ION GNSS 22 25 ION Sept GNSS 2009

ION GNSS 22 -25 ION Sept. GNSS 2009 - ENRI Savannah, GA Sept. 22 -25, 2009 Modeling Vertical Structure of Ionosphere for SBAS T. Sakai, T, Yoshihara, S. Saito, K. Matsunaga, and K. Hoshinoo, ENRI T. Walter, Stanford University

ION GNSS 22 -25 Sept. 2009 - ENRI Introduction 1 • 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: – 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: – Modeling accuracy is improved by the multiple layer model.

ION GNSS 22 -25 Sept. 2009 - ENRI 2 SBAS Corrections Ionospheric Correction • Function of user location; • Up to 100 meters; • Vertical structure is described as a thin shell. Ionosphere Clock Correction • Same contribution to any user location; • Not a function of location; • Needs fast correction. Orbit Correction • Different contribution to different user location; • Not a function of user location; but a function of line-of-sight direction; • Long-term correction. Tropospheric Correction Troposphere • Function of user location, especially height of user; • Up to 20 meters; • Corrected by a fixed model.

ION GNSS 22 -25 Sept. 2009 - ENRI 3 SBAS Message Preamble 8 bits Message Type 6 bits Data Field 212 bits 1 message = 250 bits per second Transmitted First MT CRC parity 24 bits Contents Interval [s] MT Contents Interval [s] 0 Test mode 6 17 GEO almanac 300 1 PRN mask 120 18 IGP mask 300 Fast correction & UDRE 60 24 FC & LTC 6 6 UDRE 6 25 Long-term correction 7 Degradation factor for FC 120 26 Ionospheric delay & GIVE 300 9 GEO ephemeris 120 27 SBAS service message 300 10 Degradation parameter 120 28 Clock-ephemeris covariance 120 12 SBAS time information 300 63 Null message 2～ 5 120 —

ION GNSS 22 -25 Sept. 2009 - ENRI 4 SBAS IGP 60 Latitude, N 60 • Vertical ionospheric delay information at IGPs ( ) located at 5 -degree grid points will be broadcast to users. 45 • User receiver computes vertical ionospheric delays at IPPs with bilinear interpolation of delays at the surrounding IGPs. 30 • Vertical delay is converted to slant delay by multiplying a factor socalled obliquity factor. 30 15 IGP 0 0 120 150 Longitude, E 180 IPP IGP

ION GNSS 22 -25 Sept. 2009 - ENRI 5 Bilinear Interpolation IGP 2 IGP 1 IPP ypp IGP 3 xpp IGP 4 DIPP = xppypp. DIGP 1 + (1 -xpp)ypp. DIGP 2 + (1 -xpp)(1 -ypp)DIGP 3 + xpp(1 -ypp)DIGP 4 • User receiver computes ionospheric delay at the IPP by interpolation of delays at the surrounding IGPs.

ION GNSS 22 -25 Sept. 2009 - ENRI Generates IGP Data: Planar Fit 6 • The SBAS MCS needs to generate the vertical ionospheric delay information at every IGPs; Vertical Delay Cutoff Radius IPP Fit Plane IGP • 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; • Model parameters are estimated by the least square fit for each IGP; The estimated vertical delay is broadcast to users.

ION GNSS 22 -25 Sept. 2009 - ENRI Considering Vertical Structure 7 • 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 22 -25 Sept. 2009 - ENRI 8 Thin Shell Ionosphere Vertical Delay Iv IPP Slant Delay Ionosphere EL F(EL) • Iv Shell Height Earth • • • The ionosphere model used by the current standard; 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).

ION GNSS 22 -25 Sept. 2009 - ENRI Obliquity Factor 9 • 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.

ION GNSS 22 -25 Sept. 2009 - ENRI 10 Slab Ionosphere Vertical Delay Iv IPP Slant Delay Ionosphere EL F • Iv Shell Height Earth • • • Assume that The ionosphere has a certain slab thickness; Slab structure with constant thickness lies above thin shell; How about obliquity factor F for this model. Slab Thickness

ION GNSS 22 -25 Sept. 2009 - ENRI 11 Slab Ionosphere (200, 0) (100, 0) (300, 0) Bottom height and Slab thickness (350, 0) (400, 0) (500, 0) (600, 0) • 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.

ION GNSS 22 -25 Sept. 2009 - ENRI Variable Height Shell Model 12 • 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 22 -25 Sept. 2009 - ENRI Planar Fit Residual 13 • 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 200 -300 km.

ION GNSS 22 -25 Sept. 2009 - ENRI Bias Estimation Residual 14 • Residual error in the estimation of instrumental bias, so-called interfrequency bias or L 1/L 2 bias; Depends upon the shell height; • Smooth against the shell height, but a little difference.

ION GNSS 22 -25 Sept. 2009 - ENRI 15 Measuring Shell Height Bias Estimation Planar Fit • 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.

ION GNSS 22 -25 Sept. 2009 - ENRI 16 Multi-Layer Shell Model Iv(3) IPP 3 Iv(2) Ionosphere IPP 2 IPP 1 Iv(1) F(h 3, EL) • Iv(3) F(h 2, EL) • Iv(2) EL F(h 1, EL) • Iv(1) Earth • Ionospheric delay along with the ray path is represented as the sum of delays caused by multiple thin shells; Three layers for this example.

ION GNSS 22 -25 Sept. 2009 - ENRI Multi-Layer Shell Model 17 • 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: – 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: – Residual Optimization algorithm; Originally developed to optimize the vertical ionospheric delay distribution, but for this time extended to slant delay.

ION GNSS 22 -25 Sept. 2009 - ENRI Past Investigation: Unstable Total Delay 18 1 st Layer at 250 km Similar Distribution 2 nd Layer at 350 km 3 rd Layer at 450 km Negative Delay

ION GNSS 22 -25 Sept. 2009 - ENRI Residual Optimization 19 • 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, Iv, 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 22 -25 Sept. 2009 - ENRI 20 Residual Optimization Vertical Delay IPP measurements Interpolated plane for users Adjust IGP delay to minimize residual Residual IGP i+1 Location • 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.

ION GNSS 22 -25 Sept. 2009 - ENRI 21 IGP Location IPP 3 IGP Layer 3 IPP 2 Layer 2 IPP 1 Layer 1 • 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.

ION GNSS 22 -25 Sept. 2009 - ENRI Ionosphere Layers at 13: 00 LT Total Delay 1 st Layer at 350 km 2 nd Layer at 600 km 3 rd Layer at 1, 000 km 22

ION GNSS 22 -25 Sept. 2009 - ENRI Ionosphere Layers at 01: 00 LT Total Delay 1 st Layer at 350 km 2 nd Layer at 600 km 3 rd Layer at 1, 000 km 23

ION GNSS 22 -25 Sept. 2009 - ENRI Residual Error (1) 24 1 -Layer Model 2 -Layer Model 3 -Layer Model Shell Height 1 -Layer: (350) 2 -Layer: (350, 600) 3 -Layer: (350, 600, 1000) • 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; • Some periods that multi-layer models returns larger residual error.

ION GNSS 22 -25 Sept. 2009 - ENRI 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; • Reduces residual error further; However the worst residual becomes larger.

ION GNSS 22 -25 Sept. 2009 - ENRI Conclusion 26 • 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: – 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: – – – Analyze and prevent large residual situations for multiple layer models; Consider to use a priori information for modeling; Temporal variation and scintillation effects.