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Rainy Lake Experiment: Targets

The key elements of The Rainy Lake Experiment were the Targets. This page describes the targets, how they are planted and how their GPS Vectors (positions) were measured.

ZoomImg 1: All targets ordered by distance

Image 1: The target dimensions get bigger with increasing distance as described in Calculating Target Size. At the same time the height of the upper Tangent targets increases according to Calculating Tangent Target Heights [1]. The data is listed at Target Positions and Sizes relative to the Observer.

ZoomImg 2: Bedford targets (1), (3) and (5)
ZoomImg 3: Bedford and Tangent targets (2) and (4)

Image 2 and 3: Details of the target plates (1) to (5). Note the dimension shown in the images are the dimensions used in the computer model as listet in the table Target Positions and Sizes relative to the Observer, not the real dimensions. But the difference is small.

Planting the Targets

ZoomImg 4: Using a chain saw to mill a hole into the ice
ZoomImg 5: Rectangular hole for pole

Image 4 and 5: To plant the targets (1) to (6), holes were milled into the 75 cm thick ice using a chain saw or drilled using an ice auger about 50 cm deep [3].

ZoomImg 6: Making sure the pole is upright with a spirit level
ZoomImg 7: Fixing the pole with snow, ice and water

Image 6 and 7: The poles were placed in the holes and the space around it filled with snow and water that turned into ice over night.

ZoomImg 8: Planting the 6.5 m high target (6) at 6.4 km, watch Video
ZoomImg 9: Targets are adjustable attached with a clamp to the poles

Image 8: It was quite an efford to plant the bigger targets alone [4].

Image 9: The higher targets were mounted on wooden sticks with a clamp so they could easily be adjusted as needed.

ZoomImg 10: Jesse Kozlowski with GNSS Receiver at target (7)

Image 10: The last Tangent target (7) had to be mounted high on a tree on Home Island to be 10.8 m above water level so it appeared at eye level at an observer height of 3.91 m in 9.46 km distance. The target plate size is about 1×1.6 m.

The Bedford targets were all mounted as accurate as possible 1.85 m above water level. The Tangent targets however were not mounted exactly at the pre-calculated heights. George Hnatiuk wanted to align the Tangent targets visually to eye level of the observer. He observed the targets through the auto level at the observer location at times with low refraction, estimated the height deviation from eye level, drove to the target and adjusted it accordingly [5]. Although the Tangent target heights were set visually, their hight is close to the pre-calculated heights, only diverging in the expected range of common low refraction variations.

Because the Tangent targets were adjusted at different times and days, the resulting heights depended now on the refraction of the time the targets were observed and adjusted. This is the reason why the Tangent targets appear not in a consistent height. Apparent Lift due to Refraction can change considerably after some km. But this does not change the outcome of the Experiment.

George states that he has much experience from observations over many months, at what conditions refraction is minimal [6].

ZoomImg 11: Drilling a hole to find water level
ZoomImg 12: The hole fills with water

Image 11: To adjust the Bedford target heights and measure the Tangent target heights with respect to the water surface of the lake, a hole was drilled into the ice near each pole using an ice auger, all the way through the 75..85 cm thick ice to the water below.

Image 12: The holes filled with water almost to the top of the ice surface indicating the water level of the lake. A small channel lead the water to the base of the poles from where the height of the target centers was measured using a measuring tape.

Measuring the Targets

The positions of the targets were measured by Jesse Kozlowski to cm accuracy using his Differential GPS equipment and post-processing of the collected data. The center of the farthest Tangent target (7) was also measured with GPS. All other target center heights were measured by George Hnatiuk using a measuring tape from water and ice level. See Location Graph and Data for all measurement results.

The whole measuring process was as follows:

  1. George Hnatiuk planted the targets at planed distances from the observer location. He used his Magellan SporTrak Pro GPS receiver to locate their planed positions.
  2. The Bedford targets were all mounted on the poles at a height of exactly 1.85 m above the water level at the target position using a measuring tape.
  3. The Tangent targets were mounted by repeated trial and error over many days on low refraction conditions so they appeared finally at about eye level as seen from the observer location at an observer height of 3.91 m. The final target heights above water level were then measured using a measuring tape, except the last target height, which was measured using a theodolite from a nearby location on the ice as shown on the image 8 at Corner Reflector.
  4. The height of the ice surface above water level at each target was also measured using the measuring tape or ruler.
  5. Jesse Kozlowski placed his GNSS Base Station on the ice near the observer locations and recorded its position for later post-processing of all measured GPS Vectors. The Base Station is used to calculate an error correction signal for the other mobile GNSS Receiver.
  6. Jesse Kozlowski measured and recorded the GPS Vectors (3D positions) in ECEF Cartesian (x,y,z) coordinates to the ice beneath each target, except for the last Tangent target (7). The vector to the last Tangent target in the tree was measured by holding the GNSS Receiver up to the target as shown in image 14.
  7. Each GPS Vector was automatically measured and recorded multiple times in sequence by the mobile GNSS Receiver to be able to calculate and increase the accuracy of the measurement using statistics.
  8. Later in the office Jesse Kozlowski used GNSS software that uses data from Continuously Operating Reference Station (CORS) to post-process all measurements to further improve the recorded measurements to cm accuracy: horizontal < 2.9 cm, vertical < 5 cm.
  9. The software also computes latitude, longitude and ellipsoid height of the GPS Vectors and calculates the elevation above the GEOID12B Geoid (mean sea level), see Obtaining Elevations.
  10. From the post-processed, error corrected GPS Vectors he calculated the vectors to the water levels and target centers using the target and ice heights measured by George.
ZoomImg 13: Base Station sending Corrections to mobile GNSS Receiver
ZoomImg 14: George holding GNSS Receiver to center of target (7)
ZoomImg 15: Measuring GPS Vector to ice at target
ZoomImg 16: Accuracy of Measurement on Trimbel TSC3 Controller

At the end we had a collection of GPS Vectors to the center, ice level and water level of each target with cm accuracy (horizontal < 2.9 cm, vertical < 5 cm). This vectors were transformed to a local coordinate system at the observers location by Walter Bislin for his Computer Model using his WGS84 Calculator. This calculator was also used to confirm the post-processed transformations into Geodetic Ellipsoidal coordinates done by Jesse Kozlowski. See WGS84 Coordinate System for the math involved with this transformations.

Accuracy of common GPS

Common GPS receivers e.g. in your smartphone have an accuracy of only about 15 m horizontally and even worse vertically. So how can cm accuracy be achieved using GPS?

A GPS receiver uses the positions of at least 4 satellites to calculate its position. The calculated position accuracy depends on many factors: how many satellites can be received, their location distribution in space, the accuracy of their clocks, accuracy of the transmitted satellite position data (ephemeris) and atmospheric delays.

Improving GPS accuracy with Differential GPS

How Differential GPS works

The error factors are common for all receivers in the same vicinity. So if we have a receiver at an exactly known position, it can calculate its position vector from the GPS signals and take the difference to its known exact position to calculate the position error vector. This position error vector can then be transmitted to other GPS receivers which can correct their position vectors accordingly. This method is called Differential GPS.

There are multipe methods to get the position error.

We can use our own base station. That is a special GPS receiver placed at an exactly known position, capable of calculating the position error and transmiting it to other receivers in real time. You can get better than 1..5 m accuracy with this method.

We can use Satellite-based augmentation system (SBAS) to get the position error. Corrections are computed from ground station observations and then uploaded to geostationary satellites. This data is then broadcast to GPS devices which are equipped with corresponding receivers. Wide Area Augmentation System WAAS, EGNOS, and MSAS are examples of satellite-based augmentation systems. George's Magellan SporTrak Pro is a WAAS enabled GPS receiver.

The most accurate positions can be achieved by post-processing the vectors from the GPS receivers. Post-processing methods take place upon return to the office rather than in the field to take advantage of base station data available on the internet. Base station files are posted on the internet daily or hourly. The most accurate positions can be achieved with post-processed carrier phase differential GPS correction: 1..30 cm!

National Geodetic Survey NGS manages a network of Continuously Operating Reference Stations (CORS) that provide Global Navigation Satellite System (GNSS) data consisting of carrier phase and code range measurements in support of three dimensional positioning, meteorology, space weather, and geophysical applications throughout the United States, its territories, and a few foreign countries.

The accuracy of GPS can be further improved by using Survey grade GNSS receivers that are capable of receiving multiple GPS satellite systems like Navstar and GLONASS simultaneously.

For more information about GPS see:

Videos

References

George, Soundly & Jesse Talk About The Work Planned On Rainy Lake
George commenting on the targets
http://www.youtube.com/watch?v=lL3693c0RxI#t=4204
Survey Overview Rainy Lake - is the earth curved?
George explaining setup for planed targets on the whiteboard
http://www.youtube.com/watch?v=GUO-mbxybVA#t=485
George, Soundly & Jesse Talk About The Work Planned On Rainy Lake
Drilling a whole with chain saw to plant target (6) and planting of target
http://www.youtube.com/watch?v=lL3693c0RxI#t=5622
George, Soundly & Jesse Talk About The Work Planned On Rainy Lake
George planting tall target (6)
http://www.youtube.com/watch?v=lL3693c0RxI#t=5701
Rainy Lake Survey Progress Report
Jesse explains how the tangent targets were set up
http://www.youtube.com/watch?v=kOqlAir8cdI#t=414
Rainy Lake Survey Progress Report
George talking about his experience with refraction at the Rainy Lake
http://www.youtube.com/watch?v=kOqlAir8cdI#t=5299
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