Not clear how mathematical analysis of radar signals is on-topic for Aviation. Sure, ATC uses the finished product of radar processing, but the processing itself seems more like a Mathematics or Physics stack. After all, meals are served on flights, but preparing those meals is a Seasoned Advice topic, not Aviation.

I think this question can be better answered at signal processing stackexchage

@mins What you are talking about is relevant to what I mean. What I have is a set of measured flight paths of various aircraft. They are clearly noisy. And I need to extract some useful information using statistical methods. But what this information is, what methods are used for this, I do not know, because this is the first time I encounter such a task in practice. Maybe you can suggest how I can improve the question so that it fits into this stack, while I get answers to my questions, at least partially?

@RalphJ I thought that perhaps people who have relations or understand aviation issues could suggest something to me, since this is the first time I encountered such a task in practice.

@sophit It’s there now too. Let’s see what happens.

@ayr The problem isn't that nobody here would be able to make helpful suggestions -- there are at least a couple of active users here who are highly accomplished in fields like this. That fact, however, doesn't make the question itself on-topic. If someone were to ask for a headset recommendation, plenty of Aviation regulars could offer good advice, but opinion-based questions are off-topic here. If the question isn't on-topic per the Help Center, it will probably be closed, irrespective of the ability of contributors here to answer it.

"What I have is a set of measured flight paths of various aircraft. They are clearly noisy.". Measured with what? If this is with SSR/S, then the noise if just the noise of the GNSS receiver in the aircraft, not radar echo noise. Your question should give a precise context to be answered. Then "I need to extract some useful information [but I do not know] what this information is", The format of this stack (and other SE ones) doesn't allow this kind of open exchange of ideas. You need first to know what you want to do, try by yourself, and then ask about the problems you encounter.

Now there are plenty of books about radar and radar signal processing that could potentially help. E.g.in Knowledge based radar detection, tracking, and classification you will find a section "Statistical Modeling of Statistical Representation of Clutter- and Target-Related Information". You can read it here.

@RalphJ Is this an opinion-based question? Isn't there some broadly established framework for statistical analysis of radar data?

@mins Thanks, I've edited the question a bit and added search results for my research.

Your question is still unclear, in my opinion you should state your question(s) as actual and crisp and clear questions (and remove anything else). I fear this will lead to "which is the nature of track and velocity error distributions of SSR mode S?" and "what can be inferred from filtering the errors?". The first question is possibly a candidate for DSP.SE (but your should edit your existing post accordingly), and the second is open and not appropriate for SE.

You say you have time series of position, velocity and acceleration, but radar usually does not measure those values directly. Azimuth, range, elevation and radial speed (doppler shift) are what classical radars would measure. Can you tell what the source of the data is? How has it been processed before it was delivered to you?

I don't think that signal processing is the right site for this question either. It would be if the domain of your question was closer to the antenna, and thus the radio signal of the radar would be processed. Your question is in the domain of Air traffic control surveillance data processing, which could fit here.

However, your question needs to be focused on a problem you are trying to solve. This site is not going to provide you with a listening of all possible statistical analysis methods that may be useful in radar data analysis, nor can you expect people to do your literature research for you

@DeltaLima A classic radar is used. The system receives signals reflected in the survey, and then outputs them through the primary navigation information processing device. The device does not perform secondary trajectory processing, so the consumer is provided with only raw, unfiltered measurement information.

@DeltaLima I did some literature review myself (which I indicated in the question editorial) and found that statistical processing of radar data often means studying the nature and characteristics of noise, as well as the quality of fitting motion models. But it seems to me that there must be something else...

@mins None of the options you suggested are suitable (except for the first option, perhaps). I need to understand what exactly is extracted from statistical processing of raw, unfiltered radar data using statistical analysis. As I found from my literature review, it is usually the noise characteristics and the quality of the fit of the chosen motion model that are examined. That's all for now. It seems to me that there must be something more...

@mins SSR mode S does not use aircraft based GNSS receiver position data. The position is determined by the radar from bearing/range measurements

@DeltaLima, I stand corrected, thanks, confused with ADS-B. Deleting my comment.