Requirements for Generating. A Geometrically Correct Point Cloud

Transcription

1 Requirements for Generating A Geometrically Correct oint Cloud Dr. eter Friess Optech International AGENDA 1. Introduction rinciple of airborne laser mapping (ALM) Characteristics of ALM roducts and product quality 2. Mathematical model for laser point computation Functional model (basic) Stochastic model Lab calibration Effects of model (calibration) parameters on laser points Extended functional model 3. Laser point block adjustment Description/definition Mathematical model arameter determinability Empirical results 4. Summary ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 2

2 Airborne Laser Mapping rinciple Z- Y- z x y X- ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 3 Airborne Laser Mapping rinciple Sensor Orientation osition by GS Attitudes by INS Sensor Measurements Laser ranges Scanner angles Z- Y- z x y X- ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 4

3 Airborne Laser Mapping Characteristics Distance measurements to almost any type of surface Ability to measure several elevations along same direction (multiple returns) Detected signal strength of the target-reflected laser-emitted pulse (intensity) Lambertian-ype Surface R Specular-ype Surface arget surface ALS Detector Signal (most natural surfaces) (glass, water,, smooth-wet surfaces) first pulse laser points time t o t 1 t 2 t 3 t n last pulse laser points first last ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 5 Laser oint Information Height Intensity Return ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 6

4 Airborne Laser Mapping Instrument Development khz 1000 m max. AGL height ± 20 degree scan angle first or last return 4 5 m point spacing (single 1000 m AGL) 2007 up to ~170 khz up to 4500 m max. AGL height up to ± 32 degree scan angle multiple returns to full wave form 8 16 bit intensity values < 1 m point spacing (single 1000 m AGL) ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 7 Airborne Laser Mapping roducts Service ALM survey flight Key products Laser point cloud Classified laser point cloud Derivative products E.g. digital elevation models Intensity images Digital photos, ortho-photos SCO - Manual, inpho GmbH ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 8

5 Airborne Laser Mapping roduct Quality Service ALM survey flight Key products Laser point cloud Classified laser point cloud Derivative products E.g. digital elevation models General quality attributes Schedule, completeness, point density, etc. Accuracy Laser point accuracy Classification accuracy DM accuracy Intensity images Digital photos, ortho-photos ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 9 Laser oint Accuracy Accuracy Closeness of the computed laser point position to the position of the true laser footprint Expressed he degree as of standard closeness deviations of an observed of the laser value point to the coordinates true value Affected by observation errors ε = l t laser beam laser point footprint ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 10

6 Classification Accuracy he degree of correctness of assigned attributes Expressed in probability for the correctness of the assigned attribute Geometry Attributes lane, line, ground, etc. Object Attributes Building, street, tree, etc. Material Attributes Asphalt, concrete, water, etc. ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 11 DM Accuracy Vertical closeness of the DM surface to the true physical terrain surface Expressed as RMS of the differences between the interpolated height and the measured height of check points Representation Surface Roughness ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 12

7 ALM roduct Accuracies Key products Laser point cloud Classified laser point cloud have quite distinct accuracy characteristics Derivative products E.g. digital elevation models Currently, ALM products are usually only empirically evaluated for accuracy by comparison to ground truth data. ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 13 Empirical Accuracy ests rue laser footprint position is NO known! herefore: No direct point to point correspondence between laser points ( ) and control points ( ). hus: Correspondence via surface, e.g. DEM ( ). H = H L H C-DEM minimum H maximum H mean H rms H ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 14

8 Empirical Accuracy Interpretation Asphalt Farmland, meadows, Forest rms h = 0.05 m rms h = 0.23 m rms h = 0.41 m ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 15 Mathematical Model Observations Mathematical model arameters l [ r x y z η χ α ] = Θ Functional model X = [ x y z ] L L L L C ll σ 2 r 2 = σ Θ Stochastic model C σ c c = 2 x xy xz 2 XX cxy σ y cyz 2 cxz cyz σ z ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 16

9 [Geo] Referencing rinciple Z - RFA γ Orientation arameters, or Orientation Elements, or ransformation arameters, or Z - RFB A set of values describing the relationship between two reference frames. α β 3 rotation angles X - RFA y RFB ORFA z RFB ORFA x RFB ORFA Y - RFA Y - RFB 3 translations RFA = Reference Frame A RFB = Reference Frame B X - RFB ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 17 Rotation Matrices R X ( α ) = cos α sin α 0 sin α cos α R Y cos β ( β ) = 0 sin β sin β 0 cos β R Z cosγ sinγ ( γ ) = sinγ cosγ he rotations are positive in the counterclockwise sense as viewed along the axis toward the origin (right-hand-rule). he rotation matrices are orthogonal: R 1 ( Θ) = R ( Θ) = R( Θ) hus: 1 ( R ( γ ) R ( β ) R ( α )) = ( R ( γ ) R ( β ) R ( α )) = R ( α ) R ( β ) R ( γ ) Z Y X Z Y X X Y Z ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 18

10 Laser oint Computation Functional Model Z- Y- z x y X- ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 19 Laser oint Computation Functional Model Y- y X = X? with: O + R X X- X = x y z Z- Z- z O z X X O R = x y z = xo yo zo = R ECE F ( α, β, γ ) Y- x O y O x y x z = Sensor Body Frame = Earth Centered X- ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 20

11 Sensor Model Y- 0 0 sin ( ) 0 r cos Θ p rp X =? rp Θ = R X Θ with: X- X = x y z Θ Θ = scan angle Z- r r = range z Observation model: Θ = s Θ Θ obs + Θ y r s Θ, Θ = robs + r = scan angle corrections = Sensor Body Frame r = range corrections ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 21 Geo-Referencing - osition C Y- X- x C y C z C y X with: X = X O + R X = x y z Z- Z- z O z AC z X = X O R =? X =? C R X C Y- x O y O x AC x y AC y x z C = ositioning Center = Sensor Body Frame = Earth Centered X- ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 22

12 Geo-Referencing - Orientation R =? Y - IBF X - IBF Z - IBF Y - X - Z - IBF = IMU Body Frame = Sensor Body Frame ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 23 Geo-Referencing Orientation Y - IBF χ Y - LGF LGF R = R? R R with: LGF IBFF IBF F X - LGF R = R ( E ) R ( E ) R ( E ) IBF Z Z Y Y X X X - IBF η Z - IBF α Z - LGF R = R ( α ) R ( χ ) R ( η ) LGF IBF Z π R = R ( λ ) R ( ϕ + ) LGF Z Y Y E X, EY, E Z = -IBF relative orientation η, χ, α = roll, pitch, heading X 2 Y - E Y ϕ, λ = latitude, longitude X - E X E Z Z - LGF = Local Geodetic Frame IBF = IMU Body Frame = Sensor Body Frame ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 24

13 Laser oint Computation Functional Model (Basic) with: R = R ( E ) R ( E ) R ( E ) IBF LGF IBF E X, EY, E Z = -IBF relative orientation η, χ, α = Roll, pitch, heading ϕ, λ Z Z Y Y X X R = R ( α ) R ( χ ) R ( η ) LGF Z π R = R ( λ ) R ( ϕ + ) Z Y Y = Latitude, longitude X 2 ( ) GF IBF X = X + R R R X X L C LGF IBF C X C X C X = Sensor position center = osition center eccentricities e.g. Sensor Model - ALS Camera x0 0 y X = µ r sin Θ = R ( Θ ) 0 p X r cos fθ p rp with: Θ x, y = scan image angle coordinates r f = range focal length µ = scale factor = Sensor Body Frame IBF = IMU Body Frame LGF = Local Geodetic Frame = Laser point in sensor body frame = Earth Centered Earth Fixed ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 25 Laser oint Computation Functional Model (Basic) Observations GS antenna center position X C IMU roll, pitch, heading η, χ, α R LGF IBF ALS scan angle, laser range Θ, r X Mounting parameters ALS-IMU relative orientation ALS-osition center eccentricities E X, EY, E Z X C R IBF Corrections Observation corrections r, Θ, s ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 26

14 Laser oint Computation Stochastic Model C XX =? for ( X C ) X = X + R R R X X C LGF IBF AC C LGF IBF F AC Indirect observations Indirect observations C GS Indirect observations C IMU C XX C GS C IMU C XX = Covariance matrix of antenna position = Covariance matrix of roll, pitch, heading = Covariance matrix of laser point in ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 27 Covariance Law Functional Model x = f( l) with: [ ] x = x1 x2 x u l = [ ] and l1 l2 l n ( ) x = f l l l n ( ) x = f l l l n Stochastic Model CXX = J Cll J with: J x x x l1 l 2 l x x x = l1 l 2 l n x x x l1 l 2 l u u u n n = Jacobian matrix ( ) x = f l l l u u 1 2 n C XX C ll = Covariance matrix of parameters x = Covariance matrix of observations l ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 28

15 Laser oint Computation Stochastic Model C = C? + J? C J + J C J C = + IBF? XX GS IMU IMU IMU XX XX XX for with: C GS C IMU C XX = Covariance matrix of antenna position ( X X A C ) F LGF IBF IBF X = δ X AC + R LGF R R X X δ X δ X AC J IMU = δη δχ δα C XX = Jll C ll Jll Indirect observations C XX δ Indirect observations C XX = X with: J IMU δ X δ X δ X Indirect observations C J GS ll = δ r obs δθ Obs X = Covariance matrix of roll, pitch, heading = Covariance matrix of laser point in = Laser point in Stochastic Sensor Model C σ r σ Θ ll 2 σ r = 2 σ Θ = Standard dev. of laser range = Standard dev. of scan angle X = Laser point in ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 29 Stochastic Model Error ropagation Random Observation Errors Laser range Scan angle (mechanical) GS antenna position IMU attitudes σ R = m σ Θ = deg σ X = m σ Y = m σ Z = m σ R = deg σ = deg σ H = deg Resulting Random Errors for Laser oints (AGL 1000 m) East (Cross-Flight) σ min = m σ mean = m σ max = m North (In-Flight) σ min = m σ mean = m σ max = m Height σ min = m σ mean = m σ max = m Resulting Random Errors for Laser oints (AGL 2000 m) East (Cross-Flight) σ min = m σ mean = m σ max = m North (In-Flight) σ min = m σ mean = m σ max = m Height σ min = m σ mean = m σ max = m ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 30

16 Stochastic Model Example AGL 1000 Errors in Easting (Cross-Flight) 1.2 m 1.0 m 0.8 m 0.6 m 0.4 m 0.2 m 0.0 m -0.2 m -0.4 m -0.6 m -0.8 m -1.0 m -1.2 m Empirical max. ε = m min. ε = m mean ε = m rms ε = m -σ ε σ = 68.2 % heoretical σ max σ min σ mean = m = m = m Scan angle ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 31 Stochastic Model Example AGL 1000 Errors in Northing (In-Flight) 1.2 m 1.0 m 0.8 m 0.6 m 0.4 m 0.2 m 0.0 m -0.2 m -0.4 m -0.6 m -0.8 m -1.0 m -1.2 m Empirical max. ε = m min. ε = m mean ε = m rms ε = m -σ ε σ = 68.5 % heoretical σ max σ min σ mean = m = m = m Scan angle ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 32

17 Stochastic Model Example AGL 1000 Errors in Height 1.2 m 1.0 m 0.8 m 0.6 m 0.4 m 0.2 m 0.0 m -0.2 m -0.4 m -0.6 m -0.8 m -1.0 m -1.2 m Empirical max. ε = m min. ε = m mean ε = m rms ε = m -σ ε σ = 68.5 % heoretical σ max σ min σ mean = m = m = m Scan angle ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 33 Stochastic Model Example Errors in Easting (Cross-Flight) 1.2 m 1.0 m 0.8 m 0.6 m 0.4 m 0.2 m 0.0 m -0.2 m -0.4 m -0.6 m -0.8 m -1.0 m -1.2 m -730 m -365 m For AGL 1000 m σ max σ min σ mean = m = m = m For AGL 2000 m σ max = m σ min = m σ mean = m m 730 m Cross Flight Line ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 34

18 Stochastic Model Example Errors in Northing (In-Flight) 1.2 m 1.0 m 0.8 m 0.6 m 0.4 m 0.2 m 0.0 m -0.2 m -0.4 m -0.6 m -0.8 m -1.0 m -1.2 m -730 m -365 m For AGL 1000 m σ max σ min σ mean σ max σ min σ mean m 730 m = m = m = m For AGL 2000 m = m = m = m Cross Flight Line ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 35 Stochastic Model Example Errors in Height 1.2 m 1.0 m 0.8 m 0.6 m 0.4 m 0.2 m 0.0 m -0.2 m -0.4 m -0.6 m -0.8 m -1.0 m -1.2 m -730 m -365 m For AGL 1000 m σ max σ min σ mean σ max σ min σ mean m 730 m = m = m = m For AGL 2000 m = m = m = m Cross Flight Line ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 36

19 ALM recision Map 2500 m 775 m e.g. height standard deviations for the individual laser points ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 37 Laser oint Computation Functional Model (Basic) Observations GS antenna center position X C IMU roll, pitch, heading η, χ, α R LGF IBF ALS scan angle, laser range Θ, r X Mounting parameters ALS-IMU relative orientation ALS-osition center eccentricities E X, EY, E Z X C Corrections Observation corrections r, Θ, s R IBF? ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 38

20 Lab (Manufacturer) Calibration ALS sensor/observation parameters Realization of sensor body frame () Laser range offsets Scanner offset Scanner scale factor ALS-IMU relative orientation Orientation Eccentricity ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 39 Lab Calibration Sensor Body Frame Scanner rotation axis X- Y- Laser beam Scanner mirror Z- X- Y- Z- hysically realized by the scanner rotation axis oints into flight direction hysically realized by the incoming laser beam Incoming laser beam lies in a plane which is perpendicular to X- oints to the right side of the aircraft hysically realized by the outgoing laser beam at zero scan angle o be perpendicular to XY-plane (completes right-hand cartesian system) oints down ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 40

21 Lab Calibration ALS IMU Relative Orientation X-IBF Y-IBF X- Y- Z-IBF Z- X- (scanner rotation axis) to be parallel to X-IBF (roll axis) Scanner angle Θ is equivalent to roll angle η Y- to be parallel to Y-IBF (pitch axis) Scanner angle Θ = 0 corresponds to roll η = 0 and pitch χ = 0 ermits scanning about local vertical ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 41 Lab Calibration Laser Range Offset n r 1 r 2 r3 r n lace flat targets ( 1 n ) at several accurately measured distances (r 1 r n ) Measure a large number of ranges to each of the targets Compute the range offset from differences between true and measured ranges ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 42

22 Lab Calibration Scanner arameters n surveyed targets C 2 Θ max distance m osition and orient ALS that scanning laser beam superimposes with targets Set scan angle = 0 and position beam at center target C Measure large number of scan angles for the n targets Compute scan angle offset and scale from differences between true and measured scan angles ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 43 Laser Range Offset Example ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 44

23 Scan Angle Scale Factor Example ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 45 Scan Angle Offset Example ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 46

24 IMU-ALS Relative Orientation E Y Example ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 47 IMU-ALS Relative Orientation E Z Example ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 48

25 Relative Kinematic ositioning Empirical Accuracy Analysis ALM Flight April 12, :05 15:30 UC 54.0 km 36.4 km opscan GmbH ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 49 Relative Kinematic ositioning Least Squares Solution Baseline: Ravensburg Biberach (36.4 km) dual frequency / fixed = (true position computed position) [m] E[cm] N[cm] h[cm] mean rms σ :05 9:05 11:15 13:15 15:30 ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 50

26 Relative Kinematic ositioning KFS Solution Baseline: Ravensburg Biberach (36.4 km) dual frequency 0.15 E[cm] N[cm] h[cm] = (true position computed position) [m] mean rms σ :05 9:05 11:15 13:15 15:30 ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 51 Relative Kinematic ositioning Least Squares Solution Baseline: Geislingen Biberach (54.0 km) dual frequency / float = (true position computed position) [m] line i line j E[cm] N[cm] h[cm] mean rms σ :05 9:05 11:15 13:15 15:30 ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 52

27 Laser oint Computation Geo-Referencing ( X Lab X C ) X = X + X + R R R R R X LGF LGF IBF IBF C C LGF IBF IBF, Lab C, Observations Laser point in X AC, obs GS antenna center position IMU roll, pitch, heading η, χ, α R LGF, X IBF obs Sensor Mounting parameters ALS-IMU relative orientation ALS-osition eccentricities E, E, E X, Lab Y, Lab Z, Lab X C, Lab R IBF, Lab Corrections GS position corrections IMU attitude corrections ALS-IMU orientation corrections Eccentricities corrections X C η, χ, α R LGF IBF E, E, E R IBF X Y Z X C ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 53 Laser oint Computation Sensor Model X [ ] = R( Θ ) 0 0 with: r = r + r + r obs Lab ( s s) Θ = Θ + + Θ + Θ r obs Lab Lab Y- X- Observations Θ Laser range Scan-angle r obs Θ obs Z- r Calibration parameters Laser range offset Scan-angle offset and scale factor Corrections Laser range offset Scan-angle offset and scale factor r Lab, Θ Lab r Θ, s s Lab z y = Sensor Body Frame ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 54

28 L Block Adjustment Approach Analogy to photogrammetric block adjustment Use of planes analytically as tie described and control surface features features as tie and control information Determine a set of corrections for observations and instrument parameters by minimizing the weighted square sum of the observation residuals Requires: Mathematical sensor model Automated planar surface extraction Automated planar surface correspondence arameter estimation (least-squares solution) ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 55 L Block Adjustment Goal he goal is a geometrically correct point cloud with known accuracy characteristics free of blunders and systematic errors accuracy given in form of standard deviations for laser point coordinates only systematic random and errors random are left errors accuracy = precision 0.4 Height errors [m] across flight line ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 56

29 Correspondence roblem Actual, true laser footprint is NO known! i herefore: easy No direct point to point correspondence between laser points ( ) and control points ( ) laser points (, ) of overlapping flight lines j hus: Correspondence via surface, surface-features ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 57 Correspondence roblem Interpolation & Matching rinciple Matching techniques provide the horizontal position (X,Y) of a corresponding point Interpolation techniques provide the height (Z) for the corresponding point hus, Interpolation & matching provide tie points Requirements Matching requires height variations provided by smooth surfaces with surface normal vectors pointing in three independent directions. Limitations Occlusion areas Height jumps (e.g. on buildings) Vegetation areas ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 58

30 Correspondence roblem Surface Features rinciple Analytically modeling surface features Least squares fitting rovides tie features (e.g. planes) with quality attributes Requirements E.g planar surface patches have to exist in project area Limitations Vegetation areas? ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 59 Surface Feature lane Flight Line A Flight Line B a b c d a1 xi + b1 yi + c1 zi + d1 = 0 a + + c + d = a2 x + b2 y + c2 z + d 2 = 0 1 xi + 1 yi + 1 zi + 1 = 0 2 xi b2 yi 2 zi 2 0 i i i ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 60

31 Surface Feature Ditch Vosselman G Fitting an analytical model for a ditch height profile to the laser points for each flight line. Fitting an analytical model for an intensity edge to the laser point intensity values before applying edge detection. ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 61 Surface Feature Line Intersection of laser point planes Roof lines are horizontal Roof lines are known roof line Laser point lines (2D, 3D) Lines as tie feature Lines as control feature Simultaneous laser point and photogrammetric block adjustment ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 62

32 Empirical Studies Runway Line m 775 m Flight arameters January 2, 2003 One flight line approx m long (41.24 seconds at 60.6 m/s ground speed) Flying height 1100 m above ground ALM 35 KHz laser rep. rate, ± 20 deg scan-angle, 35 Hz scan-frequency ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 63 Empirical Studies Runway Line 25: lane- vs. None-lane oints 2500 m 775 m laser points total having two returns 2.7 % none plane points 28.2 % plane points 69.1 % ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 64

33 Empirical Studies Runway Line m 775 m Building 3 Building 1 ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 65 Empirical Studies Runway Line 25 Building 1 ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 66

34 Empirical Studies Runway Line 25 Building 1 ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 67 Empirical Studies Runway Line 25 Building 3 ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 68

35 Least Squares Adjustment Observation Equation I Observation equation g n x n y n z d i, j = X, j i + Y, j i + Z, j i + = 0 Implicit non-linear model g( l + v, x) = 0 Implicit linear model at ( l, x i ) δ g δ g g( l, xi ) + v + x = 0 δ l δ x ( l, x ) ( l, x ) i i or g + D v + A x = 0 where: l v Given observations Unknown residuals of the observations, with v N ( 0 C ), vv x Unknown parameters ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 69 Least Squares Adjustment Observation Equation II Observations GS antenna center position IMU roll, pitch, heading ALS scan angle, laser range Control plane information (seudo-observations for all unknowns) Unknowns lane parameters GS antenna eccentricity corrections ALS-IMU relative orientation corrections IMU attitude corrections osition corrections Laser range correction Scan angle corrections X AC, obs ηobs, χ obs, α obs Θ, r obs obs λ, ϕ, d, or x, y, z r S S S S S λ S, ϕ S, d x, y, z C C C E, E, E Θ, s X Y Z η, χ, α x, y, z C C C ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 70

36 Least Squares Adjustment Solution Best linear unbiased estimate ˆx for : x and where ( ) ˆ vv ( vv ) 1 1 A D C D A x = A D C D g xˆ xˆ 1 ( ( ) ) 1 vv 1 ( ) ( ˆ vv ) C = A D C D A vˆ = C D D C D A x g vv D C D = D C D A C A vv ˆ ˆ vv xx ˆ ˆ C x ˆ x ˆ ˆv C vv ˆ ˆ Covariance matrix of the estimated parameters Estimated residuals of the observations Covariance matrix of the estimated residuals ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 71 L Block Adjustment arameter Determinability I Observation corrections Scan angle corrections Scan angle corrections Laser range correction Mounting parameters ALS-IMU orientation ALS-IMU orientation ALS-IMU orientation osition eccentricity osition eccentricity osition eccentricity Θ s r E E E X Y Z x C y C z C Geo-Referencing corrections per block osition correction x LF C osition correction y LF C osition correction z LF C Attitude correction Attitude correction Attitude correction η χ α ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 72

37 L Block Adjustment Simulation Study I Block Configuration 1235 Overlap areas: all left combinations left right right FL6-E-1 right left center center center left center right Overlap: FL1-N-1 FL2-S-1 FL3-N-1 FL3-S-1 FL4-S-1 FL5-N-1 FL3-S-1 2 fold 3 fold ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 73 L Block Adjustment Simulation Study II lane Orientation N lane ype NW NE W E SW SE aligned rotated single roof lane Size lane Slope 10 m 20 m 20 m large 10 m 5 m 10 m small ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 74

38 L Block Adjustment arameter Determinability II (5 of 11) Observation corrections Scan angle corrections Scan angle corrections Laser range correction Mounting parameters ALS-IMU orientation ALS-IMU orientation Θ s r E Y E Z can always be determined (sloped horizontal (> 10 ) control control plane(s) planes in the at the swath swath center edges with normal vector perpendicular to the flight direction) sloped planes ( 5 ) with normal vectors parallel to the flight direction Basically one cross flight line and (a) horizontal control plane(s) located in the swath center allow for the determination of Θ, s, r, E and E Y Z ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 75 L Block Adjustment arameter Determinability III (7 of 11) Observation corrections Scan angle corrections Scan angle corrections Laser range correction Mounting parameters ALS-IMU orientation ALS-IMU orientation Θ s r E Y E Z can always be determined horizontal control plane(s) in the swath center sloped planes ( 5 ) with normal vectors parallel to the flight direction Highly Highly correlated correlated!! Only Only one one of of them them can can be be determined determined Geo-Referencing corrections per block osition correction osition correction osition correction x LF C y LF C z LF C sloped control planes (> 10 ) with normal vectors perpendicular to each other horizontal control plane(s) in the swath center ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 76

39 L Block Adjustment arameter Determinability IV (9 of 11) Observation corrections Scan angle corrections Scan angle corrections Θ s can always be determined Mounting parameters ALS-IMU orientation ALS-IMU orientation osition eccentricity osition eccentricity osition eccentricity E Y E Z x C Geo-Referencing corrections per block osition correction osition correction osition correction y C z C x LF C y LF C z LF C sloped planes ( 5 ) with normal vectors parallel to the flight direction two different flying heights required, but sloped planes (> 5 ) with Highly Highly normal correlated correlated vector perpendicular!! to flight direction Only Only one one of of them them can can be be determined determined sloped control planes (> 10 ) with normal vectors perpendicular to each other horizontal control plane(s) in the swath center ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 77 Empirical est Rheine Flight ath Flight arameters November 5, h 25 m flight duration 950 m flying height AGL ALM KHz laser rep. rate 25 Hz scan-frequency ± 20 deg scan-angle opscan GmbH ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 78

40 Empirical est Rheine Sub-Blocks Sub-block Rheine Sub-block Mesum opscan GmbH ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 79 Empirical est Rheine Sub-Block Mesum Area 01 4 km km ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 80

41 Empirical est Rheine Sub-Block Mesum Area 01 ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 81 Empirical est Rheine Sub-Block Mesum Area 01 L Block Adjustment 472 planes plane points ~ 322 points/plane 500 m 500 m ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 82

42 Sub-Block Mesum Area 01 Unknown arameters Observation corrections Scan angle corrections Scan angle corrections Mounting parameters ALS-IMU orientation ALS-IMU orientation Θ s E E Y Z Geo-Referencing corrections per n-1 flight lines osition correction z LF C No control information ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 83 Sub-Block Mesum Area 01 Unadjusted max. 25 cm 15 cm 7.5 cm cm -15 cm -25 cm -max. mean h rms h = = 5.1 cm 33.0 cm ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 84

43 Sub-Block Mesum Area 01 Adjusted max. 25 cm 15 cm 7.5 cm cm -15 cm -25 cm -max. mean h rms h = = 0.2 cm 6.2 cm ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 85 Sub-Block Mesum Area 01 arameter recision Observation corrections Scan angle corrections Scan angle corrections Θ s ˆ Θ ˆ s σ = deg σ = 7.7 ppm Mounting parameters ALS-IMU orientation ALS-IMU orientation E E Y Z σˆ E Y σˆ E Z = deg = deg Geo-Referencing corrections per n-1 flight lines osition correction z LF C σ ˆ Z = mm ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 86

44 Accuracy Verification he laser point accuracy can be verified at each of the tie-planes by computing the normal vectors n for the individual laser points deriving statistics for the normal vectors components and lengths: mininum dx, dy, dz, ds maximum dx, dy, dz, ds rms dx, dy, dz, ds n dz dx dy ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 87 BIBLIOGRAHY I Burman H., Calibration and orientation of airborne image and laser scanner data using GS and INS, Dissertation, Royal Institute of echnology, Department of Geodesy and hotogrammetry, Stockholm, Sweden, ISSN Filin, S., Csathó, B., Schenk,., An analytical model for in-flight calibration of laser altimetry systems using natural surfaces. In roceedings of the Annual Conference of the American Society of hotogrammetry and Remote Sensing (ASRS), St. Louis, MO, USA. Filin, S., Recovery of systematic biases in laser altimetry using natural surfaces. In International Archives of hotogrammetry and Remote Sensing, Vol. XXXIV, 3/W4, pp , Annapolis, MD, USA. Filin, S., Vosselman, G., Adjustment of airborne laser altimetry strips. In International Archives of hoto-grammetry and Remote Sensing, Vol. XXXV, B3, pp. 5-9, Istanbul, urkey. Friess., 2006, owards a rigorous methodology for airborne laser mapping, International Calibration and Orientation Workshop EuroCOW, Castelldefels Kager, H., Discrepancies between overlapping laser scanner strips Simultaneous fitting of aerial laser scanner strips. In International Archives of hotogrammetry and Remote Sensing, Vol. XXXV, B/1, pp , Istanbul, urkey. ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 88

45 BIBLIOGRAHY II Kraus, K., Briese, C., Attwenger, M., feifer, N., Quality measures for digital terrain models. In International Archives of hotogrammetry and Remote Sensing, Vol. XXXV, B/2, pp , Istanbul, urkey. Lee, I., Schenk,., (2001). Autonomous extraction of planar surfaces from airborne laser scanning data. In roceedings of the Annual Conference of the American Society of hotogrammetry and Remote Sensing (ASRS), St. Louis, MO, USA. Maas H-G. (2000). Least-squares matching with airborne laserscanning data in a IN structure, International Archives of hotogrammetry and Remote Sensing, 33 (art 3A) pp Maas H-G. (2002). Methods of measuring height and planimetry discrepancies on airborne laserscanner data, hotogrammetric Engineering & Remote Sensing Vol. 68, No. 9, September 2002, pp Morin K.W. (2002). Calibration of airborne laser scanners, M.Sc. hesis, University of Calgary, Department of Geomatics Engineering, UCGE Reports No ark, J.Y., Data fusion techniques for object space classification using airborne laser data and airborne digital photographs. hd Dissertation, University of Florida, USA. ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 89 BIBLIOGRAHY III Schenk., Modeling and analyzing systematic errors in airborne laser scanners, echnical Notes in hotogrammetry No. 19, Department of Civil and Environmental Engineering and Geodetic Science, Ohio State University, Columbus OH. Sithole, G., Vosselman, G., Comparison of filtering algorithms. In International Archives of hotogrammetry, Remote Sensing and Spatial Information Sciences, Vol. 34, part 3/W13, Dresden, Germany, pp oth C., et al 2002, Automating the calibration of airborne multisensor imaging systems, FIG XXII International Congress Washington, D.C., April Vosselman G., 2002a, On the estimation of planimetric offsets in laser altimetry data, In International Archives of hotogrammetry and Remote Sensing, Vol. XXXIV, 3A, pp , Graz, Austria Vosselman, G., 2002b, Strip offset estimation using linear features. In 3rd International Workshop on Mapping Geo-Surfical rocesses using Laser Altimetry, Columbus, OH, USA. ISRS Summer School 2007 Requirements for generating a geometrically correct point cloud - 90