1. Mapping forest plots: An efficient method combining photogrammetry and field triangulation/trilateration
MMVAR-Colloquim May 4, 2007 Korpela, Tuomola and Välimäki

2. 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

3. 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

4. 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: 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.

5. 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 LS- adjustment 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.

6. 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

7. 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

8. Background - MATHEMATICS - LS-adjustment of intertree azimuths and distance observations
Standard errors of unknowns
eig(Qxx) => Error ellipses in XY
Search for gross errors in observations

9. 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.

10. Simulation results

11. 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

12. 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

13. Practical issues – accuracy of photogrammetric obs

14. Practical issues – some results

15. 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!

16. Young stands: use Network-RTK satellite positioning
Young stands: use Network-RTK satellite positioning. One investigator – cm-level accuracy
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