Assimilative Modeling of Ionospheric Dynamics for Now-casting of HF Propagation Channels in the Presence of TIDs Dr. L. J. Nickisch, Dr. Sergey Fridman, Dr. Mark Hausman, Dr. Shawn Kraut NorthWest Research Associates, Monterey, California Dr. George Zunich Zunicalc, Inc., Monterey, California Presented at the 2015 Ionospheric Effects Symposium 12 May 2015 1
Background • IARPA HFGeo program seeks improvements in ionospheric modeling and to mitigate the effects of traveling ionospheric disturbances on geolocating HF emitters • Our approach is to use the GPSII ionospheric data assimilation model, assimilating information from known reference point (KRP) emitters in the region of interest – Delay/Doppler/Angle-of-Arrival measurements of KRPs • Theory for delay-Doppler-AoA assimilation presented in a companion paper (Fridman, et al., IES 2015) • Here we present results from the IARPA HFGeo WSMR collection campaign of January 2014 AoA = Angle of Arrival 2
The Ionospheric Reconstruction Problem: Tikhonov Method = u ( r , t ) N ( r , t ) N ( r , t ) e 0 { } = U { u ( r , t )}, Biases ≈ Y M [ U ] Y is the set of measured absolute/relative TEC values and data points from other types of ionospheric measurements. The solution must fit the data within − − − ≤ T 1 ( Y M [ U ]) S ( Y M [ U ]) dim( Y ) 1 errors of measurements. Error covariance matrix There are infinitely many such solutions: − U → U T 1 P min The smoothest solution is selected by minimizing the stabilizing functional Pseudo-covariance matrix -The pseudo-covariance P matrix is defined in such a way that the stabilizing functional tends to take on larger values for unreasonably behaving solutions (“reasonable” “smooth”). -The nonlinear optimization problem is solved iteratively (Newton- Kontorovich). 3 3
Delay-Doppler Assimilation 35.0 ° N KAFB • Good results on TID = Tx SITE (BLUE) modeling can be = Rx SITE (RED) attained by = LINK MIDPOINT (COLOR MATCHES LINK) assimilating only ASSIMILATED LINKS delay-Doppler data RP1 to G10 RP1 to Green of receptions from 34.0 ° N RP1 to KAFB Known Reference RP1 to NSO G r Fran to G10 e N e Point (KRP) 1 n Q Green to G10 Green u P O e o s e Rob to G10 n emitters F c n d r u a r n P a R 6 1 o 6 b • Links used in the Roswell R following results P 1 are shown here 33.0 ° N NSO G10 50 0 50 100 150 200 km 104.0 ° W 105.0 ° W 106.0 ° W 107.0 ° W 4
Results on an assimilated link In-plane Err. w.r.t. Array Est. Degrees East of Zenith (Fran to G10): train O, trace O 4 1 3 0 in-plane vertical error (deg) 2 deg. East of Zenith -1 1 0 -2 -1 -3 -2 -4 -3 Govt. (Clean,culled) J-S Ray Trace (IS) -4 -5 -4 -3 -2 -1 0 1 2 3 4 16:00 17:00 18:00 19:00 20:00 in-plane horizontal error (deg) time (on Jan 19) Degrees North of Zenith (Fran to G10): train O, trace O Solid Angle Error Emp. CDF 18 1 0.9 16 empirical CDF probability 0.8 deg. North of Zenith 0.7 14 0.6 0.5 12 0.4 0.3 10 0.2 Govt. (Clean,culled) With bias 0.1 J-S Ray Trace (IS) Bias removed 8 0 16:00 17:00 18:00 19:00 20:00 0 1 2 3 4 5 6 7 8 9 10 5 time (on Jan 19) circular solid angle error (mSR)
Results on a non-assimilated link In-plane Err. w.r.t. Array Est. Degrees East of Zenith (N1 to G10): train O, trace O 6 3 5 4 2 in-plane vertical error (deg) 3 deg. East of Zenith 2 1 1 0 0 -1 -2 -1 -3 -4 -2 Govt. (Clean,culled) -5 J-S Ray Trace (IS) -6 -3 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 16:00 17:00 18:00 19:00 20:00 in-plane horizontal error (deg) time (on Jan 19) Degrees North of Zenith (N1 to G10): train O, trace O Solid Angle Error Emp. CDF 22 1 0.9 20 0.8 empirical CDF probability deg. North of Zenith 0.7 18 0.6 16 0.5 0.4 14 0.3 0.2 12 Govt. (Clean,culled) With bias 0.1 J-S Ray Trace (IS) Bias removed 10 0 16:00 17:00 18:00 19:00 20:00 0 1 2 3 4 5 6 7 8 9 10 6 time (on Jan 19) circular solid angle error (mSR)
Delay-Doppler-AoA Assimilation 0 ° 3 5 . N KAFB • Better results on = Tx SITE (BLUE) TID modeling can = Rx SITE (RED) = VERTICAL SOUNDER (MAGENTA) be attained by also = LINK MIDPOINT (COLOR MATCHES LINK) assmilating Angle- of-Arrival (AoA) ASSIMILATED LINKS data in addition to RP1 to G10 0 ° 3 4 N Fran to G10 . delay-Doppler data Green Green to G10 N1 Cherry of receptions from Queen Green Pond Oscura Fran Known Reference P616 Rob Point (KRP) Roswell emitters RP1 • Links used in the 0 ° 3 3 N . following results Cherry NSO are shown here G10 50 0 50 100 150 200 km 0 ° 105.0 ° W 106.0 ° W 0 ° W 1 0 4 . 1 0 7 . W 7
Results on an assimilated link In-plane Err. w.r.t. Array Est. Degrees East of Zenith (Green to G10): train O+VI, trace O 3 0 2 in-plane vertical error (deg) -1 deg. East of Zenith 1 -2 0 -3 -1 -4 -2 Govt. (Clean,culled) J-S Ray Trace (IS) -3 -5 -3 -2 -1 0 1 2 3 16:00 17:00 18:00 19:00 20:00 in-plane horizontal error (deg) time (on Jan 19) Degrees North of Zenith (Green to G10): train O+VI, trace O Solid Angle Error Emp. CDF 22 1 0.9 20 empirical CDF probability 0.8 deg. North of Zenith 0.7 18 0.6 16 0.5 0.4 14 0.3 0.2 12 Govt. (Clean,culled) With bias 0.1 J-S Ray Trace (IS) Bias removed 10 0 16:00 17:00 18:00 19:00 20:00 0 1 2 3 4 5 6 7 8 9 10 8 time (on Jan 19) circular solid angle error (mSR)
Results on a non-assimilated link In-plane Err. w.r.t. Array Est. Degrees East of Zenith (Pond to G10): train O+VI, trace O 3 1 2 in-plane vertical error (deg) 0 deg. East of Zenith 1 -1 0 -2 -1 -3 -2 Govt. (Clean,culled) J-S Ray Trace (IS) -3 -4 -3 -2 -1 0 1 2 3 16:00 17:00 18:00 19:00 20:00 in-plane horizontal error (deg) time (on Jan 19) Degrees North of Zenith (Pond to G10): train O+VI, trace O Solid Angle Error Emp. CDF 20 1 0.9 18 empirical CDF probability 0.8 deg. North of Zenith 0.7 16 0.6 14 0.5 0.4 12 0.3 0.2 10 Govt. (Clean,culled) With bias 0.1 J-S Ray Trace (IS) Bias removed 8 0 16:00 17:00 18:00 19:00 20:00 0 1 2 3 4 5 6 7 8 9 10 9 time (on Jan 19) circular solid angle error (mSR)
Ionogram comparison 3 4 5 6 7 8 9 MHz 10
Lessons • Notably, delay-Doppler assimilation of KRP data is sufficient to define TIDs in the ionosphere model and track AoA deviations • Delay-Doppler-AoA assimilation of KRPs works a bit better (not surprisingly) 11
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