Tagged: passive radar

KerberosSDR Batch 2 Ships Soon! Pricing will Rise on Monday

KerberosSDR Batch 2 will begin shipping very soon! Thank you to all who have supported this project so far. If you didn't already know KerberosSDR is our experimental 4x Coherent RTL-SDR product made in partnership with Othernet. With it, coherent applications like radio direction finding (RDF), passive radar and beam forming are possible.

We just wanted to note that this Monday the reduced preorder pricing of US$130 + shipping will end, and the price will rise to the retail price of $149.95 + shipping. So if you have been thinking about ordering a unit, now would be a good time. Ordering is currently possible through Indiegogo. On Monday we will change to our own store. EDIT: Now available to purchase on the Othernet Store.

For shipping, US orders will be sent domestically from Othernet's office in Chicago. They are still waiting on the US shipment to arrive, but it is expected to arrive by the end of next week. Once shipped locally you will receive a shipment notification.

For international orders, the packages are being labelled now, and should be going out early next week, or sooner.

KerberosSDR Inside and Outside the Enclosure
KerberosSDR Inside and Outside the Enclosure

Future Updates to KerberosSDR

With the profits raised from KerberosSDR sales we are looking to continue funding development on the open source server software and visualization software being created (as well as applying updates ourselves). In future updates we will be looking at features such as:

  • Streamlining the sample and phase sync calibration process.
  • Experimenting with software notch filters for calibration (may reduce the need to disconnect the antennas during calibration).
  • Reworking the buffering code for improved sample ingestion performance and increased averaging.
  • Direction finding and passive radar algorithm improvements.
  • Creating a networked web application for combining data from two or more physically distributed KerberosSDRs over the internet for immediate TX localization.
  • Updates and bug fixes for the Android mobile direction finding app for use in vehicles.
  • Improving passive radar to be able to use all four RX ports for surveillance so that larger areas can be covered.
  • Plotting passive radar pings on a map.
  • Beginning experimentation with beam forming.
  • In the farther future we hope to eventually have even more clever software that can do things like locate multiple signals in the bandwidth at once, automatically plot them on a map, and track them via their unique RF fingerprint, or other identifiers.
  • Future hardware updates may see more streamlined calibration and smaller sizes.
KerberosSDR Android App for Direction Finding
KerberosSDR Android App for Direction Finding

KerberosSDR Batch One End of Stock, Batch Two Preorders Available

If you weren't aware, KerberosSDR is our recently released 4x Coherent RTL-SDR which can be used for tasks such as direction finding and passive radar. KerberosSDR was successfully crowdfunded over on Indiegogo, and we have recently completed shipments to all backers. Currently there is only about 20 units of the batch one production left in stock.

We are currently offering discounted preorders for batch two units on Indiegogo which we expect will be ready to ship in July or hopefully earlier. If you are interested, please order soon to avoid missing out as the price will be raised again once we are shipping. Batch two will be the same as batch one except for some minor changes. For example we have decided to convert the microUSB port into a USB-C port as we have found that there are many very poor quality microUSB cables on the market which could cause issues for users. USB-C cables are generally of a higher quality.

More information about KerberosSDR is available on the Indiegogo page.

KerberosSDR Updates

Since our last post on this blog about KerberosSDR we have made some enhancements to the software.

  • The KerberosSDR code is now fast enough to run at 1-2 Hz update rates for direction finding and passive radar on a Raspberry Pi 3 B+.
  • There is now a web interface, so the KerberosSDR can be controlled via a WiFi hotspot and internet browser. Useful for use on the Pi 3 and Tinkerboard.

For future updates we are currently working on several new features:

  • Filters to remove low confidence DoA results on the Android app.
  • A secondary heatmap type display on the Android app based on signal strength, for two direction finding indications.
  • Methods to determine the center of multiple bearing intersection points.
  • Further enhancements to processing speed, possible improved results from processing gain and possible better accuracy from improved DoA algorithms.

Within the next few weeks we will also release full tutorial videos that will show how to set up and use the KerberosSDR for direction finding and passive radar with a Raspberry Pi 3 or Tinkerboard. If you prefer a text based explanation we already have a guide up at rtl-sdr.com/ksdr.

Below is an image that demonstrates the KerberosSDR direction finding Android app. A user of KerberosSDR has also submitted two of his own screenshots that show that he was able to determine the location of a GSM transmitter with a linear antenna array.

KerberosSDR Direction Finding Results
KerberosSDR Direction Finding Results. Multiple data points collected during a drive, with bearings pointing towards the TX tower (red marker). Circular array of whip antennas used at freq. 858 MHz.

KerberosSDR Updates: Demo Software Speed Improvements, Android App, Manufacturing Updates

If you weren't already aware, over the past few months we've been working with the engineering team at Othernet.is to create a 4x Coherent RTL-SDR that we're calling KerberosSDR. A coherent RTL-SDR allows you to perform interesting experiments such as RF direction finding, passive radar and beam forming. In conjunction with developer Tamas Peto, we have also had developed open source demo software for the board, which allows you to test direction finding and passive radar. The open source software also provides a good DSP base for extension.

If you're interested and missed out in the early campaign, don't worry we still have about 250 units left from this batch for sale at a price of $140 + shipping over on our Indiegogo Campaign.

Demo Program Updates

Over the past few weeks we've been working on a few code speed improvements to the demo software, and we now believe that it should be fast enough to run on a Pi 3 B+ at decent update rates.  In particular the passive radar display frame rate has been improved and we're able to get about 1 FPS on a Tinkerboard now.

We will soon release the full code, but for now you can see the main two libraries developed by Tamas' that are used in the KerberosSDR code. These libraries contain the direction finding and passive radar processing algorithms.

pyAPRIL - Python Advanced Passive Radar Library. Available on PyPi and GitHub

pyArgus - Python Beamforming and Direction Finding Algorithms. Available on PyPi and GitHub.

Android Direction Finding Companion App Updates

Over the holidays we've been working on a simple companion Android app for the direction finding feature. Using the GPS and/or compass sensors on the Android phone, and the transmitter bearing given by the KerberosSDR we can plot a bearing towards the transmitter that we are tuned to.

The phone connects to a laptop/SBC WiFi hotspot running the KerberosSDR Linux software, and reads the bearing via a simple php HTML server.

Driving around with the KerberosSDR gives better results than when stationary as we can take multiple readings at different points which helps to average out multipath distortions.

In the image below we used a linear antenna array of four dipoles attached to the windscreen of a car. KerberosSDR was tuned to a TETRA transmitter at 858 MHz.

We drove down a street and then back up it. The red lines indicate the direction of the car as determined by GPS, the blue lines indicate the forward direction towards the transmitter, and the green lines the reverse direction. (a linear antenna array won't know if the transmitter is in front or behind it). 

You can see that the majority of blue/green lines point towards the TETRA transmitter which we've marked with a red location marker at the known location.

KerberosSDR Results from a Linear Antenna Array of Dipoles
KerberosSDR Results from a Linear Antenna Array of Dipoles

Getting a bearing from GPS requires that you are moving. However if you are stationary it is also possible to use the compass sensor in the Android app, but Android compass sensors are not particularly accurate.

We also tested the app with a circular array of antennas and found it to work well too. A circular array has the benefit over a linear array of providing only one direction towards the detected signal, but may be more susceptible to multipath issues. In our test the circular array was simply four magnetic whips placed on top of a car.

KerberosSDR using Whip Antennas in a Circular Array on a Vehicle
KerberosSDR using Whip Antennas in a Circular Array on a Vehicle

This time we then drove around for a longer time while logging the data in the Android app. We can see that the majority of blue lines point towards the known transmitter location. Blue lines pointing away from the transmitter may be due to multipath or a briefly incorrect GPS heading (e.g. during a turn). Sometimes reflections or refractions of the signal can be more likely to be picked up if the direct path to the transmitter is really blocked. However if you have enough data points from driving around, it becomes much more clear where the actual transmitter is. 

KerberosSDR Results from the Circular Array
KerberosSDR Results from the Circular Array

Manufacturing Updates

We now have some pictures of the boards being manufactured at the factory. Unfortunately we are behind our initial shipping target of mid-Jan due to the previous unexpected payment delays from Indiegogo, and because of this we may hit the Chinese New Year holidays which could delay us further as factories take a 2 week holiday starting late Jan. We're really hoping to have them shipped off just before then, but we don't know if we can beat the clock. I know some of you are anxious to get started with KerberosSDR, and so I do apologize for the delay.

KerberosSDR in it's metal case (no screen printing yet)
KerberosSDR in it's metal case (no screen printing yet)

 

KerberosSDR: One Week of Discounted Preorders Remaining

Just a reminder that one week remains in the KerberosSDR Indiegogo campaign. This is your last chance to grab a KerberosSDR at a discounted preorder price. And at the time of posting there are still 50 "second early bird" units remaining at a discounted price of only $115 USD.

If you weren't already aware, over the past few months we've been working with the engineering team at Othernet.is to create a 4x Coherent RTL-SDR that we're calling KerberosSDR. A coherent RTL-SDR allows you to perform interesting experiments such as RF direction finding, passive radar and beam forming. In conjunction with developer Tamas Peto, we have also had developed open source demo software for the board, which allows you to test direction finding and passive radar. The open source software also provides a good DSP base for extension.

More information available on our KerberosSDR page, and the Indiegogo page.

Updates

Due to the higher than anticipated number of preorders, we have been able to immediately fund further work on improving the demo software, and will be able to continue to work on improving it throughout this and next year. First on the agenda is improving the code buffering structure and DSP processing speed. Shortly after we'll be looking at adding additional features to aide with calibration and direction finding.

We have also now begun ordering parts, begun prototyping the metal enclosure, and have finalized the PCB. Manufacturing is on track to begin shortly after the campaign ends.

KerberosSDR with Calibration Board Attached (Metal Enclosure with SMA connectors Not Shown)
KerberosSDR Prototype with Calibration Board Attached (Metal Enclosure with SMA connectors Not Shown)

More KerberosSDR Passive Radar Demos

KerberosSDR is our upcoming low cost 4-tuner coherent RTL-SDR. With four antenna inputs it can be used as a standard array of four individual RTL-SDRs, or in coherent applications such as direction finding, passive radar and beam forming. More information can be found on the KerberosSDR main postPlease remember to sign up to our KerberosSDR mailing list on the main post or at the end of this post, as subscribers will receive a discount coupon valid for the first 100 pre-order sales. The list also helps us determine interest levels and how many units to produce.

In this post we're showing some more passive radar demos. The first video is a time lapse of aircraft coming in to land at a nearby airport. The setup consists of two DVB-T Yagi antennas, with KerberosSDR tuned to a DVB-T signal at 584 MHz. The reference antenna points towards a TV tower to the west, and the surveillance antenna points south. Two highlighted lines indicate roughly where reflections can be seen from within the beam width (not taking into account blockages from mountains, trees etc).

The second video shows a short time lapse of a circling helicopter captured by the passive radar. The helicopter did not show up on ADS-B. On the left are reflections from cars and in the middle you can see the helicopter's reflection moving around.

We are expecting to receive the final prototype of KerberosSDR within the next few weeks. If all is well we may begin taking pre-orders shortly after confirming the prototype.

KerberosSDR Passive Radar Timelapse 2

KerberosSDR Passive Radar Helicopter Detection

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Creating a Passive Traffic Radar with DVB-T Signals and KerberosSDR our 4-tuner Coherent RTL-SDR

KerberosSDR is our upcoming low cost 4-tuner coherent RTL-SDR. With four antenna inputs it can be used as a standard array of four individual RTL-SDRs, or in coherent applications such as direction finding, passive radar and beam forming. More information can be found on the KerberosSDR main postPlease remember to sign up to our KerberosSDR mailing list on the main post or at the end of this post, as subscribers will receive a discount coupon valid for the first 100 pre-order sales. The list also helps us determine interest levels and how many units to produce.

In this post we'll show KereberosSDR being used as a passive traffic radar. Passive radar works by using an already existing transmitter such as a FM, DAB, TV or GSM and listening to the reflections of those signals created by moving objects like aircraft, boats and cars. A simple passive radar consists of two directional antennas. One antenna points at the 'reference' transmitter (the transmitting tower), and the other towards the 'surveillance' area that you want to monitor. The result is a speed vs distance plot that shows all the moving objects.

For this test we parked our car to the side of a highway and pointed a cheap DVB-T Yagi antenna towards a DVB-T transmission tower, and another cheap Yagi down the road. The video shown below displays the results captured over a 5 minute period. The blips on the top half of the display indicate vehicles closing on our location (positive doppler shift), and the blips on the bottom half indicate objects moving away (negative doppler shift). 

Highway Passive Radar Traffic Monitor with DVB-T and KerberosSDR a 4x Coherent RTL-SDR

DVB-T Antennas In Car
DVB-T Antennas In Car

The resolution of each individual vehicle is not great, but it is sufficient to see the overall speed of the highway and could be used to determine if a road is experiencing traffic slowdowns or not. When larger vehicles pass by it is also obvious on the display by the brighter blip that they show. The display also shows us that the highway direction coming towards us is much busier than the direction moving away.

In the future we'll be working on optimizing the code so that the display updates much faster and smoother. It may also be possible in the future to use the third and fourth tuners to obtain even greater object resolution.

Subscribe to our KerberosSDR Announcement

When preorders start subscribers to this list will receive a discount coupon valid for the first 100 pre-order sales. This list also helps us determine interest levels and how many units to produce, so please sign up if you're interested.

Please select all the ways you would like to hear from RTL-SDR Blog:

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KerberosSDR Preview: A 4x Coherent RTL-SDR for Direction Finding, Passive Radar and more

KerberosSDR is now available for pre-order over on Indiegogo!

Over the last few months we've been working on a 4-input coherent RTL-SDR called 'KerberosSDR' (formerly known as HydraSDR) that is designed to be a low cost way to get into applications such as RF direction finding, passive radar, beam forming and more. It can also be used as a standard 4-channel SDR for monitoring multiple frequencies as well.

Phase coherent RTL-SDRs have been worked on and demonstrated several times over the past few years, but we've been disappointed to find that so far there hasn't been any easy way to replicate these experiments. The required hardware has been difficult to build and access, and the software has been kept as unreleased closed source or has been too complicated to install and use. With KerberosSDR we aim to change that by making phase coherent applications easier to access and run by providing ready to use hardware and software.

Thanks to our developer Tamás Peto, a PhD student at Budapest University of Technology and Economics whom we hired via the ad in our previous post, and the Othernet (formerly Outernet) engineering team who are our partners on this project, we've been able to build a working system, and demonstrate coherent direction finding and passive radar working as expected (demo videos below). We plan to eventually release Tamás' code as open source so that the entire community can benefit and build on it. Also if KerberosSDR turns a profit, we plan to reinvest some of the profits into continually improving the software and expanding the list of use cases.

KerberosSDR will be usable for coherent applications from ~80-100 MHz up to 1.7 GHz (as a standard receiver it will work down to 24 MHz like a regular RTL-SDR). The lower coherent limitation is due to the phase calibration board, and could be improved by custom creating a larger calibration PCB.

At the moment we are finalizing our prototype, and plan to begin final production within the next 2-3 months.

If you have any interest in KerberosSDR, please sign up to our Kerberos mailing list

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Direction Finding

KerberosSDR can be used to find the bearing towards a signal using it's coherent direction finding capabilities. The software by Tamás currently implements several direction finding algorithms such as Bartlett, Capon, Maximum Entropy (MEM) and MUSIC. In the video below we show a quick test of the direction finding system working with a HackRF being used as a signal source, and four dipole antennas connected to KerberosSDR in a linear array. The MUSIC algorithm is used.

KerberosSDR Direction Finding Test

In the image below we also attempted to find the direction towards a known TETRA transmitter. We were able to confirm the direction with an Android compass app that points towards the known transmitter location. As the two angles match, we can be confident that Kerberos is finding the correct direction to the transmitter.

Finding the direction of a TETRA Transmitter
Finding the direction of a TETRA Transmitter

Passive Radar

KerberosSDR can also be used for passive radar. Normal radar systems work by transmitting a pulse of RF energy, and listening to the reflections from objects like planes, cars and ships. Passive radar works by using already existing transmitters such as those for FM/TV and listening for reflections that bounce of objects.

With a simple passive radar system you need two directional antennas and two coherent receivers. One antenna points at the transmitting 'reference' tower, and the other at the 'surveillance' area where you want to listen for reflections. It's important to try and keep as much of the reference signal out of the surveillance antenna as possible, which is why directional antennas like Yagi's are used.

The result is a doppler vs time delay graph, where the reflection of aircraft, cars, ships and other objects can be seen. The doppler gives you the speed of the object relative to your antenna and the transmitting tower, and the time delay gives you the distance relative to your antenna and the transmitter tower.

Below is an example time lapse video of KerberosSDR being used for passive radar. The reference antenna points towards a DVB-T transmitter at 588 MHz, and the surveillance antenna overlooks a small neighborhood, with aircraft sometimes flying over. The antennas we used were two very cheap TV Yagis.

You can constantly see the reflections from vehicles at small doppler values (low speeds), and every now and then you see an aircraft reflection which shows up at much higher doppler (speed) and further time delay (distance) points. 

KerberosSDR Passive Radar Timelapse Test 1

More information about KerberosSDR

KerberosSDR includes:

  • 4x Coherent R820T2 based RTL-SDR dongles with standard 24 MHz - 1.7 GHz frequency range
  • On board GPIO switched wide band noise source for sample sync and phase calibration
  • Special phase calibration PCB for 4x inputs. Required to make the Kerberos phase coherent.
  • On board USB Hub, so only one USB port is required on the PC
  • Shielded metal enclosure

KerberosSDR can also be extended to 8x receivers by daisy chaining two boards together, so that their clocks and noise sources are connected. We've also taken into account undesirable effects such as heat related PLL drift which can be an issue for phase coherence.

At the moment we are also investigating whether singleboard computers like the Raspberry Pi 3 or Tinkerboard can be used, and there will be a header available for powering them via the Kerberos PCB. In the future we also plan to work on optimizing the code and potentially using CUDA/OpenCL GPU optimizations for passive radar so everything runs smoothly.

Once released we plan to have extensive tutorials and documentation that show exactly how to set up and replicate direction finding and passive radar experiments with low cost antennas.

Screenshots of KerberosSDR software:

Screenshots of each KerberosSDR software screen
Screenshots of each KerberosSDR software screen

Remember, if you're interested please sign up to the KerberosSDR mailing list for announcements and the chance to get in early with the cheaper first 100 units.

Be on the look out for more interesting demos that will be posted in the coming weeks!

Update: Please note that due to a Trademark complaint, we have changed the name of this unit from HydraSDR to KerberosSDR.

KerberosSDR Updates: 27 August 18

This week we've managed to get the KerberosSDR demo software made by Tamás Peto functioning on a TinkerBoard. The TinkerBoard is a US$60 single board computer. It's similar to a Raspberry Pi 3, but more powerful. We've also tested the app running on the Raspberry Pi 3 and Odroid XU4. The Pi 3 is capable of running the software but it is a little slow, and the Odroid XU4 is a little faster than the TinkerBoard. In the future we hope to further optimize the code so even Raspberry Pi 3's will be smooth.

In the video below we used a circular array of four whip antennas connected to KerberosSDR. The TinkerBoard is connected to KerberosSDR and is set up to generate a WiFi hotspot, which we connect to with an Android phone and a Windows laptop. The Windows laptop connects to the TinkerBoard's desktop via VNC, and the Android phone receives an HTML/JavaScript based compass display via an Apache server running on the Tinkerboard. With this setup we can wirelessly control and view information from KerberosSDR and the TinkerBoard.

We've also tested the KerberosSDR system on a real signal, and have found it to work as expected. More demo's of that coming later.

For more info on KerberosSDR please see our previous announcement post.

KerberosSDR Direction Finding Test 2: Tinkerboard + Circular Array

KerberosSDR Prototype
KerberosSDR Prototype with TinkerBoard Running Computations

KerberosSDR Updates: 4 September 2018

In this post we'll show an experiment that we performed which was to pinpoint the location of a transmitter using KerberosSDR's coherent direction finding capabilities. RF direction finding is the art of using equipment to determine the location of a transmitting signal. The simplest way is by using a directional antenna like a Yagi to try and determine the bearing based on signal strength. Another method is using a pseudo-doppler or coherent array of antennas to determine a bearing based on phase information.

For the test we tuned the KerberosSDR RTL-SDRs to listen to a signal at 858 MHz and then drove to multiple locations to take direction readings. The antennas were set up as a linear array of four dipole antennas mounted on the windshield of a car. To save space, the dipoles were spaced at approximately a 1/3 the frequency wavelength, but we note that optimal spacing is at half a wavelength. The four dipole antennas were connected to KerberosSDR, with a laptop running the direction finding demo software. 

Low cost direction finding array mounted to vehicle windshield.
Low cost direction finding array mounted to vehicle windshield.

Our open source demo software (to be released later when KerberosSDR ships) developed by Tamás Peto gives us a graph and compass display that shows the measured bearing towards the transmitter location. The measured bearing is relative to the antenna array, so we simply convert it by taking the difference between the car's bearing (determined approximately via road direction and landmarks in Google Earth) and the measured bearing. This hopefully results in a line crossing near to the transmitter. Multiple readings taken at different locations will end up intersecting, and where the intersection occurs is near to where the transmitter should be. 

KerberoSDR SDR Directing Finding DOA Reading
KerberoSDR SDR Directing Finding DOA Reading

In the image below you can see the five bearing measurements that we made with KerberosSDR. Four lines converge to the vicinity of the transmitter, and one diverges. The divergent reading can be explained by multipath. In that location the direct path to the transmitter was blocked by a large house and trees, so it probably detected the signal as coming in from the direction of a reflection. But regardless with four good readings it was possible to pinpoint the transmitting tower to within 400 meters.

In the future we hope to be able to automate this process by using GPS and/or e-compass data to automatically draw bearings on a map as the car moves around. The readings could also be combined with signal strength heatmap data for improved accuracy.

This sort of capability could be useful for finding the transmit location of a mystery signal, locating a lost beacon, locating pirate or interfering transmitters, determining a source of noise and more.

KerberosSDR pinpointing a transmitters location
KerberosSDR pinpointing a transmitters location

KerberosSDR Updates 7 September 2018

For this test we parked our car to the side of a highway and pointed a cheap DVB-T Yagi antenna towards a DVB-T transmission tower, and another cheap Yagi down the road. The video shown below displays the results captured over a 5 minute period. The blips on the top half of the display indicate vehicles closing on our location (positive doppler shift), and the blips on the bottom half indicate objects moving away (negative doppler shift). 

Highway Passive Radar Traffic Monitor with DVB-T and KerberosSDR a 4x Coherent RTL-SDR

DVB-T Antennas In Car
DVB-T Antennas In Car

The resolution of each individual vehicle is not great, but it is sufficient to see the overall speed of the highway and could be used to determine if a road is experiencing traffic slowdowns or not. When larger vehicles pass by it is also obvious on the display by the brighter blip that they show. The display also shows us that the highway direction coming towards us is much busier than the direction moving away.

In the future we'll be working on optimizing the code so that the display updates much faster and smoother. It may also be possible in the future to use the third and fourth tuners to obtain even greater object resolution.

KerberosSDR Updates 27 September 2018

In this post we're showing some more passive radar demos. The first video is a time lapse of aircraft coming in to land at a nearby airport. The setup consists of two DVB-T Yagi antennas, with KerberosSDR tuned to a DVB-T signal at 584 MHz. The reference antenna points towards a TV tower to the west, and the surveillance antenna points south. Two highlighted lines indicate roughly where reflections can be seen from within the beam width (not taking into account blockages from mountains, trees etc).

The second video shows a short time lapse of a circling helicopter captured by the passive radar. The helicopter did not show up on ADS-B. On the left are reflections from cars and in the middle you can see the helicopter's reflection moving around.

We are expecting to receive the final prototype of KerberosSDR within the next few weeks. If all is well we may begin taking pre-orders shortly after confirming the prototype.

KerberosSDR Passive Radar Timelapse 2

KerberosSDR Passive Radar Helicopter Detection

Information on Time Correlating Signals with RTL-SDRs

In a previous post back in September 2017 Stefan Scholl (DC9ST) treated us to a very interesting write up about how to localize transmitters to within a few meters using time difference of arrival (TDOA) techniques with multiple RTL-SDR dongles spread out over an area.

Stefan has recently added to his post now with some additional information on how to properly correlate signals received between multiple RTL-SDR dongles, which is one of the key parts to TDOA. He writes that he covers the following questions:

- What signal parameters influence the quality of the correlation?
- Which type of correlation calculations are available (four)
- Which are suitable with RTL-SDRs, considering noise and phase and frequency offset?

Stefan writes that his findings could be interesting to people interested in the following techniques:

- TDOA localization
- Synchronizing several RTL-SDRs
- Passive Radar

Comparing various bandwidth sizes on correlation quality
Comparing various bandwidth sizes on correlation quality