T. Sakai, T, Yoshihara, S. Saito, K. Matsunaga, and K. Hoshinoo, ENRI T. Walter, Stanford University...

T. Sakai, T, Yoshihara, S. Saito, K. Matsunaga,and K. Hoshinoo, ENRI

T. Walter, Stanford University

T. Sakai, T, Yoshihara, S. Saito, K. Matsunaga,and K. Hoshinoo, ENRI

T. Walter, Stanford University

Modeling Vertical Structure of Ionospherefor SBAS

Modeling Vertical Structure of Ionospherefor SBAS

ION GNSS 2009ION GNSS 2009Savannah, GASavannah, GA

Sept. 22-25, 2009Sept. 22-25, 2009

ION GNSS 22-25 Sept. 2009 - ENRIION GNSS 22-25 Sept. 2009 - ENRI

SSLIDELIDE 22

• The ionospheric effect is a major error source for SBAS:The ionospheric effect is a major error source for SBAS:

– The SBAS broadcasts ionospheric correction messages as well as orbit and clocThe SBAS broadcasts ionospheric correction messages as well as orbit and cloc

k corrections;k corrections;

– The ionosphere varies day by day and difficult to predict the spatial distribution of The ionosphere varies day by day and difficult to predict the spatial distribution of

ionospheric propagation delay based on the limited number of measurements;ionospheric propagation delay based on the limited number of measurements;

– Also known that the geomagnetic storm causes a large uncertainty.Also known that the geomagnetic storm causes a large uncertainty.

• Ionosphere modeled as a thin shell:Ionosphere modeled as a thin shell:

– The current standard ignores height, thickness, and any vertical structure of the aThe current standard ignores height, thickness, and any vertical structure of the a

ctual ionosphere;ctual ionosphere;

– For accuracy improvement, need to consider some models suitable for the SBAS For accuracy improvement, need to consider some models suitable for the SBAS

to represent the vertical structure of the ionosphere.to represent the vertical structure of the ionosphere.

• Evaluation of the proposed models:Evaluation of the proposed models:

– Modeling accuracy is improved by the multiple layer model. Modeling accuracy is improved by the multiple layer model.

IntroductionIntroduction


SSLIDELIDE 33SBAS CorrectionsSBAS Corrections

Orbit CorrectionOrbit Correction

TroposphereTroposphere

IonosphereIonosphere

Tropospheric CorrectionTropospheric Correction

Clock CorrectionClock Correction• Same contribution to any user Same contribution to any user

location;location;• Not a function of location;Not a function of location;• Needs fast correction. Needs fast correction.

• Different contribution to different Different contribution to different user location;user location;

• Not a function of user location; but Not a function of user location; but a function of line-of-sight direction;a function of line-of-sight direction;

• Long-term correction.Long-term correction.

• Function of user location, especially height of user;Function of user location, especially height of user;• Up to 20 meters;Up to 20 meters;• Corrected by a fixed model.Corrected by a fixed model.

• Function of user location;Function of user location;• Up to 100 meters;Up to 100 meters;• Vertical structure is Vertical structure is

described as a thin shell.described as a thin shell.

Ionospheric CorrectionIonospheric Correction


SSLIDELIDE 44SBAS MessageSBAS Message

PreamblePreamble8 bits8 bits

Message TypeMessage Type6 bits6 bits

Data FieldData Field212 bits212 bits

CRC parityCRC parity24 bits24 bits

1 message = 250 bits per second

MTMT

00

11

22～～ 55

66

77

99

1010

1212

1717

1818

ContentsContents

Test modeTest mode

PRN maskPRN mask

Fast correction & UDREFast correction & UDRE

UDREUDRE

Degradation factor for FCDegradation factor for FC

GEO ephemerisGEO ephemeris

Degradation parameterDegradation parameter

SBAS time informationSBAS time information

GEO almanacGEO almanac

IGP maskIGP mask

IntervalInterval[s][s]

66

120120

6060

66

120120

120120

120120

300300

300300

300300

2424

2525

2626

2727

2828

6363

FC & LTCFC & LTC

Long-term correctionLong-term correction

Ionospheric delay & GIVEIonospheric delay & GIVE

SBAS service messageSBAS service message

Clock-ephemeris covarianceClock-ephemeris covariance

Null messageNull message

66

120120

300300

300300

120120

——

MTMT ContentsContents IntervalInterval[s][s]

Transmitted FirstTransmitted First


SSLIDELIDE 55SBAS IGPSBAS IGP

IGPIGP

IGPIGPIPPIPP

• Vertical ionospheric delay informatVertical ionospheric delay information at IGPs ( ) located at 5-degree ion at IGPs ( ) located at 5-degree grid points will be broadcast to usegrid points will be broadcast to users.rs.

• User receiver computes vertical ioUser receiver computes vertical ionospheric delays at IPPs with bilinnospheric delays at IPPs with bilinear interpolation of delays at the sear interpolation of delays at the surrounding IGPs.urrounding IGPs.

• Vertical delay is converted to slant Vertical delay is converted to slant delay by multiplying a factor so-caldelay by multiplying a factor so-called obliquity factor.led obliquity factor.

120 150 1800

30

60

Longitude, E

Latitude, N

15

30

45

0

60

IGPIGP


SSLIDELIDE 66Bilinear InterpolationBilinear Interpolation

IGP1IGP1IGP2IGP2

IGP4IGP4IGP3IGP3xxpppp

yypppp

IPPIPP

DDIPPIPP = x = xppppyyppppDDIGP1 IGP1 + (1-x+ (1-xpppp)y)yppppDDIGP2 IGP2 + (1-x+ (1-xpppp)(1-y)(1-ypppp)D)DIGP3 IGP3 + x+ xpppp(1-y(1-ypppp)D)DIGP4IGP4

• User receiver computes ionospheric delay at the IPP by User receiver computes ionospheric delay at the IPP by interpolation of delays at the surrounding IGPs.interpolation of delays at the surrounding IGPs.


SSLIDELIDE 77Generates IGP Data: Planar FitGenerates IGP Data: Planar Fit

• The SBAS MCS needs to generate the verThe SBAS MCS needs to generate the vertical ionospheric delay information at every tical ionospheric delay information at every IGPs;IGPs;

• Planar Fit algorithm is developed for US WPlanar Fit algorithm is developed for US WAAS; Japanese MSAS employs the same AAS; Japanese MSAS employs the same algorithm;algorithm;

• Assume the spatial distribution of the verticAssume the spatial distribution of the vertical ionospheric delay around the IGP can bal ionospheric delay around the IGP can be modeled as a first order plane;e modeled as a first order plane;

• Model parameters are estimated by the leaModel parameters are estimated by the least square fit for each IGP; The estimated vst square fit for each IGP; The estimated vertical delay is broadcast to users.ertical delay is broadcast to users.

Cutoff Radius

Vertical Delay

Fit Plane

IPP

IGP


SSLIDELIDE 88Considering Vertical StructureConsidering Vertical Structure

• The ionosphere has a certain vertical structureThe ionosphere has a certain vertical structure::– Currently modeled as a thin shell at fixed height of 350 km;Currently modeled as a thin shell at fixed height of 350 km;

– Suitable for a quiet ionospheric condition; How about for stormy condition?Suitable for a quiet ionospheric condition; How about for stormy condition?

– For the SBAS, the ionosphere model must be simple; Needs consideration of tFor the SBAS, the ionosphere model must be simple; Needs consideration of the number of ionospheric correction messages.he number of ionospheric correction messages.

MODEL 1: Variable Height Shell ModelMODEL 1: Variable Height Shell Model::– Thin shell ionosphere model with a variable shell height not fixed at 350 km;Thin shell ionosphere model with a variable shell height not fixed at 350 km;

– Simple and less computational load both for the MCS and users;Simple and less computational load both for the MCS and users;

– Needs to broadcast applied shell height; Only 2 to 4 bits.Needs to broadcast applied shell height; Only 2 to 4 bits.

MODEL 2: Multi-Layer Shell ModelMODEL 2: Multi-Layer Shell Model::– Ionosphere modeled as the sum of multiple layers;Ionosphere modeled as the sum of multiple layers;

– Each layer represented as a thin shell with a certain height;Each layer represented as a thin shell with a certain height;

– The number of ionosphere correction messages increases proportional to the The number of ionosphere correction messages increases proportional to the number of layers.number of layers.


SSLIDELIDE 99Thin Shell IonosphereThin Shell Ionosphere

• The ionosphere model used by the current standard;The ionosphere model used by the current standard;• Ionospheric propagation delay caused at a single point on the shell;Ionospheric propagation delay caused at a single point on the shell;• The vertical delay is converted into the slant direction via the slant-vertical cThe vertical delay is converted into the slant direction via the slant-vertical c

onversion factor so-called obliquity factor, onversion factor so-called obliquity factor, FF((ELEL).).

EarthEarth


ELEL

Vertical DelayVertical Delay

IvIvSlant DelaySlant Delay

FF((ELEL) ) •• Iv Iv

Shell HeightShell Height

IPPIPP


SSLIDELIDE 1010Obliquity FactorObliquity Factor

• Slant-vertical conversion factor as a function of the elevation angle;Slant-vertical conversion factor as a function of the elevation angle;• Also a function of the shell height; The current SBAS specifies the shell height Also a function of the shell height; The current SBAS specifies the shell height

of 350 km.of 350 km.


SSLIDELIDE 1111Slab IonosphereSlab Ionosphere

EarthEarth

IonosphereIonosphereELEL

Slant DelaySlant Delay

F F •• Iv Iv

Shell HeightShell Height

Vertical DelayVertical Delay

IvIv

SlabSlabThicknessThickness

IPPIPP

• Assume that The ionosphere has a certain slab thickness;Assume that The ionosphere has a certain slab thickness;• Slab structure with constant thickness lies above the thin shell;Slab structure with constant thickness lies above the thin shell;• How about obliquity factor How about obliquity factor FF for this model. for this model.


SSLIDELIDE 1212Slab IonosphereSlab Ionosphere

• Slant-vertical conversion factor for the ionosphere with slab thickness;Slant-vertical conversion factor for the ionosphere with slab thickness;• The obliquity factor function for the ionosphere with a certain slab thickness is The obliquity factor function for the ionosphere with a certain slab thickness is

identical with the function for the thin shell ionosphere of a higher shell height.identical with the function for the thin shell ionosphere of a higher shell height.

Bottom height and Bottom height and Slab thicknessSlab thickness(300,0)

(200,0) (100,0)

(350,0)

(400,0)

(500,0)

(600,0)


SSLIDELIDE 1313Variable Height Shell ModelVariable Height Shell Model

• Thin shell model represents both:Thin shell model represents both:

– There is a obliquity factor function used both for the slab ionosphere with a There is a obliquity factor function used both for the slab ionosphere with a

certain slab thickness and thin shell ionosphere of another shell height;certain slab thickness and thin shell ionosphere of another shell height;

– Thin shell ionosphere model with variable height shell represents the Thin shell ionosphere model with variable height shell represents the

ionosphere both with and without slab thickness; Ignoring IPP relocation;ionosphere both with and without slab thickness; Ignoring IPP relocation;

– Problem is: How to measure appropriate shell height.Problem is: How to measure appropriate shell height.

(Method 1) Planar Fit Residual(Method 1) Planar Fit Residual::

– Residual error when the SBAS MCS estimates the vertical delay at IGP;Residual error when the SBAS MCS estimates the vertical delay at IGP;

– The performance (fitting accuracy) of planar fit depends upon the shell height The performance (fitting accuracy) of planar fit depends upon the shell height

set for computation.set for computation.

(Method 2) Bias Estimation Residual(Method 2) Bias Estimation Residual::

– Residual error when the SBAS MCS estimates the instrumental bias error;Residual error when the SBAS MCS estimates the instrumental bias error;

– Estimation accuracy also depends upon the shell height.Estimation accuracy also depends upon the shell height.


SSLIDELIDE 1414Planar Fit ResidualPlanar Fit Residual

• Planar fit residual with respect to the shell height under a moderate storm Planar fit residual with respect to the shell height under a moderate storm condition of the ionosphere in July 2004;condition of the ionosphere in July 2004;

• Except higher part, the smallest residual appears at the shell height of 200-300km.Except higher part, the smallest residual appears at the shell height of 200-300km.


SSLIDELIDE 1515Bias Estimation ResidualBias Estimation Residual

• Residual error in the estimation of instrumental bias, so-called interfrequency bias Residual error in the estimation of instrumental bias, so-called interfrequency bias or L1/L2 bias; Depends upon the shell height;or L1/L2 bias; Depends upon the shell height;

• Smooth against the shell height, but a little difference.Smooth against the shell height, but a little difference.


SSLIDELIDE 1616Measuring Shell HeightMeasuring Shell Height

• Shell heights estimated based on (Grren) planar fit residual and (Red) bias eShell heights estimated based on (Grren) planar fit residual and (Red) bias estimation residual;stimation residual;

• Planar fit residual results in lower shell height while bias estimation residual rPlanar fit residual results in lower shell height while bias estimation residual returns higher results; Bias estimation seems to have 1-day period.eturns higher results; Bias estimation seems to have 1-day period.

Planar FitPlanar Fit

Bias EstimationBias Estimation


SSLIDELIDE 1717Multi-Layer Shell ModelMulti-Layer Shell Model

• Ionospheric delay along with the ray path is represented as the sum of delays caused Ionospheric delay along with the ray path is represented as the sum of delays caused by multiple thin shells; Three layers for this example.by multiple thin shells; Three layers for this example.

EarthEarth


ELEL

IvIv(1)(1)

IvIv(2)(2)

IvIv(3)(3)

FF((hh11,,ELEL) ) •• Iv Iv(1)(1)

FF((hh22,,ELEL) ) •• Iv Iv(2)(2)

FF((hh33,,ELEL) ) •• Iv Iv(3)(3)

IPPIPP11

IPPIPP22

IPPIPP33


SSLIDELIDE 1818Multi-Layer Shell ModelMulti-Layer Shell Model

• Another way to represent the vertical structure of the ionosphere:Another way to represent the vertical structure of the ionosphere:

– Ionospheric delay along with the ray path is represented as the sum of delays Ionospheric delay along with the ray path is represented as the sum of delays

caused by multiple thin shells;caused by multiple thin shells;

– Each IGP has multiple delay values for the respective layers;Each IGP has multiple delay values for the respective layers;

– Still simple to compute the total slant ionospheric delay;Still simple to compute the total slant ionospheric delay;

– Need to determine the IGP delays for the multiple layers.Need to determine the IGP delays for the multiple layers.

• Known problem from the past Investigation:Known problem from the past Investigation:

– Tend to be unstable due to a number of parameters to be estimated;Tend to be unstable due to a number of parameters to be estimated;

– Sometimes negative delay appears at the middle layer.Sometimes negative delay appears at the middle layer.

• Try with a new algorithm:Try with a new algorithm:

– Residual Optimization algorithm; Originally developed to optimize the vertical iResidual Optimization algorithm; Originally developed to optimize the vertical i

onospheric delay distribution, but for this time extended to slant delay.onospheric delay distribution, but for this time extended to slant delay.


SSLIDELIDE 1919Past Investigation: UnstablePast Investigation: Unstable

TotalTotalDelayDelay

1st Layer1st Layerat 250kmat 250km

2nd Layer2nd Layerat 350kmat 350km

3rd Layer3rd Layerat 450kmat 450km

NegativeNegativeDelayDelay

Similar DistributionSimilar Distribution


SSLIDELIDE 2020Residual OptimizationResidual Optimization

• An algorithm to optimize ionospheric delays at IGPs [ION GNSS 2007]:An algorithm to optimize ionospheric delays at IGPs [ION GNSS 2007]:

– Ionospheric delays at IGPs can be optimized regarding the sum of residual error Ionospheric delays at IGPs can be optimized regarding the sum of residual error

of IPP observations;of IPP observations;

– Define residual error between the user interpolation function and each observed Define residual error between the user interpolation function and each observed

delay at IPP, delay at IPP, IIv,IPPiv,IPPi;;

– The optimum set of vertical delays minimizes the sum square of residuals;The optimum set of vertical delays minimizes the sum square of residuals;

– The optimization can be achieved by minimizing the energy function (often called The optimization can be achieved by minimizing the energy function (often called

as cost function) as cost function) EE over IGP delays (See paper for detail): over IGP delays (See paper for detail):

Function of IGP delays


SSLIDELIDE 2121Residual OptimizationResidual Optimization

• Adjust IGP delays so that the RMS of the difference between the interpolated ionosphAdjust IGP delays so that the RMS of the difference between the interpolated ionosph

eric delay function for users and observed delays at IPPs is minimized.eric delay function for users and observed delays at IPPs is minimized.

Interpolated planefor users

IGP i IGP i+1

Vertical Delay

Location

IPP measurements Adjust IGP delayto minimize residual

ResidualResidual


SSLIDELIDE 2222IGP LocationIGP Location

• IGP is located at the same location of each layer;IGP is located at the same location of each layer;

• IPP location on each layer is different from other layers; The set of surrounding IGPs IPP location on each layer is different from other layers; The set of surrounding IGPs

may differ from each other.may differ from each other.

Layer 1Layer 1

Layer 2Layer 2

Layer 3Layer 3

IGPIGPIPPIPP33

IPPIPP22

IPPIPP11


SSLIDELIDE 2323Ionosphere Layers at 13:00 LTIonosphere Layers at 13:00 LT




3rd Layer3rd Layerat 1,000kmat 1,000km


SSLIDELIDE 2424Ionosphere Layers at 01:00 LTIonosphere Layers at 01:00 LT




3rd Layer3rd Layerat 1,000kmat 1,000km


SSLIDELIDE 2525Residual Error (1)Residual Error (1)

1-Layer Model1-Layer Model



• Residual error of three models with the different number of layers;Residual error of three models with the different number of layers;• 2-layer model reduces residual to half of 1-layer; 3-layer model reduces further;2-layer model reduces residual to half of 1-layer; 3-layer model reduces further;• Some periods that multi-layer models returns larger residual error.Some periods that multi-layer models returns larger residual error.

Shell HeightShell Height1-Layer: (350)1-Layer: (350)2-Layer: (350,600)2-Layer: (350,600)3-Layer: (350,600,1000)3-Layer: (350,600,1000)


SSLIDELIDE 2626Residual Error (2)Residual Error (2)




Shell HeightShell Height1-Layer: (350)1-Layer: (350)2-Layer: (350,800)2-Layer: (350,800)3-Layer: (350,800,1500)3-Layer: (350,800,1500)

• Multi-layer models with higher shell heights;Multi-layer models with higher shell heights;• Reduces residual error further; However the worst residual becomes larger.Reduces residual error further; However the worst residual becomes larger.


SSLIDELIDE 2727

• Investigated some models to represent the vertical structure of the ionospherInvestigated some models to represent the vertical structure of the ionospher

e to improve position accuracy of SBAS:e to improve position accuracy of SBAS:– Variable Height Shell Model: Using thin shell model but the shell height is variable;Variable Height Shell Model: Using thin shell model but the shell height is variable;– Multi-Layer Shell Model: Ionospheric delay is represented as the sum of delays on Multi-Layer Shell Model: Ionospheric delay is represented as the sum of delays on

multiple thin shells with different shell heights.multiple thin shells with different shell heights.

• Evaluation of the proposed models:Evaluation of the proposed models:– Difficult to measure the proper shell height for Variable Height Shell Model;Difficult to measure the proper shell height for Variable Height Shell Model;– Multi-Layer Shell Model reduced residual error; The residual optimization algorithm Multi-Layer Shell Model reduced residual error; The residual optimization algorithm

worked functional while the past investigations had problems of unstable solution.worked functional while the past investigations had problems of unstable solution.

• Further investigations:Further investigations:– Analyze and prevent large residual situations for multiple layer models;Analyze and prevent large residual situations for multiple layer models;– Consider to use a priori information for modeling;Consider to use a priori information for modeling;– Temporal variation and scintillation effects.Temporal variation and scintillation effects.

ConclusionConclusion

T. Sakai, T, Yoshihara, S. Saito, K. Matsunaga, and K. Hoshinoo, ENRI T. Walter, Stanford University...

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