Download mapping directly in XYZ GLOBAL

Mapping forest plots: An efficient method
combining photogrammetry and field
triangulation/trilateration
MARV1 June 2007
Point positioning in the forest
- Mapping needs: When the structure, position and geometric
relations are somehow important → ecological applications
- Accuracy & precision: Local and Global
- Data acquisition for distance-dependant growth models
- Data acquisition for Remote Sensing: teaching, validation
- Misalignment - offsets (bias in XYZ)
- Distortions from Cartesian
- 2D and 3D mapping: An issue of complexity?
- Existing methods: Case: Tree mapping in a forest plot
Existing methods: Case: Tree mapping in a forest plot
Objective: Stem/Butt positions in XYZGLOBAL
Phases
1. XYZLOCAL mapping
2. XYZLOCAL → XYZGLOBAL transformation
Phase 1 - Options
- Tacheometry (Spherical coordinate system)
- Theodolite (Triangulation needed)
- Compass & EDM (Polar Coordinate system, XY)
- Grid-methods (Prism and tapes, XY)
Phase 2 - Options
- H for origin by levelling (Geodetic infra)
- XYZ / XY(H) for origin using GPS
- XY-orientation, compass, not good
- Full rigid 7-parameter transformation:
XYZ-offset, XYZ-rotations, scale, Control points.
Young stands: use Network-RTK satellite
positioning. One investigator – cm-level accuracy
New method: Point (Tree) mapping directly in XYZGLOBAL
Objective: Stem/Butt positions in XYZGLOBAL
Phases XYZLOCAL mapping and XYZLOCAL → XYZGLOBAL transformation combined.
Assumptions
1) Up-to-date (with respect to events in the forest) orientated (XYZGLOBAL) aerial
photography is available. Large scale > 1:15000. More than 1 view per target.
Enough for XY-positioning.
2) An accurate Digital Terrain Model (DTM) is available. Enables Z / H positioning.
3) Photogrammetric workstation – software for measuring XYZGLOBAL treetop
positions, called points PA. These are considered as XY control points.
4) Points PA can be found in the field and used for the positioning of other targets.
New method: Point (Tree) mapping directly in XYZGLOBAL
Background “Points PA can be used for positioning of other points”
- Points PA are treetops observed in the aerial images
with coordinates (XA,YA)
- For non-slanted trees (XA,YA) ~ stem position
- Inaccuracy XA  YA ~ 0.25 m, Control points with observational error.
Triangulation in plane
- Create a base-line with exact distance, fix the datum or let it ‘float’,
triangulate with angle observations between new points, use LSadjustment of angle-observations for the computation of XY-positions
Forward ray intersection in plane
- Observe angles or bearings/azimuths between the unknown point P0 and
known points PA. Use LS-adjustment of angles to compute the XY-position
of point P0 (and, if needed, the orientation of the angle-device).
Trilateration in space / plane
- Measure distances from known points (e.g. satellite in its orbit) to the
unknown point and use LS-adjustment of distance observations for
computing the XY- or XYZ position.
Background - MATHEMATICS - LS-adjustment
of intertree azimuths and distance observations
Objective: Obtain XY-position for P0
We have:
- Photogrammetric observations of
control points PA (XA,YA) with XA  YA
- Field observations of intertree
azimuths () and distances (d)
- Initial approximation (guess) of (X0,Y0)
- Unknowns are non-linear functions of the
observations → non-linear regression
Background - MATHEMATICS - LS-adjustment
of intertree azimuths and distance observations
- Observations include coordinates [m],
distances [m] and azimuths [rad] →
normalizing and weighting required →
WLS adjustment
- Form a design matrix A, It’s elements are
partial derivates of the observations with
respect to the unknowns
- Form a diagonal weight matrix P, with 1/
elements: a priori standard errors of
observations
- Compute residuals in observations, y given
the initial approximations of unknowns
- Solve x = (ATPA)-1ATPy
- if ||x|| is small stop, otherwise add x and
continue
Background - MATHEMATICS - LS-adjustment
of intertree azimuths and distance observations
0 
y T Py
r
Q xx  (A PA)
T
 Xi   0
1
Standard errors
of unknowns
diag (Q xx )
eig(Qxx)
=> Error ellipses in XY
Q vv  P 1  AQ xx A T
wj 
yj
0 qj
Search for gross errors in
observations
Geometric aspects
If measurements consist solely of
intertree azimuths or distances →
geometric constellation is important,
otherwise error ellipse is elongated.
If both azimuth and distance are
observed – errors cancel each other →
always ± circular error patterns (error
ellipse), unless the observation errors
are considerable, or eq. distance
dependant.
Monte-Carlo simulator well suited for
examining the potential and
weaknesses.
Simulation results
Practical issues
- Preparatory work: 1) photogrammetric measurements, 2) prepare maps,
tree labels and tally sheets (here DTM is accurate)
- Work in the forest: GPS brings you close, match tree pattern, use azimuth
pencils to verify the photo-tree, label it, map finally other objects
Practical issues
- Recall assumptions (Imagery, DTM, photogrammetric
software)
- WLS-adjustment and gross error detection should be done
in the field, instantly after first redundant observation,
requires a field computer of some sort
→ Errror estimates on the fly – continue observations untill
the required accuracy is reached
- What if magnetic anomalies are present?
- Slanted trees, very dense stands perhaps problematic
- Good for large field plots with limited visibility, one person
and low-cost equipment
Practical issues – accuracy of photogrammetric obs
Practical issues – some results
Some ideas of future work
GPS brings you within ± 5 m →
Measure a ray-pencil (azimuths to trees)
or set of distances to trees →
Adjust position with photogrammetric
treemap i.e. obtain a position fix down to
0.2 m under canopy. WORKS in theory.
THANK YOU!
Young stands: use Network-RTK satellite positioning.
One investigator – cm-level accuracy
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