CN100442077C - Usable forcasting method for receiver autonomic excellent monitoring - Google Patents

Abstract

A method for predicting usability of receiver perfectness monitor includes receiving satellite position information, satellite unusable information, satellite failure information and flight-plan data of air company; calculating parameter of satellite pseudo-distance measurement error and setting up weighting matrix based on said parameter; calculating HPL of receiver on space-time point assigned by flight-plan data according to weighting matrix, satellite observation matrix, error detection rate and undetected rate then comparing HPL with HAL for obtaining usable state of receiver RAIM.

Description

The availability Forecasting Methodology of receiver autonomous integrity monitoring

Technical field

The present invention relates to a kind of availability Forecasting Methodology of receiver autonomous integrity monitoring, relate in particular to applied global positioning system (Global Positioning System, hereinafter to be referred as GPS) in the system of navigating, the availability of the receiver autonomous integrity monitoring to aircraft during according to the airline flights project flight is carried out forecast method, belongs to the satellite navigation field.

Background technology

The gps satellite navigational system can obtain popularizing aspect military and civilian simultaneously for the land, sea and air user provides continuously accurate three-dimensional position, speed and temporal information in worldwide.World's civil aviation community is promoting the development and the application of GPS (Global Position System) (Global Navigation Satellite System is hereinafter to be referred as GNSS) and various enhanced system.(the InternationalCivil Aviation Organization of International Civil Aviation Organization, hereinafter to be referred as ICAO) defined a kind of GNSS that comprises one or more satellite navigation systems at least, its continuous global covering power makes aircraft directly fly to another place from a place under the condition that can follow.If GNSS is used for China civil aviaton, in the eastern region with GNSS as secondary navigation system and VHF Omnidirection range/stadimeter (VHF Omni-directionalRange/Distance Measuring Equipment, hereinafter to be referred as VOR/DME) and nondirectional bea con (non-directional beacon, hereinafter to be referred as NDB) cooperating, can improve navigation accuracy, avoid continuing again VOR/DME and NDB investment are guaranteed east civil aviation safety and high-level efficiency; In the west area GNSS is realized small investment as main with navigational system and inertial navigation system cooperating, navigation accuracy, navigation safety and efficient obviously improve.But, GPS can not satisfy the requirement of civil aviation for the integrity of satellite navigation system, must take measures the integrity of GPS is strengthened, the integrity of navigational system is meant that working as navigational system is in unhealthy condition, provides the ability of timely warning to the user in the time of can not accurately navigating.

Receiver autonomous integrity monitoring (Receiver Autonomous Integrity Monitoring, hereinafter to be referred as RAIM) technology is a kind of technology that is embedded in the GPS receiver, it utilizes the redundant information of gps satellite, a plurality of navigational solution to GPS are carried out consistency check, thereby reach the purpose of integrity monitoring.RAIM has guaranteed bearing accuracy on the one hand, has realized the monitoring to satellite health on the other hand, is the common method that independently obtains integrity monitoring in the present satnav effectively.The advantage of RAIM is that satellite failure is swift in response and fully automatically, need not extraneous the intervention.But RAIM has certain requirement to number of satellite in the Airborne GPS receiver visual field and satellite distribution, for example, needs 5 satellites that above geometric distributions is better or suitable, judges otherwise just can't carry out integrity.This just causes some time RAIM of certain areas not use, and promptly has the covering cavity of RAIM.When gps satellite can't be worked or do not produce distance measuring signal, this phenomenon was just more serious, was very necessary so RAIM is carried out the availability prediction.

RAIM availability forecasting techniques is utilized the unavailable information and the gps satellite fail message of satellite ephemeris/almanac data, GPS plan, in conjunction with airborne RAIM algorithm, the availability of airborne RAIM algorithm on prediction specific airport zone and the air route provides the auxiliary reference of flight planning and flight clearance for dispatch department of airline and blank pipe department of civil aviaton.Flight standard department of China Administration of Civil Aviation had issued Advisory Circulars AC-91FS-01 in 2005, RAIM availability prediction before regulation must use the RAIM predictor to fly.

Existing RAIM availability Forecasting Methodology supposes that all satellite ranging errors are identical, does not consider the situation that range error is different.For GPS, method commonly used at present has following three kinds:

1) δ H _MaxMethod.When the visible satellite number is n, at first make up n subclass, each subclass comprises n-1 satellite, calculates Horizontal Dilution of Precision (the to call HDOP in the following text) value of each subclass then, is referred to as HDOPi, i=1,2 ..., n.Secondly; Calculating is referred to as HDOP about the HDOP value of the least square solution of whole n satellite; Can get so $\mathrm{\δ}{H}_{\max }=\underset{i}{\max }{({\mathrm{HDOP}}_i^2-{\mathrm{HDOP}}^2)}^{1/2}.$ For fault detect, parameter δ H _MaxJust become reverse measuring of satellite geometry architecture quality.Integrity criterion calculation δ H according to the navigation of civil aviation applying GPS _MaxUltimate value, if this value that certain geometry calculation goes out has exceeded the ultimate value of calculating, then when satellite and receiver were in this geometry, RAIM was disabled.Ultimate value is only relevant with the visible satellite number, can calculate before prediction.The method calculated amount is little, and is simple.

2) approximate radial error protection (to call ARP in the following text) method.The method is selected Be detection statistic, wherein SSE is a statistic, and n is the number of satellites in the receiver visual range, makes itself and radial position error have identical dimension.Deviation/the error of any particular satellite all can project in site error and the detection statistic territory linearly, and its slope can be according to the satellite geometry Structure Calculation, and all is different with respect to every satellite.For fault detect, the slope maximum of the satellite correspondence of difficult detection, this slope is designated as SLOPE _MaxUnder ideal conditions, the smallest radial error that does not produce false dismissal is about: SLOPE _Max* fault detect thresholding is referred to as the approximate radial error protection with this.The threshold value of ARP method can be calculated according to the integrity standard of civil aviation applying GPS navigation, also can measure by various simulations.If calculate the threshold value of ARP, then δ H according to the integrity standard _MaxMethod and ARP method are equivalences fully.

3) horizon location error protection limit value (to call HPL in the following text) method.Based on the ARP method, select

Be detection statistic, the integrity alarming threshold as the fault detect thresholding, directly calculated the HPL value: $\mathrm{HPL}={\mathrm{SLOPE}}_{\max }^{\′}\·\mathrm{\σ}\sqrt{\mathrm{\λ}}.$ Wherein, λ is non-central χ ²The non-centrality parameter of the density function that distributes, σ is the standard deviation of satellite pseudorange error, SLOPE ' _MaxBe different from the SLOPE in the ARP method _Max, because the detection statistic difference of choosing.HPL value and horizontal alarming threshold (the to call HAL in the following text) value calculated are compared, and greater than HAL, then RAIM is unavailable as if HPL.

These methods are adapted to select the actual state of the GPS navigation before availability (Selective Availability is called for short SA) the policy cancellation, because SA is the maximum error source of all satellite pseudo range measurements, and all satellites are basic identical.The inventor finds in the process of carrying out innovation and creation: behind the decision cancellation SA of U.S. government in 2000, ionosphere delay becomes the maximum error source of gps satellite pseudo range measurement, be closely related with the elevation angle and the receiver location of receiver to satellite, so, if continue to use prior art, then the pseudo range measurement error of satellite can only be selected according to pseudo range measurement error maximum in the visible satellite, can reduce actual RAIM availability like this.

Summary of the invention

The objective of the invention is to overcome defective of the prior art, a kind of availability Forecasting Methodology of receiver autonomous integrity monitoring is provided, improve RAIM availability prediction accuracy, weaken the dependence of the availability prediction of RAIM number of satellites and layout in the receiver working range.

For achieving the above object, provide a kind of availability Forecasting Methodology of receiver autonomous integrity monitoring, comprised the steps:

Gather satellite position data, the unavailable information data of satellite, satellite fail message data and airline flights planning data, prepare data as prediction;

Prepare this airline flights of data computation parameter that goes up the pseudo range measurement error of satellite event in the works according to above-mentioned prediction;

Parameter according to the pseudo range measurement error of satellite makes up weighting coefficient;

Calculate the HPL that goes up receiver this event according to weighting coefficient, observing matrix, false drop rate and the loss of satellite on this event;

HPL and HAL are compared, obtain the upstate of described receiver autonomous integrity monitoring.

In technique scheme, can further include record and go up the status predication result of receiver RAIM this event, and the next upstate of going up receiver RAIM event of continuation prediction, finish in the whole flight planning, need the prediction of going up receiver RAIM availability a plurality of events of measuring.

Obtain predict the outcome after, further predicting the outcome according to receiver RAIM upstate, adjust flight planning, judge promptly whether the cumulative time of going up each event on this flight planning receiver RAIM down state reach certain threshold value, make it satisfy the requirement of receiver RAIM availability on the flight planning if then adjust flight planning according to predicting the outcome.

By above technical scheme as can be known, pseudo range measurement error and the elevation angle with the receiver location relevant characteristics of receiver at each satellite of SA cancellation back to satellite, the present invention proposes a kind of RAIM availability Forecasting Methodology of GPS receiver, basic design of the present invention is: the standard deviation of the pseudo range measurement error of each satellite is formed a weighting matrix, positioning equation to GPS carries out normalization, according to least-square residuals method derivation detection statistic and radial position error, and then calculate HPL, judge the availability of RAIM.Has overcome receiver RAIM availability prediction in the prior art number of satellites in its visual range and layout dependence are considered the difference of pseudo range measurement error by force and not, made the accuracy not high technical matters of predicting the outcome, so this method has following advantage:

1, can weaken the dependence of receiver RAIM availability prediction to satellites in view number and space layout, the scope of application is wider;

2, effectively improve RAIM availability prediction accuracy, can effectively reduce the false drop rate of fault detect, reduce the delay and the cancellation of flight;

3, this method has extensibility, adapts to being used in combination of multiple satellite navigation system.

Also in conjunction with the accompanying drawings the present invention is described in further detail below by specific embodiment.

Description of drawings

Fig. 1 is the availability Forecasting Methodology specific embodiment process flow diagram of receiver autonomous integrity monitoring of the present invention.

The specific embodiment process flow diagram that Fig. 2 calculates for satellite pseudo range measurement error parameter in the availability Forecasting Methodology of receiver autonomous integrity monitoring of the present invention.

Embodiment

Be illustrated in figure 1 as the availability Forecasting Methodology specific embodiment process flow diagram of receiver autonomous integrity monitoring of the present invention, this method is a kind of weighting RAIM availability Forecasting Methodology, mainly comprises the steps:

Step 100, reception satellite position data, the unavailable information data of satellite, satellite fail message data and airline flights planning data;

Step 200, prepare data according to prediction, this prediction is prepared data and is comprised satellite position data, the unavailable information data of satellite, satellite fail message data and airline flights planning data, calculates parameter that goes up satellite pseudo range measurement error event in this flight planning;

Step 300, make up weighting coefficient according to the parameter of the pseudo range measurement error of satellite;

Step 400, according to weighting coefficient, this event satellite observing matrix, false drop rate and loss calculate the HPL that goes up receiver this event;

Step 500, HPL and HAL are compared, obtain the upstate of receiver RAIM, promptly as HPL during greater than HAL, the RAIM that then should go up receiver event be a down state, otherwise was upstate.

On the basis of technique scheme, also can further comprise:

Step 600, write down the status predication result who goes up receiver RAIM this event, and execution in step 200, continue to calculate the next upstate of going up receiver RAIM event.

And also can comprise step 700, predicting the outcome according to receiver RAIM upstate, adjust flight planning, judge promptly whether the cumulative time of going up each event on this flight planning receiver RAIM down state reach certain threshold value, if then adjust flight planning so that it satisfies the requirement of receiver RAIM availability according to predicting the outcome.

In the above-mentioned steps 100, satellite position data is gps satellite ephemeris or satellite almanac information, and these two kinds of information are the same, all from the GPS receiver, all being used to calculate satellite position, is the precision difference of calculating, and employing is any in specific embodiments of the invention can.The unavailable information of GPS plan and gps satellite fail message are navigation user Advisory Circulars (the Notice Advisoryto Navigaiton Users from GPS, hereinafter to be referred as NANU) obtain in the message, this message can provide from the disabled information of certain time to certain time satellite, and this message is that the network address from the U.S. Coast Guard that is responsible for the civilian operation of GPS is directly to obtain on the website of www.navcen.uscg.gov/gps/.Flight planning obtains from the flight planning of airline, and this flight planning comprises the navigation station that experiences in original base, landing station, the flight course.Obtaining of above-mentioned information can send acquisition request or the lastest imformation that provides initiatively is provided in carrying out flight planning before the prediction of receiver RAIM availability, if above-mentioned information is upgraded, then can directly use the above-mentioned relevant information of storage in advance.

In the above-mentioned steps 200, a kind of embodiment of parameter that goes up satellite pseudo range measurement error according to event in the above-mentioned data computation flight planning is as follows, process flow diagram as shown in Figure 2:

Step 210, obtain to go up this event the location parameter of receiver, calculate satellite elevation angle parameter and magnetic azimuth parameter according to receiver location parameter, satellite position data, the unavailable information of satellite and satellite fail message according to flight planning;

Step 220, according to satellite elevation angle parameter and magnetic azimuth calculation of parameter ionosphere delay error;

Step 230, to obtain the pseudo range measurement mean square of error according to satellite clock/ephemeris error, troposphere model error, multipath noise error, receiver noise sum of errors ionosphere delay error poor, is designated as σ _i, wherein, 1≤i≤n, n are the number of satellite in the receiver visual range.

The processing procedure of step 200 is promptly: the time and the position that obtain an event to be calculated from the data of flight planning, the i.e. location parameter of this receiver, calculate the elevation angle parameter and the magnetic azimuth parameter of usable satellite according to the location parameter of receiver and the aforementioned satellite position data of obtaining, unavailable information and fail message, it is poor to calculate satellite pseudo range measurement mean square of error again.At the single frequency receiving after the SA cancellation, the main error of satellite pseudo range measurement falls into 5 types: satellite clock and ephemeris error, ionosphere delay error, troposphere model error, multipath noise and receiver noise.Standard setting service performance standard and interface according to GPS are controlled the computing method of recommending in the document, and each error can be calculated according to following steps:

Steps A 1, obtain satellite clock and ephemeris error;

Because the error that 24 hours average satellite clock of U.S. government's assurance and ephemeris cause is not more than 6 meters, so can unify in advance satellite clock and ephemeris error are set at 6 meters, this numerical value also can be adjusted as the case may be for preestablishing.

A2, calculating ionosphere delay error, the evaluated error of ionosphere delay can be calculated according to following formula:

Ionosphere delay error=Fpp * σ _Uive

$F_{\mathrm{PP}}={[1-{\left(\frac{R_e\cos E}{R_e+h_I}\right)}^2]}^{-1/2}$

Wherein:

Wherein, Re is an earth radius, and E is the satellite elevation angle, h _IBe layer height, φ _mMagnetic azimuth for satellite.

A3, calculating troposphere model error, the troposphere model error can be calculated by following formula: troposphere model error=0.12 * m (E)

Wherein: $m\left(E\right)=\frac{1.001}{\sqrt{0.002001+{\sin }^2\left(E\right)}}.$

A4, calculating multipath error, multipath error=0.13+0.53 * e ^-E/10

A5, obtain the receiver noise error, because it doesn't matter receiver noise and satellite elevation angle, common desirable empirical value is 0.1 meter.Perhaps the thermonoise estimated value of receiver is set on the flight aircraft of being predicted that provides according to airline.

More than the quadratic sum of five kinds of errors, promptly, obtain its mean square deviation behind the evolution as the variance of each satellite pseudo range measurement error of GPS, be designated as σ _i, 1≤i≤n, n are the number of visible satellite in this operation of receiver scope.

Above-mentioned steps 300 makes up weighting coefficient according to the pseudo range measurement error, and the method that is specially weighting matrix in the present embodiment is: the pseudo range measurement mean square of error difference σ that utilizes each satellite ₁, σ ₂..., σ _nMake up weighting matrix according to following formula

Wherein, W is a weighting matrix.

In the above-mentioned steps 400, the observing matrix H of satellite calculates according to satellite ephemeris/almanac information and gets, and the specific implementation method of step 400 is: utilize weighting matrix W to the normalization of GPS positioning equation, obtain normalized observing matrix H _WWith the measurement vector, then according to χ ²The Distribution calculation detection statistic.Concrete steps comprise:

Step 410, calculate the normalization observing matrix according to formula (1):

Hw＝WH (1)

Wherein, W is a weighting matrix, H _WBe normalized observing matrix;

Step 420, calculate H according to formula (2) _wThe Moore-Penrose pseudo inverse matrix:

$A_w={\left({H_w}^T{H}_w\right)}^{-1}{H_w}^T---\left(2\right)$

Wherein, A _WBe H _WThe pseudo-quasi-moments battle array of Moore-Penrose;

A _IjThe capable j column element of i for matrix A;

H _W ^-1Be matrix H _WContrary;

H _W ^TBe matrix H _WTransposition;

Step 430, calculate H according to formula (3) _WProjection matrix:

P _w＝H _wA _w(3)

Wherein, P _wBe H _WProjection matrix;

Step 440, calculate detection statistic according to formula (4):

$\sqrt{{\mathrm{SSE}}_i}=b_i\sqrt{1-P_{w,\mathrm{ii}}}---\left(4\right)$

Wherein, b _iBeing the pseudo range measurement deviation, is a calculating intermediate quantity, will be eliminated in computation process;

For calculating detection statistic;

I is the row, column sequence number in the matrix, 1≤i≤n;

Step 450, according to formula (5) calculated level positioning error:

$R_{\mathrm{hi}}=b_i\sqrt{A_{w,1i}^2+A_{w,2i}^2}---\left(5\right)$

Wherein, R _hBe horizon location error;

Step 460, calculate the HPL value according to formula (6), (7) and (8):

${\mathrm{SLOPE}}_{w,i}=\frac{R_{\mathrm{hi}}}{\sqrt{{\mathrm{SSE}}_i}}---\left(6\right)$

${\mathrm{SLOPE}}_{w,\max }=\underset{i}{\max }{\mathrm{SLOPE}}_{w,i}---\left(7\right)$

$\mathrm{HPL}={\mathrm{SLOPE}}_{w,\max }\·\sqrt{{\mathrm{\λ}}_{\min }}---\left(8\right)$

Wherein, SLOPE _{W, i}Be the intermediate value of calculating;

SLOPE _{W, max}For SLOPE _{W, i}Maximal value;

λ _MinBe the χ that calculates according to the false drop rate in the integrity standard and loss ²The decentralization parameter that distributes;

HPL is horizon location error protection restriction.

λ _MinCalculating, at first according to the regulation of false drop rate in the integrity standard, obtain fault detect thresholding T according to formula (9) inverse operation, according to the regulation of loss in the integrity standard, calculate χ again ²The decentralization parameter that distributes, promptly inverse operation gets λ according to formula (10) _Min

P _FA＝G(T/n-4)(9)

P _MD＝F(T|n-4，λ _min)(10)

The partial function implication of Chu Xianing is as follows in the present embodiment:

F (x ²| r) be χ ²The distribution function that distributes;

G (x ²| r) be G (x ²| r)=1-F (x ²| r);

F (x ²| r Φ) is acentric χ ²The distribution function that distributes.

The value of HAL is to be provided with according to the regulation in the integrity standard in the above-mentioned steps 500.

In the above-mentioned steps 600, go up the availability of RAIM, generally need prediction in a minute once predicting a plurality of events the event on the flight planning.In step 700, it is 5 minutes that threshold value is set, if the disabled cumulative time of RAIM reaches 5 minutes, then needs according to this adjustment flight planning that predicts the outcome.

One of ordinary skill in the art will appreciate that: all or part of step that realizes said method embodiment can be finished by the relevant hardware of programmed instruction, aforesaid program can be stored in the computer read/write memory medium, this program is carried out the step that comprises said method embodiment when carrying out; And aforesaid storage medium comprises: various media that can be program code stored such as ROM, RAM, magnetic disc or CD.

It should be noted that at last: above embodiment only in order to technical scheme of the present invention to be described, is not intended to limit; Although with reference to previous embodiment the present invention is had been described in detail, those of ordinary skill in the art is to be understood that: it still can be made amendment to the technical scheme that aforementioned each embodiment put down in writing, and perhaps part technical characterictic wherein is equal to replacement; And these modifications or replacement do not make the essence of appropriate technical solution break away from the spirit and scope of various embodiments of the present invention technical scheme.

Claims (8)

1, a kind of availability Forecasting Methodology of receiver autonomous integrity monitoring comprises the steps:

Gather satellite position data, the unavailable information data of satellite, satellite fail message data and airline flights planning data, prepare data as prediction;

Prepare the described airline flights of data computation parameter that goes up the pseudo range measurement error of satellite event in the works according to described prediction;

Parameter according to the pseudo range measurement error of described satellite makes up weighting coefficient;

Calculate the horizon location error protection limit value of going up receiver described event according to described weighting coefficient, observing matrix, false drop rate and the loss of satellite on described event;

Described horizon location error protection limit value and horizontal alarming threshold are compared, obtain the upstate of described receiver autonomous integrity monitoring.

2, the availability Forecasting Methodology of receiver autonomous integrity monitoring according to claim 1 is characterized in that also comprising:

Write down the status predication result who goes up receiver autonomous integrity monitoring described event, and continue the next upstate of going up receiver autonomous integrity monitoring event of prediction.

3, the availability Forecasting Methodology of receiver autonomous integrity monitoring according to claim 1 and 2 is characterized in that also comprising: according to predicting the outcome of receiver autonomous integrity monitoring upstate, adjust flight planning.

4, the availability Forecasting Methodology of receiver autonomous integrity monitoring according to claim 1 is characterized in that: according to described prediction prepare the described airline flights of data computation in the works a parameter that goes up the pseudo range measurement error of satellite event be specially:

Plan obtains to go up described event the location parameter of receiver according to airline flights, calculates satellite elevation angle parameter and magnetic azimuth parameter according to receiver location parameter, satellite position data, the unavailable information of satellite and satellite fail message;

According to satellite elevation angle parameter and magnetic azimuth calculation of parameter ionosphere delay error;

It is poor to obtain the pseudo range measurement mean square of error according to the described ionosphere delay error of satellite clock/ephemeris error, troposphere model error, multipath noise error, receiver noise sum of errors.

5, the availability Forecasting Methodology of receiver autonomous integrity monitoring according to claim 1 is characterized in that the step that parameter according to the pseudo range measurement error of described satellite makes up weighting matrix is specially: make up weighting coefficient according to following formula:

$W=\left[\begin{array}{cccc}1/{\mathrm{\σ}}_1& 0& 0& 0\\ 0& 1/{\mathrm{\σ}}_2& 0& 0\\ M& M& O& M\\ 0& 0& L& 1/{\mathrm{\σ}}_n\end{array}\right]$

Wherein, W represents weighting coefficient; σ _iRepresent the pseudo range measurement mean square of error of satellite poor; I is the satellite sequence number, 1≤i≤n; N is the number of satellite in the receiver visual range.

6, according to the availability Forecasting Methodology of claim 1,2,4 or 5 described receiver autonomous integrity monitorings, it is characterized in that: also comprise the step of calculating the observing matrix of the satellite on described event according to described satellite position data.

7, the availability Forecasting Methodology of receiver autonomous integrity monitoring according to claim 3 is characterized in that: also comprise the step of calculating the observing matrix of the satellite on described event according to described satellite position data.

8, the availability Forecasting Methodology of receiver autonomous integrity monitoring according to claim 5 is characterized in that: the step of calculating the horizon location error protection limit value of going up receiver described event according to described weighting coefficient, observing matrix, false drop rate and the loss of satellite on described event is specially:

Calculate following formula successively and obtain horizon location error protection limit value:

H _w＝WH (1)

A _w＝(H _w ^TH _w) ^-1H _w ^T (2)

P _w＝H _wA _w (3)

$\sqrt{{\mathrm{SSE}}_i}=b_i\sqrt{1-P_{w,\mathrm{ii}}}---\left(4\right)$

$R_{\mathrm{hi}}=b_i\sqrt{A_{w,1i}^2+A_{w,2i}^2}---\left(5\right)$

${\mathrm{SLOPE}}_{w,i}=\frac{R_{\mathrm{hi}}}{\sqrt{{\mathrm{SSE}}_i}}---\left(6\right)$

${\mathrm{SLOPE}}_{w,\max }=\underset{i}{\max }{\mathrm{SLOPE}}_{w,i}---\left(7\right)$

$\mathrm{HPL}={\mathrm{SLOPE}}_{w,\max }\·\sqrt{{\mathrm{\λ}}_{\min }}---\left(8\right)$

Wherein,

H is an observing matrix;

H _wFor utilizing weighting coefficient W described observing matrix H to be carried out the normalization observing matrix H that obtains after the normalized _w

A _wBe H _wThe pseudo-quasi-moments battle array of Moore-Penrose;

P _wBe H _wProjection matrix;

I is the capable sequence number in the matrix, 1≤i≤n;

For calculating detection statistic;

b _iBe the pseudo range measurement deviation;

R _hBe horizon location error;

SLOPE _{W, i}Be the intermediate value of calculating;

SLOPE _{W, max}For SLOPE _{W, i}Maximal value;

λ _MinBe the χ that calculates according to the false drop rate in the integrity standard and loss ²The decentralization parameter that distributes;

HPL is a horizon location error protection limit value.

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