Error Theory and Measurement Principles in Surveying

Error Theory and Measurement Principles

Gross errors (faults or outliers) are errors that can be considered as not belonging to a single sample from a given distribution. They correspond to the false identification or registration of the value of a given measurement, so that the measurement of redundant or supernumerary elements may help detect them. Their origin lies in a lack of understanding or care, or in confusion at some stage of the process. They are generally not classified as errors and can only be removed with a careful check of the data, isolating the gross error.

Systematic Errors and Inaccuracies

Systematic errors or inaccuracies occur under the same conditions, have equal magnitude and direction (quantifiable), and thus affect observations consistently in the same way while having a specific source. Usually due to physical causes or conditions that respond to natural physical laws, they can be represented as a mathematical function or result from the habits or tendencies of the operator. All detectable systematic errors must be eliminated or minimized prior to the assessment of accidental errors.

Examples: Refraction, instrument calibration, misallocation of prism constant, temperature not calibrated for a correction, and zero error rate in vertical angles, among others.

Accidental or Random Errors

Accidental or random errors (or simply errors) are probabilistic fluctuations whose dispersion is controlled by the standard deviation of the mean or a distribution law. They do not have a fixed relationship with respect to the conditions or circumstances under which the observation was performed. They are produced by complex and irregular causes beyond the control of the observer. They are generally small and can be both positive and negative, with unpredictable magnitude and sign. Furthermore, they are inevitable, not constant, and cannot be removed by models. In this way, each random error is an independent phenomenon occurring at random.

Precision and Accuracy

Precision: The degree of consistency, dispersion, or refinement of a set of observations. It is based on the magnitude of the discrepancies between the measured values (dispersion), referring to the most probable value (average).

Accuracy: The degree of closeness or coincidence of a certain outcome with respect to a true or absolute value, or with respect to a particular pattern of comparison.

Surveying and Measurement Methods

Grading

Grading consists of the primary measurements in direct or indirect vertical distances in order to obtain a level difference between points of land or buildings.

Triangulation

Triangulation consists of determining the coordinates of a series of points distributed on the basis of two known triangles, which define the base, and measuring all the angles of the triangles.

Trilateration

Trilateration is a survey method which is complementary to triangulation. This involves measuring the lengths of the sides of a triangle to determine these, and thus the trigonometric values of the angles of the triangles described; this is the operation contrary to triangulation.