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This is a repost of a question that I've previously asked in the EE section of SE. Unfortunately, I've not solved my problem.

I'm seeking insight into the typical values of sampling times or refresh rates in radar systems. Specifically, I want to understand the time interval a radar operator must wait to receive new output from a radar system. I'm particularly interested in the special cases of Synthetic Aperture Radars (SARs) and Inverse Synthetic Aperture Radars (ISARs).

Currently, I'm delving into some literature on SARs and ISARs, but they haven't mentioned sampling time, sampling interval, or refresh frequency explicitly. The closest information I've come across, although I suspect it might not be directly related, is the pulse repetition period. This parameter denotes the time interval between two consecutive pulses. Therefore, I presume the sampling time cannot be shorter than this period. However, given that some signal processing is conducted on the raw data collected by these systems, I suspect the sampling time is typically longer than the pulse repetition period.

At present, I estimate the typical values of sampling time to fall within the range of [1s, 1ms]. My upper bound is in the order of seconds because I consider radars with mechanically rotating antennas, where a complete revolution typically takes several seconds. I believe radars that aren't mechanically steered can have shorter sampling times. My lower bound is based on the values I've found for the pulse repetition frequencies of SARs and ISARs.

Unfortunately, I'm completely new to this topic, so I would greatly appreciate assistance from someone more experienced than myself.

I try to add additional details to clarify what I'm searching for. I'm attempting to develop a Kalman filter to estimate the position, attitude, and shape of an airplane. This filter recursively processes the measurements generated by a sensor, which is assumed to produce a new measurement every T seconds. I understand that air surveillance is typically conducted using ground-based ISAR sensors. Therefore, I'm trying to determine reasonable values of T for my specific application of Kalman filtering.

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    $\begingroup$ So, are you trying to perform object tracking within a series of ISAR images? $\endgroup$
    – Baddioes
    Commented Apr 6 at 15:27
  • $\begingroup$ Exactly, and as a starting step I would like to understand what kind of data I have to process $\endgroup$
    – matteogost
    Commented Apr 6 at 15:33
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    $\begingroup$ @matteogost So in your situation, you're already receiving detection reports to pass the to filter yeah? Also, is this a real ISAR or are you just using that term as a catch-all that includes your run of the mill detection and tracking systems? By "real", I mean that it's forming an actual 2D image, a picture of the target. In the other case, a nominal system will provide a target's range/velocity/angle and feed those to a tracking filter to track it in space. $\endgroup$
    – Envidia
    Commented Apr 6 at 20:19
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    $\begingroup$ @matteogost In this case, that depends on how fast the system can form the image. Usually the accuracy of tracking a target is determined by whatever requirements you have, and then those are levied against the sensor. For a set of accuracy requirements, the sensor needs to provide the measurements (the images), at a certain update rate and quality (think SNR), so that the filter can converge. If the image formation rate is already determined, then you communicate that you need a faster rate and image quality, or you're stuck with what you have and have work on your end to improve performance. $\endgroup$
    – Envidia
    Commented Apr 7 at 5:21
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    $\begingroup$ @matteogost If you're in the trade space where you're designing the tracker and achieve some performance goal, then you will need to simulate inputs to determine how fast and at what quality the images need to come in. You can do this while being sensor agnostic to get in the ball park. Also apologies for the idiom. By "run of the mill" I mean just your typical radar systems that produces range/velocity/angle measurements against point targets. $\endgroup$
    – Envidia
    Commented Apr 7 at 5:25

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For a coherent system that uses the pulse-to-pulse phase change, the PRF needs to meet or exceed the expected Doppler bandwidth of the system. For a SAR imaging the ground, the Doppler bandwidth is often determined by the beamwidth of the antenna(s), where you compute the Doppler at, perhaps, the $-20(\mathrm{dB})$ points of the beam and then use that extent to set your PRF. For a stationary radar that is trying to image moving targets in the sky, the PRF might be set based on the expected min and max radial velocity of the targets. There are finer points, more nuanced issues, and special use-cases, but that is the gist of it. If the PRF exceeds the Doppler bandwidth, then you should get an alias free sampling of the Doppler for the targets.

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