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Issue 7. January – Feb. 2008 |
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Also at www.zupt.com |
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COME VISIT WITH US AT OI 2008 BOOTH 1514 |
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In this issue of Zest:
Inertial, Seismic, Survey and Other NEWS
A short History of Error Estimation
Why don’t we all use ECEF coordinates?
Underground Mine Surveys
Underwater Metrology
Iranian Remote Sensing
Etc... Etc...
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INERTIAL NEWS
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A SHORT HISTORY OF ERROR ESTIMATION The history of human error is exactly as long as the history of human measurement.
Early Babylonian and Egyptian records and the Bible indicate that length was first measured with the forearm, hand, or finger and that time was measured by the periods of the sun, moon, and other heavenly bodies. When it was necessary to compare the capacities of containers such as gourds or vessels, they were filled with plant seeds which were then counted to measure the volumes. For instance, the carat, still used as a unit for gems, was derived from the carob seed.
He knew that on the summer solstice at noon in the Egyptian city of Swenet (Syene) the sun would be at its zenith, directly overhead (a water well there, had no shadow at that moment). He also knew, from measurements of shadows of buildings, that in his hometown of Alexandria, the angle of elevation of the Sun was 1/50 of a full circle that day at that same time. Assuming that Alexandria was due north of Syene he concluded that the distance from Alexandria to Syene must be 1/50 of the total circumference of the Earth. His estimated distance between the cities was 5000 stadia which implies a circumference of 250,000 stadia for the Earth. If we assume that Eratosthenes used the Greek "walking stadion" of about 157.5 m, his measurement was in error of less than 1%. - (17 centuries later, Columbus estimation of the size of the Earth was off by 30%).
Al-Khwarizmi.
The book was a compilation of known rules for solving quadratic equations, and considered to be the foundation of modern algebra. Its inspiration could have been Indian.
In that Age of Exploration scientists started a systematic approach to the observation of celestial bodies to help Navigation. Each of these observations had a certain accuracy and therefore a certain error. The theory of errors may be traced back to Roger Cotes’ Opera Miscellanea (published posthumously in 1722).
The differences between the predicted and observed values in a linear regression are called residuals.
The method of least squares used to minimize errors in data measurement, was published independently by Adrien-Marie Legendre (1805), Robert Adrain (1808), and Carl Friedrich Gauss (1809). The Gauss-Newton algorithm is used to solve nonlinear least squares problems. It is a modification of Newton's method for optimizing a function. Least squares estimation for linear models is notoriously non-robust to outliers. If the distribution of the outliers is skewed, the estimates can be biased.
The early 20th century saw the development of Control theory, in particular to tackle the issue of control of dynamic systems.
In a random (stochastic) process there is some indeterminacy in the future evolution of the process as described by probability distributions. This means that even if the initial condition is known, there are many possibilities the process might go to, but some paths are more probable and others less.
During WWII the wide use of RADAR and the study of signals and electronic noises aided the development of signal processing. Various physical and mathematical filters were developed to separate noise from signal, as well as minimize interferences. Rudolf Emil Kálmán was born on May 19, 1930 in Budapest, Hungary. An electrical engineer by training. He is most famous for his co-invention of the Kalman filter, a mathematical technique widely used in control systems and avionics to extract a signal from a series of incomplete and noisy measurements.
The Kalman filter has two distinct phases: Predict and Update. The predict phase uses the state estimate from the previous timestep to produce an estimate of the state at the current timestep. Kálmán's ideas on filtering were initially met with skepticism, so much so that he was forced to first publish his results in a mechanical (rather than electrical) engineering journal in 1960. He had more success in presenting his ideas, however, while visiting the NASA Ames Research Center in 1967, when he realized that his mathematics could be used to solve NASA’s problem of predicting the trajectory of a rocket, knowing its current state and location. This led to the use of Kálmán filters during the Apollo program. Kalman Filters are now widely used for navigation in general and inertial navigation in particular.
A wide variety of Kalman filters have now been developed, from Kalman's original formulation, now called the simple Kalman filter, to Schmidt's extended filter, the information filter and a variety of square-root filters developed by Bierman, Thornton and many others.
The basic Kalman filter is limited to a linear assumption. However, most non-trivial systems are non-linear. In the extended Kalman filter, (EKF) the state transition and observation models need not be linear functions of the state but may instead be functions.
New types of Kalman Filters (“extended”, “unscented”) are often more adapted to new technologies such as Micro-Electro-Mechanical (MEMS) inertial systems… |
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• ECEF • Graphically Cool Site of the Month …
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• Alignment. The inertial system can not operate properly if not aligned correctly. Remember 20-5-5-5, meaning the unit must be static on the start point for 20 minutes; the correct position of the start point must be entered. At the end of the 20’ period, the INS must be moved some distance 20 to 60 feet, put back on the ground at about 90 degrees from the original direction and left to zupt for 5 minutes. This procedure (motion + rotation + 5’ zupt) should be accomplished three times before returning to the start point for a position update, before starting the survey. • Put the pack on the back. Very carefully, and without brisk motion, put the pack on the back of the operator. A helping person should hold the pack both by the handle and with a hand underneath (in case the handle breaks). • Zupt immediately. Many operators tune the harness to their right size, and look for a file in the data collector (Recon™), as soon as they have the B-PINS on their back. It is better to accomplish a complete zupt (zero velocity update) first. • Do several zupts at short interval at the start of the day. Soon after the alignment (first thing in the morning) it is always better to accomplish a few zupts before being prompted. These extra zupts will simply improve the performance of the pack. • ZUPT every minute. From the moment the B-PINS is aligned, till the end of survey (when the unit is turned off), a zupt must be accomplished every minute or so. It is true when the operator is walking, riding, driving, floating, flying etc… • Always do a zupt before recording a position. The navigation solution being better after a zupt than before, it is always better to zupt before recording. • At the end of the traverse: TIE to a control point. If you want your survey traverse to be post-processed you must tie before shutting down the INS or else you have no way to compensate the error. • These are the rules. Practically 99% of customer support calls correspond to one of the rules being broken. Here are examples of what not to do: - Do not move the B-PINS during alignment. If the pack is sitting on the data collector cable or your map… you’ll have to wait 20’ to get it. - Enter the correct position of the control point you are aligning on. Some control points have the same or similar name as points from the last project (200 miles away). Make sure you use the correct point from the right file etc… - Make sure the INS is not moving during zupts: if it is on the ground, is the soil stable or sinking or slippery? etc…If it is on the back is the operator still or moving, talking, reading a map or having a snack? etc… - Zupt every minute. You can transport the B-PINS from one survey line to another by vehicle, boat, aircraft etc…, but it must zupt perfectly every minute or so even in that vehicle. If in a boat or helicopter you might have to land every minute or so for that operation. Some customers have tried longer periods (up to 15 minutes) and succeeded, but we do not recommend or guaranty the results… - Other rules include do not drop the system, do not hit the trees, do not fall in the river, do not jump over fences with B-PINS pack on your back etc… (we know we are missing something…). And yet they keep on ticking…
UNDERGROUND MINES
Keep and eye on this section in the future. We will inform you on the hundreds of applications of Inertial Positioning in underground mines.
After the SAGO mine and other “incidents”, The Mine Safety and Health Administration is <<requesting data, comments, and other information on issues relevant to underground mine rescue equipment and technology. Over the last several years, improvements have been made to communication devices, sensors and other forms of technology in general industry. As such, continuous development and deployment of mine rescue equipment and technology are crucial to enhancing the effectiveness of mine rescue operations and improving miners' survivability in the event of a mine emergency.>>
Let’s say that if underground mine operators were using inertial navigation systems for their rescue crews, some miners would be rescued in a matter of hours rather than days...
ZUPT LLC has demonstrated the productivity of its Backpack Portable INS in underground mine operations. Contact us for details... More on this in our future issues. |
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Metrology being the science of precise measurement, underwater metrology is used primarily to survey the position of jumpers (connection pipes) between subsea receptacles with a 0.04m accuracy.
Read more about underwater metrology in the future issues of Zest. A good presentation of this business (with excellent graphics) can be found here: Click Here
GLOSSARY:
“SAGNAC EFFECT”. Georges Sagnac (1869-1926) was a French physicist and one of the first people in France to study X-rays, while he was still a lab assistant at the Sorbonne. Marie Curie said that the Curie couple had traded ideas with Sagnac around the time of the discovery of radioactivity. In 1913, Sagnac showed that if light is sent in two opposite circular directions on a revolving platform, the speed of the light beam turning in the same direction as a platform will be greater than the speed of the light beam that is turning opposite the direction. The results of this experiment seemed to contradict the new theory of relativity. Georges Sagnac was an ardent opponent of the theory of relativity, but it was soon proven that the results could very well be explained by general relativity and later on special relativity. A Sagnac interferometer measures its own angular velocity with respect to the local inertial frame, hence just as a gyroscope it can provide the angular reference for an inertial guidance system. Sagnac Effect is used in both IFOG and RLG gyroscopes.
Many professionals exchange position information such as X, Y, Z or Latitude, Longitude and Height etc… It is nowhere more true than in Oil and Seismic companies, where exploration surveys containing tens of thousands of seismic locations are surveyed, processed, exchanged and traded within and between companies…
The nightmare comes from the seemingly infinite combination of Datums, projections, and coordinate systems used in the world: if a point A or say “101501” has the following coordinates: 123456, 7654321, 43.2… do you know where in the world it is? No? So why do you give me these coordinates? What units are they in?, What projection?, what datum?
There is one Global system that can position a point unequivocally on Earth (or under and above ground): and that is the ECEF system (Earth Centered, Earth Fixed). Why don’t we all use it once and for all (points)?
In the ECEF system, the point (0,0,0) denotes the mass center of the earth, hence the name Earth-Centered. The z-axis is defined as being parallel to the earth rotational axes, pointing towards north. The x-axis intersects the sphere of the earth at the 0° latitude, 0° longitude. This means the ECEF rotates with the earth around its z-axis. Therefore, coordinates (in meters) of a point fixed on the surface of the earth do not change, hence the name earth-fixed.
Send us your opinion on this: jg@zupt.com
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