Hello everyone! As you understand, high-precision positioning using global navigation satellite systems or simply high-precision determination of a random variable. At what point does your estimates precision fall into the "highly precision" category? Is this always a convention associated with the method of determining a random variable or is there a general formulation for classifying estimates as highly precision?
A "high-precision" determination of a random variable typically refers to obtaining measurements or values with a level of accuracy that involves a large number of significant figures or decimal places. Precision in this context relates to the degree of detail or granularity in representing the values of the random variable.
For example, if you are measuring a physical quantity (e.g., length, weight, temperature) that is considered a random variable, a high-precision determination might involve using instruments or methods that provide measurements with many decimal places or significant figures. This increased precision allows for a more detailed and nuanced representation of the random variable's values.
In statistics or probability theory, precision can also refer to the level of detail in the representation of probabilities or parameter estimates. High precision in statistical calculations often involves using more decimal places to capture subtle variations or nuances in the data.
It's important to note that high precision does not necessarily imply accuracy. Precision deals with the level of detail in measurements, while accuracy reflects how close these measurements are to the true or target values. Sometimes, an increased level of precision may not improve the overall accuracy of the determinations.
The precision of a random variable is the deviation from its mean value and is usually expressed by the standard deviation. The smaller the standard deviation, the higher the recession. Satellite navigation expresses precision as PDOP (Position Dilution Of Precision), which is calculated as the square root of the sum of the three diagonal elements of the covariance matrix from the navigation solution, which correspond to the X, Y, and Z coordinates. PDOP closer to one is of high precision, and it is acceptable for smaller than six. There are several other methods used to express the precision, such as Root mean square error (RMS), Circular error probable (CEP), Spherical error probable (SEP), error ellipse, and error ellipsoid.
John Hatzopoulos, thank you for your answer! Yes, everything you said has to do with the concept of accuracy. But my question is at what point should you consider your estimate of a random variable to be “high-precision” or maybe correct in English language "highly accurate".
Accuracy differs from precision, being the deviation from its true value. However, accuracy and precision are the same if there is no systematic error.
If you take the formula for precision σ=σο.Q, then σο is the precision (standard deviation) of the measuring instrument, and Q is the diagonal element of the covariance matrix that expresses the geometry. Therefore to have high precision, you must have highly precise instrumentation and strong geometric configuration.
John Hatzopoulos, Thanks for your explanation! Unfortunately, my question sounds different, but most likely due to the fact that my native language is not English, it is difficult for me to convey the idea correctly. The main point of my question is that I am trying to understand at what point we are talking about estimates or measuring instruments, etc., that they belong to the class or type of High Precision. For example, speaking about measurements in navigation, the root mean square error of measurements for external convergence of 10 cm for each of the coordinates can be classified as high-precision, at least in articles this is found, at the same time, using a different method or approach in measurements, you can obtain root mean square errors for external convergence for each of the coordinates is at the level of 1 cm and this will also belong to the high-precision class. So, at what point exactly do we consider our estimates of a random variable to be highly accurate? Dr. Lekia Nkpordee, talks about the number of significant figures, I believe that this is a fairly weighty explanation, but I will be grateful if you also tell me your opinion, I hope I was able to convey my idea correctly, thank you!
The precision of a class must be defined by specifications, which define the RMS and the instruments to be used. If there are no specifications, then people involved in such a class get together and decide about the specifications for the class.
The number of digits also characterizes the precision of an instrument. If a theodolite measures an angle with a direct reading of one second, its precision is one second. If you want to test it you measure several times the three angles of a triangle, and you see how much the closing error is.
In any case, you define precision by specifications; you test precision by statistical analysis of measurements of a well-designed experiment.
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