pseudorange error mark
Quasi- difference confidence upper limit, obtains N standard deviation confidence upper limit sequence；The smallest pseudorange error standard deviation confidence is selected at each moment
The upper limit；Above-mentioned steps finally realize real-time pseudorange error envelope and can calculate protected level.
In fact, if LmSize is suitable, then the smallest standard deviation confidence upper limit should appear in segment level 1, because
The statistical uncertainty of the grade is minimum.On the contrary, if the smallest standard deviation confidence upper limit appears in other segment levels,
Illustrate current LmIt is excessive, suitable L need to be recalculatedm。
As shown in Figure 1, may also include the Real-time Error envelope Computational frame established include in cable architecture and offline structure, and
Obtain protected level；This step is to be based on above-mentioned step to realize the real-time Computational frame of error envelope for having online+offline structure
Suddenly the method provided finally realizes real-time pseudorange error envelope using the frame and protected level is calculated.
Wherein, it realizes in cable architecture and is analyzed using temporal correlation of the time series models to pseudorange error, obtained
The thick tail error sample of temporal correlation is eliminated, and using EC GARCH GARCH to thick tail error sample
This normalization；
The offline structure carries out Gaussian envelope calculating to normalized thick tail error sample；
The confidence upper limit that pseudorange error standard deviation is also determined in cable architecture, and determine that optimal pseudorange error sequence is long
Degree, obtains real-time pseudorange error envelope in conjunction with the Gaussian envelope that offline structure obtains, and is calculated and is protected using the Real-time Error envelope
Grade.
Realize the example that real-time envelope and protected level calculate as a frame diagram, as Fig. 5 show have in cable architecture and
The Real-time Error envelope Computational frame figure of offline structure, firstly, using GARCH model analysis pseudorange domain error sequence, and estimate t
The error to standard deviation at momentThen error sample will be normalizedThe normalization sample pool for being sent into offline structure is counted offline
Unified error Gaussian envelope；Then, consider it is non-stationary, choose suitable sequence length and estimation error criterion difference set
Believe the upper limit.Finally, the Gaussian envelope returned in conjunction with offline structure obtains Real-time Error envelope, and utilize the Real-time Error envelope meter
Calculate protected level.Certain above-mentioned Computational frame can also be the processing mode in cable architecture.
Compared with prior art, the invention proposes:
1, generilized auto regressive conditional heteroskedastic (GARCH) modeling of satellite navigation reinforcing system error thickness tail characteristic.
2, the integrated conduct method of model of error distribution statistical uncertainty and distribution uneven stability.
3, has the real-time Computational frame of error envelope of online+offline structure.
The present invention is directed to protect a kind of real-time enveloping method of civil aviaton's satellite navigation integrity enhancing systematic error, when utilization
Between series model the temporal correlation of pseudorange error is analyzed, the thick tail error sample for the temporal correlation that is eliminated, and
Using EC GARCH GARCH to progress envelope calculating after the processing of thick tail error samples normalization；It determines
The confidence upper limit of pseudorange error standard deviation, and determine optimal pseudorange error sequence length；Foundation is included in cable architecture and offline knot
The Real-time Error envelope Computational frame of structure, and obtain protected level.
Real-time Error envelope of the present invention and protected level calculation method can't introduce additional integrity risk.Meanwhile by
In the reason that envelope is tighter, be less than using the protected level that the method for the present invention calculates in real time it is calculated using conventional method, from
And improve the availability of satellite navigation reinforcing system.Although the protected level sequence of calculating occurs not because sequence is segmented
Continuous situation, but this has no effect on the validity of this method.
Although the protected level that the present invention theoretically calculates may be greater than the protected level that conventional method calculates, big
The protected level that (especially error lesser moment) calculates under the actual conditions of part is smaller than the protected level calculated using conventional method.
It should be understood that above-mentioned specific embodiment of the invention is used only for exemplary illustration or explains of the invention
Principle, but not to limit the present invention.Therefore, that is done without departing from the spirit and scope of the present invention is any
Modification, equivalent replacement, improvement etc., should all be included in the protection scope of the present invention.In addition, appended claims purport of the present invention
Covering the whole variations fallen into attached claim scope and boundary or this range and the equivalent form on boundary and is repairing
Change example.
Claims (7)
1. the real-time enveloping method of civil aviaton's satellite navigation integrity enhancing systematic error, which is characterized in that
It is analyzed using temporal correlation of the time series models to pseudorange error, the thick tail for the temporal correlation that is eliminated misses
Difference sample, and envelope is carried out after handling using EC GARCH GARCH thick tail error samples normalization
It calculates；
It determines the confidence upper limit of pseudorange error standard deviation, and determines optimal pseudorange error sequence length, realize real-time pseudorange error
Envelope simultaneously calculates protected level.
2. the real-time enveloping method of civil aviaton's satellite navigation integrity enhancing systematic error according to claim 1, feature
It is, also sets up including the real-time pseudorange error envelope Computational frame in cable architecture and offline structure, realize pseudorange error envelope
And obtain protected level.
3. the real-time enveloping method of civil aviaton's satellite navigation integrity enhancing systematic error according to claim 1, feature
It is, the temporal correlation of the pseudorange error is introduced by linear system G, temporal correlation error sequence { ytIt is independent defeated
Enter pseudorange error sequence { rtVia obtained by linear system G, linear system G is fitted using time series models, and base
It is theoretical in ball symmetric envelope, obtain linear system G input pseudorange error sequence { rtEnvelope and output temporal correlation error
Sequence { ytEnvelope between relationship, finally obtain eliminate temporal correlation thick tail error sample.
4. the real-time enveloping method of civil aviaton's satellite navigation integrity enhancing systematic error according to claim 3, feature
It is, is modeled using Conditional heterosedasticity of the GARCH model to thick tail distribution error sample, obtain pseudorange error sequence { rt?
Conditional variance and the normalization sample for being normalized to standardized normal distribution carry out Gaussian envelope calculating to normalization sample.
5. the real-time enveloping method of civil aviaton's satellite navigation integrity enhancing systematic error according to claim 4, feature
It is, the confidence upper limit of pseudorange error standard deviation is calculated using the parametric covariance and Gauss Cumulative Distribution Function of GARCH model,
The confidence upper limit and optimal pseudorange error sequence length for determining the smallest pseudorange error standard deviation, wherein making pseudorange error standard deviation
The smallest pseudorange error sequence length of confidence upper limit be optimal pseudorange error sequence length.
6. the real-time enveloping method of civil aviaton's satellite navigation integrity enhancing systematic error according to claim 5, feature
It is, determines the confidence upper limit of the smallest pseudorange error standard deviation and optimal pseudorange error sequence length includes:
Determine the maximum length L of pseudorange error sequence held stationarym；
Will held stationary longest pseudorange error sequence segment, wherein segment level be N, be able to maintain stable longest
Pseudorange error sequence be divided into 2 according to segment levelN-1A equal long sub-sequences；
GARCH models fitting is carried out to all subsequences of each segment level, and calculates corresponding pseudorange error standard deviation and sets
Believe the upper limit, obtains N standard deviation confidence upper limit sequence；The smallest pseudorange error standard deviation confidence upper limit is selected at each moment.
7. civil aviaton's satellite navigation integrity according to claim 2 or 6 enhances the real-time enveloping method of systematic error, special
Sign is that foundation includes the Real-time Error envelope Computational frame in cable architecture and offline structure, realizes pseudorange error envelope and obtains
To protected level, is analyzed, obtained using temporal correlation of the time series models to pseudorange error wherein being realized in cable architecture
The thick tail error sample of temporal correlation is eliminated, and using EC GARCH GARCH to thick tail error sample
This normalization；
The offline structure carries out Gaussian envelope calculating to normalized thick tail error sample；
The confidence upper limit that pseudorange error standard deviation is also determined in cable architecture, and determine optimal pseudorange error sequence length, knot
It closes the Gaussian envelope that offline structure obtains and obtains real-time pseudorange error envelope, calculate protected level using the Real-time Error envelope.
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| CN110542911A (en) * | 2019-09-16 | 2019-12-06 | 中国民航大学 | Beidou airborne equipment RAIM performance conformance testing method and system |
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| CN113985457B (en) * | 2021-11-01 | 2022-07-22 | 北京航空航天大学 | GBAS protection level calculation method |
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