L MADE TO MEASURE SKI-Pro Adjustment Result Analysis - 1 SKI-Pro Adjustment Result Analysis Leica GPS System 500

L MADE TO MEASURE SKI-Pro Adjustment Result Analysis - 2 SKI-Pro Adjustment Result Analysis  Content:  SKI-Pro Statistical Tests  Adjustment Logfile Examination  Exercise:  Adjustment Troubleshooting.  Identify, remove and correct Bad Vector(s).

L MADE TO MEASURE SKI-Pro Adjustment Result Analysis - 3 SKI-Pro Statistical Hypothesis Testing  Statistical testing involves accepting or rejecting a statement using a Prime and Alternate Hypotheses:  The rejection of the Prime hypothesis while in fact the statement is true leads to a Type I decision error having a probability given by .  The acceptance of the Prime hypothesis while in fact the statement is false leads to a Type II decision error having a probability given by  (where (1-  ) is the power of the test). StatementDecision: accept PrimeDecision: reject Prime (reject Alternate) (accept Alternate) Truecorrect decision: Type I error: probability = (1 -  )probability =  FalseType II error:correct decision: probability =  probability = (1 -  )

L MADE TO MEASURE SKI-Pro Adjustment Result Analysis - 4 SKI-Pro Statistical Test Error Probability Levels Error Probability Levels (Alpha)

L MADE TO MEASURE SKI-Pro Adjustment Result Analysis - 5 SKI-Pro Statistical Test Power Levels Power Levels (1-Beta)

L MADE TO MEASURE SKI-Pro Adjustment Result Analysis - 6 SKI-Pro Variance Ratio F - Test F - Critical Value  (1-  ) F - Distribution F - Test Confidence Level (%) F - Test Error Probability Level (%)  (1-  ) Prime Hypothesis Alternate Hypothesis Acceptance RegionRejection Region Power of test

L MADE TO MEASURE SKI-Pro Adjustment Result Analysis - 7 SKI-Pro Individual Blunder Detection W - Test (1-  ) Tau - Distribution W -Test Confidence Level (%) W - Test Error Probability Level (%)  /2  (1-  ) Prime Hypothesis Alternate Hypothesis Acceptance Region Rejection Region Power of test - (W - Critical Value)W - Critical Value

L MADE TO MEASURE SKI-Pro Adjustment Result Analysis - 8 SKI-Pro Group Blunder Detection T - Test T - Critical Value (1-  ) Tau - Distribution T -Test Confidence Level (%) T - Test Error Probability Level (%)   (1-  ) Prime Hypothesis Alternate Hypothesis Acceptance Region Rejection Region Power of test

L MADE TO MEASURE SKI-Pro Adjustment Result Analysis - 9 SKI-Pro Adjustment Logfile Header Information 3D minimally constrained network on WGS'84 ellipsoid STATIONS Number of (partly) known stations 1 Number of unknown stations 3 Total 4 OBSERVATIONS GPS coordinate differences 18 (6 baselines) Known coordinates 3 Total 21 UNKNOWNS Coordinates 12 Total 12 Degrees of freedom 9 ADJUSTMENT Number of iterations 1 Max coord correction in last iteration m # of Stations x 3 # of Observations - # of Unknowns Solution Convergence # of Baselines x 3

L MADE TO MEASURE SKI-Pro Adjustment Result Analysis - 10 SKI-Pro Adjustment Logfile Statistical Test Values TESTING Alfa (multi dimensional) Alfa 0 (one dimensional) Beta 0.80 Critical value W-test 1.96 Critical value T-test (3 dimensional) 1.89 Critical value F-test 1.20 F-test accepted W-Test Error Probability (5%) (1-Beta) Power Level (80%) Computed Variance Ratio and F-Test Acceptance Tau Critical Value for W-Outlier Detection Test Tau Critical Value for T-Outlier Detection Test F- Critical Value for Variance Ratio Test F-Test Error Probability (29%)

L MADE TO MEASURE SKI-Pro Adjustment Result Analysis - 11 SKI-Pro Adjustment Logfile Initial Coordinates Results based on a-posteriori variance factor ELLIPSOID CONSTANTS Ellipsoid WGS'84 Semi major axis m Inverse flattening INPUT APPROXIMATE GPS COORDINATES Station Latitude Longitude Height (m) BABBAGE N W BOSSLER N* W* * known DUNROBIN N W PIER N W Initial WGS-84 Coordinate Values 3-D Cartesian Reference System Computed Variance Factor  2 applied to Adjustment Error Estimates

L MADE TO MEASURE SKI-Pro Adjustment Result Analysis - 12 SKI-Pro Raw Observations & Initial Error Estimates INPUT OBSERVATIONS Station Target St ih Tg ih Reading DX BABBAGE BOSSLER m DY m DZ m DX BABBAGE DUNROBIN m DY m DZ m INPUT STANDARD DEVIATIONS OF OBSERVATIONS Station Target Sd abs Sd rel Sd tot DX BABBAGE BOSSLER m DY cor m DZ cor cor m DX BABBAGE DUNROBIN m DY cor m DZ cor cor m GPS Vector Covariance Lower Triangular Part of GPS Vector Covariance Matrix GPS Raw Vector Components

L MADE TO MEASURE SKI-Pro Adjustment Result Analysis - 13 SKI-Pro Adjusted Coordinates COORDINATES (MINIMALLY CONSTRAINED NETWORK) Station Coordinate Corr Sd BABBAGE Latitude N m Longitude W m Height m BOSSLER Latitude N* fixed m Longitude W* fixed m Height * fixed m DUNROBIN Latitude N m Longitude W m Height m PIER51 Latitude N m Longitude W m Height m Adjusted Coordinates Network Constraining Status Coordinates held fixed Coordinate Standard Deviations (1-Sigma precision estimates) Correction from initial to adjusted coordinate values

L MADE TO MEASURE SKI-Pro Adjustment Result Analysis - 14 SKI-Pro External Reliability on Coordinates EXTERNAL RELIABILITY Station Ext Rel Station Target BABBAGE Latitude m DY BABBAGE BOSSLER Longitude m DX BABBAGE DUNROBIN Height m DZ BABBAGE BOSSLER BOSSLER Latitude m DY BOSSLER PIER51 Longitude m DX BOSSLER PIER51 Height m DZ BOSSLER PIER51 DUNROBIN Latitude m DZ BOSSLER DUNROBIN Longitude m DX BOSSLER PIER51 Height m DY DUNROBIN PIER51 PIER51 Latitude m DY BOSSLER PIER51 Longitude m DX BOSSLER PIER51 Height m DY BOSSLER PIER51 External Reliability

L MADE TO MEASURE SKI-Pro Adjustment Result Analysis - 15 SKI-Pro Absolute & Relative Confidence Regions ABSOLUTE STANDARD ELLIPSES Station A B A/B Phi BABBAGE m deg BOSSLER m deg DUNROBIN m deg PIER m deg RELATIVE STANDARD ELLIPSES Station Station A B A/B Psi Sd Hgt BABBAGE BOSSLER m deg m BABBAGE DUNROBIN m deg m BABBAGE PIER m deg m DUNROBIN PIER m deg m BOSSLER DUNROBIN m deg m Point Confidence Regions Error Ellipse Orientation from North Semi Major Axis Semi Minor AxisAxis Ratio Confidence Regions between Points Standard Deviation in Height Difference

L MADE TO MEASURE SKI-Pro Adjustment Result Analysis - 16 SKI-Pro Residuals & Adjusted Observations ADJUSTED OBSERVATIONS Station Target Adj obs Resid Resid(ENH) Sd DX BABBAGE BOSSLER m DY m DZ m DX BABBAGE DUNROBIN m DY m DZ m DX BABBAGE PIER m DY m DZ m DX DUNROBIN PIER m DY m DZ m DX BOSSLER DUNROBIN m DY m DZ m Residuals in Cartesian Units Residuals in Geographic Units Standard Deviations of Adjusted Observations

L MADE TO MEASURE SKI-Pro Adjustment Result Analysis - 17 SKI-Pro Blunder Detection & Internal Reliability TEST OF OBSERVATIONS Station Target MDB Red BNR W-test T-test DX BABBAGE BOSSLER m DY m DZ m DX BABBAGE DUNROBIN m DY m DZ m DX DUNROBIN PIER m DY m DZ m ** DX BOSSLER DUNROBIN m ** DY m DZ m ** Blunder Detection W & T Tests Minimum Detectable Bias Redundancy Number in %Bias to Noise RatioStandardized Residuals Vector Standardized Residuals Flagged Measurements as “possible” Blunders

L MADE TO MEASURE SKI-Pro Adjustment Result Analysis - 18 SKI-Pro Estimated Errors from W & T Test Failures ESTIMATED ERRORS FOR OBSERVATIONS WITH REJECTED W-TESTS (max 10) Record Station Target W-test Fact Est err 5 DZ BOSSLER DUNROBIN m 4 DZ DUNROBIN PIER m ESTIMATED ERRORS FOR OBSERVATIONS WITH REJECTED T-TESTS (max 10) Record Station Target T-test Fact Est err 5 DX BOSSLER DUNROBIN m DY m DZ m Estimated Errors on Rejected Standardized Residuals from Blunder Detection W-Test Estimated Errors on Rejected Vector Residuals from 3-D Blunder Detection T-Test