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I am not sure whether this is the right forum for this question but I reckon that since it gathers experts in GIS, the odds of someone having valuable insights is higher than anywhere else. So here's my problem.

I have a positioning system in which the manually measured positions of objects are (for technical reasons) a common position if these objects are within a determined area. I know, it sounds weird, but bear with me. Now, on the other hand, the system regularly triangulates each object's position and returns the calculated position (planar). Hence, over time, I have a series of predicted positions for each object.

As the TRUE position is not recorded, I cannot estimate (as far as I know) the accuracy of the system. However, I still can estimate the precision since I have a large amount of readings for each object.

My question is then: Can I ever infer accuracy from precision for a positioning system? And if so, under which conditions?

I know this is possible in other areas of science, e.g. Medical sciences. In these cases "Accuracy may be inferred once precision, linearity and specificity have been established". Specificity tells us about the degree of interference of other systems, object and so on, as linearity of a method can be explained as its capability to show “results that are directly proportional to the concentration of the analyte in the sample” (e.g. the effect of a drug is proportional to the dose given). I fail to find any positioning equivalents to this.

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  • In my opinion, for both accuracy and precision you need to record the "true" position. Because both can be computed as statistical properties of the deviation (between predicted and true positions) series.
    – Gabriel De Luca
    Sep 9, 2021 at 9:36
  • This is not true. A series of point tightly clustered in a specific region (whether it'd be in space or the results of an experiement), i.e. normally distributed with a very small standard deviation, you will be able to say something about the precision. That is particularly true if this the case for a set of sequences exhibiting that property. It says nothing at all about accuracy but definitly something about the precision. One can have poor accuracy but high precision. As I explained, in some very special cases one can say something about the accuracy with the knowledge of the precision.
    – Serge de Gosson de Varennes
    Sep 9, 2021 at 9:46
  • Yes, I understand it. But I probably didn't understand your experiment.
    – Gabriel De Luca
    Sep 9, 2021 at 9:52
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    We predict a point position when we want to estimate it at a future time. If not, we are measuring it. When we measure a position using a triangulation method, we have methods that cancel out the systematic error in the measurement of angles, allowing us to say something about the accuracy of those measurements. When we measure by trilateration instead, we cannot nullify the systematic errors of the instruments, so our only option to know their accuracy is to calibrate them against a known position.
    – Gabriel De Luca
    Sep 9, 2021 at 10:12
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    We can also calculate how these errors propagate in the trilateration solution equations, knowing the spatial distribution of the stations from which the measurements are made. And knowing the accuracy of their positions. But without having any calibration method we cannot say much about the systematic error of our measurement.
    – Gabriel De Luca
    Sep 9, 2021 at 10:15

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