Airborne GPS Positioning with cm-Level Precisions at Hundreds of km Ranges Gerald L. Mader National Geodetic Survey Silver Spring, MD National Geodetic Survey National Ocean Service National Oceanic and Atmospheric Administration

National Geodetic Survey National Ocean Service National Oceanic and Atmospheric Administration G. L. Mader - 2/25 ION – Savannah, GA Sept. 25, 2009 Outline Some results How it works Some more results Focus on airborne GPS NGS KINPOS program Post-processing Interactive, semi-automated Graph oriented

National Geodetic Survey National Ocean Service National Oceanic and Atmospheric Administration G. L. Mader - 3/25 ION – Savannah, GA Sept. 25, 2009 Kinematic GPS Multiple base stations Find mean trajectory Look differences from mean 1 st example  LIDAR Mapping Project San Andreas Fault May 21, 2005  No external calibration  No repetitive measurements  1 epoch of data for each position  Positions can never be reoccupied Challenges: Emulate static

National Geodetic Survey National Ocean Service National Oceanic and Atmospheric Administration G. L. Mader - 4/25 ION – Savannah, GA Sept. 25, 2009

National Geodetic Survey National Ocean Service National Oceanic and Atmospheric Administration G. L. Mader - 5/25 ION – Savannah, GA Sept. 25, 2009

National Geodetic Survey National Ocean Service National Oceanic and Atmospheric Administration G. L. Mader - 6/25 ION – Savannah, GA Sept. 25, 2009 North RMS=0.7cm East RMS=0.5cm Up RMS=2.0cm All component differences with tropo estimation

National Geodetic Survey National Ocean Service National Oceanic and Atmospheric Administration G. L. Mader - 7/25 ION – Savannah, GA Sept. 25, 2009 Aircraft Height Differences Distances from Base Stations Aircraft Height

National Geodetic Survey National Ocean Service National Oceanic and Atmospheric Administration G. L. Mader - 8/25 ION – Savannah, GA Sept. 25, 2009 λ k (dd(Φ j ) k + dd(N j ) k ) = dd(R i j ) dd(N j ) k = dd(R i j ) / λ k - dd(Φ j ) k R i j = [ ( x j – x i ) 2 + (y j – y i ) 2 + ( z j – z i ) 2 ] ½ KINPOS Technique Double Difference, Integer Fixed, Ion-free solutions Estimate integers from differential code solution

National Geodetic Survey National Ocean Service National Oceanic and Atmospheric Administration G. L. Mader - 9/25 ION – Savannah, GA Sept. 25, 2009 Integer Search Range Search volume (integer range) must be large enough to include true position (correct integers). sv L1 L ± ± ± ± ± ± ± ± ± ± ± ± 2

National Geodetic Survey National Ocean Service National Oceanic and Atmospheric Administration G. L. Mader - 10/25 ION – Savannah, GA Sept. 25, 2009 dd(Φ j ) 1 + dd(N j ) 1 = dd(R i j ) / λ 1 + I 1 dd(Φ j ) 2 + dd(N j ) 2 = dd(R i j ) / λ 2 + ( λ 2 / λ 1 ) I 1 I 1 = [λ 1 2 ( dd(Φ j ) 1 + dd(N j ) 1 ) – λ 1 λ 2 ( dd(Φ j ) 2 + dd(N j ) 2 )] / (λ 1 2 – λ 2 2 ) Ionosphere Filter Too many integer pairs  filter by predicted ion delay Insert all possible integer pairs Observed phases Predicted ionosphere

National Geodetic Survey National Ocean Service National Oceanic and Atmospheric Administration G. L. Mader - 11/25 ION – Savannah, GA Sept. 25, N1/N Change in L1 Ionosphere Delay with N1,N2 Integer Pairs

National Geodetic Survey National Ocean Service National Oceanic and Atmospheric Administration G. L. Mader - 12/25 ION – Savannah, GA Sept. 25, N1/N Select L1 Ionosphere Delays Near Zero

National Geodetic Survey National Ocean Service National Oceanic and Atmospheric Administration G. L. Mader - 13/25 ION – Savannah, GA Sept. 25, 2009 {λ 1 λ 2 2 [( dd(Φ j ) 1 + dd(N j ) 1 )] – λ 1 2 λ 2 [( dd(Φ j ) 2 + dd(N j ) 2 )]} / (λ 2 2 – λ 1 2 ) = dd(R i j ) RMS = [ Σ j (A ij x i – v j ) 2 / (N j -1)] ½ Use integer pairs surviving ion filter to do ion-free, least squares solution Evaluate solutions using Root Mean Square (RMS) Least Squares Solutions Integer Search Principles 1. Correct integers give good RMS 2. Wrong integers give bad RMS 3. However, wrong integers can temporarily give good RMS

National Geodetic Survey National Ocean Service National Oceanic and Atmospheric Administration G. L. Mader - 14/25 ION – Savannah, GA Sept. 25, 2009 Integer Pair Summary Permutation Sequence # sv L1 L2 # sv L1 L2 # sv L1 L2 118 … … 1 02 … … 1 12 … … 1 22 … … 1 14 … … 1 02 … … 218 … … 2 02 … … 2 12 … … 2 14 … … 2 02 … … 318 … … 3 02 … … 3 12 … … 3 14 … … 418 … … 4 02 … … 4 12 … … 4 14 … … 518 … … 5 02 … … 5 12 … … 5 14 … … 618 … … 6 02 … … 6 02 … … 718 … … 7 02 … … 7 14 … … 818 … … … … 918 … …

National Geodetic Survey National Ocean Service National Oceanic and Atmospheric Administration G. L. Mader - 15/25 ION – Savannah, GA Sept. 25, Permutation Procedure Solution w/ 1 st 4 DDs If RMS good: Add next DD If RMS good: Add next DD If all DDs used and gave good RMS – Save the integer set If RMS bad: Advance to next 4 DD group

National Geodetic Survey National Ocean Service National Oceanic and Atmospheric Administration G. L. Mader - 16/25 ION – Savannah, GA Sept. 25, 2009 RMS (mm) seconds Correct integer suite Incorrect integer suites contrast Evolution of RMS for Several Integer Suites Optimal is not always correct !

National Geodetic Survey National Ocean Service National Oceanic and Atmospheric Administration G. L. Mader - 17/25 ION – Savannah, GA Sept. 25, 2009 dd(Φ j ) ion-free = dd(R i j ) + (ZTD 1 – ZTD R ) M 1 j – (ZTD 1 – ZTD R ) M jo dd(Φ j ) ion-free = dd(R i j ) + (C 1 * Δh + C 2 * Δh 2 ) ( M 1 j – M jo ) ZTD = ZTD 0 + C 1 * h + C 2 * h 2 + C 3 * h 3 + … ZTD = ZTD 0 e –h/H dd(Φ j ) ion-free = dd(R i j ) + ZTD 0 e –h/H ( M 1 j – M jo ) 1 st case – low altitude 2nd case – high altitude Troposphere Estimation

National Geodetic Survey National Ocean Service National Oceanic and Atmospheric Administration G. L. Mader - 18/25 ION – Savannah, GA Sept. 25, 2009 Phase Center Fixed Radius 090 -π-π +π+π elv 0 Antenna Calibration Troposphere estimation assumes all elevation dependent effects are due to troposphere Any residual or unmodeled elevation dependencies will perturb troposphere delay solution Can cause significant height errors GPS antenna is primary contributor

National Geodetic Survey National Ocean Service National Oceanic and Atmospheric Administration G. L. Mader - 19/25 ION – Savannah, GA Sept. 25, 2009

National Geodetic Survey National Ocean Service National Oceanic and Atmospheric Administration G. L. Mader - 20/25 ION – Savannah, GA Sept. 25, 2009 Antenna Calibration L1 & L2 Phase Center Variation (PCV)

National Geodetic Survey National Ocean Service National Oceanic and Atmospheric Administration G. L. Mader - 21/25 ION – Savannah, GA Sept. 25, 2009

National Geodetic Survey National Ocean Service National Oceanic and Atmospheric Administration G. L. Mader - 22/25 ION – Savannah, GA Sept. 25, 2009 Aircraft Height Differences Distances from Base Stations Aircraft Height

National Geodetic Survey National Ocean Service National Oceanic and Atmospheric Administration G. L. Mader - 23/25 ION – Savannah, GA Sept. 25, 2009 Quality Control Consistently low RMS Continuity of ionosphere delays Agreement of multiple trajectories

National Geodetic Survey National Ocean Service National Oceanic and Atmospheric Administration G. L. Mader - 24/25 ION – Savannah, GA Sept. 25, 2009 Comparison – GRAFNAV & KINPOS

National Geodetic Survey National Ocean Service National Oceanic and Atmospheric Administration G. L. Mader - 25/25 ION – Savannah, GA Sept. 25, 2009 Conclusions Ionosphere filtering aids ambiguity resolution Estimating troposphere parameters improves heights Antenna calibrations strongly recommended Within limits used here, cm-level precisions achieved independent of range, elevation, altitude Accuracies (?)