Download Understanding Precision, Accuracy, and Error Types in Hydrographic Surveying with GPS - Pr and more Study notes Engineering in PDF only on Docsity! BAE 1022 Lecture 3 Today: Error Theory GPS Lab: GPS surveying Lab meets in Ag Hall 225 (classroom), not BAEL Reference: Hydrographic Surveying: A Practical Guide to Error Management at: http://www.solent.ac.uk/hydrography/ 1 Error Theory No measuring instrument is entirely free from errors. A knowledge of errors allows us to: Obtain the most probable value (MPV) from a set of scattered observations. Assess the accuracy of a set of measurements. Obtain a measure of instrument precision. Assess whether the measurement meets the required (specified) accuracy. Determine which observations and errors, if any, can be disregarded. 2 Types of Error Blunders: Errors caused by carelessness of the observer. Blunders will always occur, but must never be allowed to occur undetected. Bias or Constant Errors: Errors of constant magnitude and sign. Their most common cause is improper calibration of the instrument. They can sometimes, but not always be eliminated. 5 Systematic Errors: Errors of varying magnitude but constant sign. These are usually caused by an error in the instrument, poor calibration or by the improper technique of the operator. Like bias errors, they can sometimes, but not always be eliminated. Periodic Errors: Errors of varying magnitude and sign, but obeying some systematic law. An example would be a protractor with variable graduations. Being of varying sign, they can be reduced or eliminated by repetition of observations under different conditions. 6 Periodic Errors; A bad protractor
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Random Errors Assumptions/Limitations Errors assumed to be normally distributed. Each measurement is independent of any others in the data set (sample) Accurate determination of standard error () is not possible for small datasets. 10 Characteristics: Small errors occur frequently and are therefore more probable than large ones. Large errors happen infrequently and are therefore less probable. Very large errors (>3) are likely to be blunders rather than random errors. Positive and negative errors of the same size are equally probable and happen with equal frequency. 11 Standard Error (Deviation) () The Standard Error of an observation is found from an analysis of repeated observations or of a series of observations. This analysis will give an estimate of the size of the errors in the observations, and hence the precision. With large numbers of observations this estimate will be very reliable, and can be used with certainty to check that the results from the observations. 12 Quantitative Measures of Precision The width of the curve at the points of inflexion (1 is used for measuring precision. The smaller the width, the higher the precision. 15 Most Probable Value (MPV) Least squares analysis shows that the MPV obtained from a set of measurements of equal precision is the arithmetic mean. If the precision varies a more detailed analysis is required to obtain the MPV. Probable Error (P.E.) We use this value of P.E. to assess the quality of our observations. P.E. = 0.67 Expanded Uncertainty (NIST) E.U. = k Coverage factor, k = 2, (or justified other value) 16 Adding or subtracting measurements If a series of measurements of independent values are added or subtracted, the standard deviation of the result is given by, n i isum 1 where n is the number of values added. If each has the same standard deviation , nsum 17
