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 Ionosphere for SBAS Modeling Vertical Structure of Ionosphere for SBAS ION GNSS 2009 Savannah, GA Sept , 2009

ION GNSS Sept ENRI S LIDE 1 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 clock corrections; –The ionosphere varies day by day and difficult to predict the spatial distribution of ionospheric propagation delay based on the limited number of measurements; –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 actual ionosphere; –For accuracy improvement, need to consider some models suitable for the SBAS 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. Introduction

ION GNSS Sept ENRI S LIDE 2 SBAS Corrections Orbit Correction Troposphere Ionosphere Tropospheric Correction Clock Correction Same contribution to any user location;Same contribution to any user location; Not a function of location;Not a function of location; Needs fast correction.Needs fast correction. Different contribution to different user location;Different contribution to different user location; Not a function of user location; but a function of line-of-sight direction;Not a function of user location; but 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 described as a thin shell.Vertical structure is described as a thin shell. Ionospheric Correction

ION GNSS Sept ENRI S LIDE 3 SBAS Message Preamble 8 bits Message Type 6 bits Data Field 212 bits CRC parity 24 bits 1 message = 250 bits per second MT 0 1 2～52～52～52～ Contents Test mode PRN mask Fast correction & UDRE UDRE Degradation factor for FC GEO ephemeris Degradation parameter SBAS time information GEO almanac IGP mask Interval[s] FC & LTC Long-term correction Ionospheric delay & GIVE SBAS service message Clock-ephemeris covariance Null message — MTContentsInterval[s] Transmitted First

ION GNSS Sept ENRI S LIDE 4 SBAS IGP IGP IGP IPP Vertical ionospheric delay information at IGPs ( ) located at 5-degree grid points will be broadcast to users.Vertical ionospheric delay information at IGPs ( ) located at 5-degree grid points will be broadcast to users. User receiver computes vertical ionospheric delays at IPPs with bilinear interpolation of delays at the surrounding IGPs.User receiver computes vertical ionospheric delays at IPPs with bilinear interpolation of delays at the surrounding IGPs. Vertical delay is converted to slant delay by multiplying a factor so- called obliquity factor.Vertical delay is converted to slant delay by multiplying a factor so- called obliquity factor Longitude, E Latitude, N IGP

ION GNSS Sept ENRI S LIDE 5 Bilinear Interpolation IGP1IGP2 IGP4IGP3 x pp y pp IPP D IPP = x pp y pp D IGP1 + (1-x pp )y pp D IGP2 + (1-x pp )(1-y pp )D IGP3 + x pp (1-y pp )D IGP4 User receiver computes ionospheric delay at the IPP by interpolation of delays at the surrounding IGPs.User receiver computes ionospheric delay at the IPP by interpolation of delays at the surrounding IGPs.

ION GNSS Sept ENRI S LIDE 6 Generates IGP Data: Planar Fit The SBAS MCS needs to generate the vertical ionospheric delay information at every IGPs;The SBAS MCS needs to generate the vertical ionospheric delay information at every IGPs; Planar Fit algorithm is developed for US WAAS; Japanese MSAS employs the same algorithm;Planar Fit algorithm is developed for US WAAS; Japanese MSAS employs the same algorithm; Assume the spatial distribution of the vertical ionospheric delay around the IGP can be modeled as a first order plane;Assume the spatial distribution of the vertical ionospheric delay around the IGP can be modeled as a first order plane; Model parameters are estimated by the least square fit for each IGP; The estimated vertical delay is broadcast to users.Model parameters are estimated by the least square fit for each IGP; The estimated vertical delay is broadcast to users. Cutoff Radius Vertical Delay Fit Plane IPP IGP

ION GNSS Sept ENRI S LIDE 7 Considering Vertical Structure The ionosphere has a certain vertical structure:The ionosphere has a certain vertical structure: –Currently modeled as a thin shell at fixed height of 350 km; –Suitable for a quiet ionospheric condition; How about for stormy condition? –For the SBAS, the ionosphere model must be simple; Needs consideration of the number of ionospheric correction messages. MODEL 1: Variable Height Shell Model: –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; –Needs to broadcast applied shell height; Only 2 to 4 bits. MODEL 2: Multi-Layer Shell Model: –Ionosphere modeled as the sum of multiple layers; –Each layer represented as a thin shell with a certain height; –The number of ionosphere correction messages increases proportional to the number of layers.

ION GNSS Sept ENRI S LIDE 8 Thin 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 conversion factor so-called obliquity factor, F(EL).The vertical delay is converted into the slant direction via the slant-vertical conversion factor so-called obliquity factor, F(EL). Earth Ionosphere EL Vertical Delay Iv Slant Delay F(EL) Iv Shell Height IPP

ION GNSS Sept ENRI S LIDE 9 Obliquity 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 of 350 km.Also a function of the shell height; The current SBAS specifies the shell height of 350 km.

ION GNSS Sept ENRI S LIDE 10 Slab Ionosphere Earth Ionosphere EL Slant Delay F Iv Shell Height Vertical Delay Iv SlabThickness IPP 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 F for this model.How about obliquity factor F for this model.

ION GNSS Sept ENRI S LIDE 11 Slab 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 identical with the function for the thin shell ionosphere of a higher shell height.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. Bottom height and Slab thickness (300,0) (200,0)(100,0) (350,0) (400,0) (500,0) (600,0)

ION GNSS Sept ENRI S LIDE 12 Variable 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 certain slab thickness and thin shell ionosphere of another shell height; –Thin shell ionosphere model with variable height shell represents the ionosphere both with and without slab thickness; Ignoring IPP relocation; –Problem is: How to measure appropriate shell height. (Method 1) Planar Fit Residual: –Residual error when the SBAS MCS estimates the vertical delay at IGP; –The performance (fitting accuracy) of planar fit depends upon the shell height set for computation. (Method 2) Bias Estimation Residual: –Residual error when the SBAS MCS estimates the instrumental bias error; –Estimation accuracy also depends upon the shell height.

ION GNSS Sept ENRI S LIDE 13 Planar Fit Residual Planar fit residual with respect to the shell height under a moderate storm condition of the ionosphere in July 2004;Planar fit residual with respect to the shell height under a moderate storm condition of the ionosphere in July 2004; Except higher part, the smallest residual appears at the shell height of km.Except higher part, the smallest residual appears at the shell height of km.

ION GNSS Sept ENRI S LIDE 14 Bias Estimation Residual Residual error in the estimation of instrumental bias, so-called interfrequency bias or L1/L2 bias; Depends upon the shell height;Residual error in the estimation of instrumental bias, so-called interfrequency bias 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.

ION GNSS Sept ENRI S LIDE 15 Measuring Shell Height Shell heights estimated based on (Grren) planar fit residual and (Red) bias estimation residual;Shell heights estimated based on (Grren) planar fit residual and (Red) bias estimation residual; Planar fit residual results in lower shell height while bias estimation residual returns higher results; Bias estimation seems to have 1-day period.Planar fit residual results in lower shell height while bias estimation residual returns higher results; Bias estimation seems to have 1-day period. Planar Fit Bias Estimation

ION GNSS Sept ENRI S LIDE 16 Multi-Layer Shell Model Ionospheric delay along with the ray path is represented as the sum of delays caused by multiple thin shells; Three layers for this example.Ionospheric delay along with the ray path is represented as the sum of delays caused by multiple thin shells; Three layers for this example. Earth Ionosphere EL Iv (1) Iv (2) Iv (3) F(h 1,EL) Iv (1) F(h 2,EL) Iv (2) F(h 3,EL) Iv (3) IPP 1 IPP 2 IPP 3

ION GNSS Sept ENRI S LIDE 17 Multi-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 caused by multiple thin shells; –Each IGP has multiple delay values for the respective layers; –Still simple to compute the total slant ionospheric delay; –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; –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 ionospheric delay distribution, but for this time extended to slant delay.

ION GNSS Sept ENRI S LIDE 18 Past Investigation: Unstable TotalDelay 1st Layer at 250km 2nd Layer at 350km 3rd Layer at 450km NegativeDelay Similar Distribution

ION GNSS Sept ENRI S LIDE 19 Residual 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 of IPP observations; –Define residual error between the user interpolation function and each observed delay at IPP, I v,IPPi ; –The optimum set of vertical delays minimizes the sum square of residuals; –The optimization can be achieved by minimizing the energy function (often called as cost function) E over IGP delays (See paper for detail): Function of IGP delays

ION GNSS Sept ENRI S LIDE 20 Residual Optimization Adjust IGP delays so that the RMS of the difference between the interpolated ionospheric delay function for users and observed delays at IPPs is minimized.Adjust IGP delays so that the RMS of the difference between the interpolated ionospheric delay function for users and observed delays at IPPs is minimized. Interpolated plane for users IGP iIGP i+1 Vertical Delay Location IPP measurements Adjust IGP delay to minimize residual Residual

ION GNSS Sept ENRI S LIDE 21 IGP 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 may differ from each other.IPP location on each layer is different from other layers; The set of surrounding IGPs may differ from each other.

ION GNSS Sept ENRI S LIDE 22 Ionosphere Layers at 13:00 LT TotalDelay 1st Layer at 350km 2nd Layer at 600km 3rd Layer at 1,000km

ION GNSS Sept ENRI S LIDE 23 Ionosphere Layers at 01:00 LT TotalDelay 1st Layer at 350km 2nd Layer at 600km 3rd Layer at 1,000km

ION GNSS Sept ENRI S LIDE 24 Residual Error (1) 1-Layer Model 2-Layer Model 3-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 Height 1-Layer: (350) 2-Layer: (350,600) 3-Layer: (350,600,1000)

ION GNSS Sept ENRI S LIDE 25 Residual Error (2) 1-Layer Model 2-Layer Model 3-Layer Model Shell Height 1-Layer: (350) 2-Layer: (350,800) 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.

ION GNSS Sept ENRI S LIDE 26 Investigated some models to represent the vertical structure of the ionosphere to improve position accuracy of SBAS:Investigated some models to represent the vertical structure of the ionosphere to improve position accuracy of SBAS: –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 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; –Multi-Layer Shell Model reduced residual error; The residual optimization algorithm 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; –Consider to use a priori information for modeling; –Temporal variation and scintillation effects. Conclusion