correct as-is TDOA

[Sinclair_76]

In the recent ED Matt video of the HTS improvement, it was mentioned you need at least 3x Vipers to get a TDOA solution. What is the reason for that?

Edit: my mistake report in bugs wasn't intended. Please move to general.

Edited November 18, 2023 by Sinclair_76

[Furiz]

2 hours ago, Sinclair_76 said:

What is the reason for that?

My best guess is maybe software limitation?

But it should work with 2 ship cause there are some basics of getting position of something in space, it is not science fiction. You can even get more or less precise position with 1 ship, if you know ships speed and direction (more or less cause of the signal spread etc.) after that just draw lines in the direction of the source every lets say 10 sec and you get its position, which is what HTS is essentially doing when trying to determine position of emitter, more precise with 2 ship sharing data and so on.

So really don't get why we need 3 ship when you can get pretty much good data from 2 ship as well. It is just direction lines crossing each other on the map after all. If you get lets say 10 lines drawn you have pretty good accuracy there.

 

Edited November 18, 2023 by Furiz

[darkman222]

Just guessing: Triangulation. Cant build a triangle out of a two ship. Possibly it works like GPS triangulation. Just replace the satellites with F16s
 

Edited November 18, 2023 by darkman222

[Furiz]

2 hours ago, darkman222 said:

Cant build a triangle out of a two ship.

You can build it with one ship, if it moves around. Go to STPT 1 and draw a line at the emitter direction, move to STPT 2 draw another line, move to STPT 3 and you have triangulation. It is basic navigation.

Those line don't have to be drawn as the image shows btw. As long as the are 2 or more lines intersecting you can determine position. More line with further distance between points of origin is better then just 2 lines off course.

Edited November 18, 2023 by Furiz

[KlarSnow]

You should go look up the principles behind TDOA, TDOA is Time difference of Arrival, not angular measurements. Each station is receiving and synchronizing the time of arrival of a particular signal and using that time sync to generate a location. With 1 station all you get is a range, thus a circle around your aircraft. 2 stations would give you a pair of potential locations, and 3 stations gives you a very accurate location.

This does not work the same way as angle based triangulation systems.

 

Each intersection of a circle is the potential location of the target, only where all three intersect is the true location.

[Sinclair_76]

The solution provided does not answer my question and is incorrect.

 

TL;DR

There are multiple variations on solving emitter locations with multilateration. In this case KlarSnow conflates 3d true-range multilateration, in the text and 2d TDOA/ pseudo-range multilateration with the visual example (both 3 receivers). But the problem in localizing a hostile emitter in DCS is a 3d TDOA (not a true-range 3d or a pseudo-range 2d) problem which according to the formula for pseudo-range multilateration, m≥d+1 (m=receivers, d=dimensions) requires at least (3+1=) 4 receivers. Hence my question; how does ED solve the 3d TDOA problem with 3 HTS equipped Vipers when technically 4 receivers are required?  

 

Now for my lengthy/nerdy explanation. 

Multilateration is difficult subject. To begin there are two distinct problem sets. Multilateration with known ranges, true-range multilateration, with unknown or biased ranges, known as pseudo-range multilateration. True-range multilateration can be done with radars for example. With just range 2 emitters can locate a target in a 2d situation. With 3 emitters a target can be defined in a 3d environment.

With the HTS and passive equipment in general, ranges cannot easily be obtained. Time Differences of Arrival (TDOA) can be used to overcome the ranging problem. TDOA is typical for pseudo-range multilateration. The formula used to determine the amount of receivers to determine the location of the emitter is: m≥d+1  (d are the amount of dimensions being dealt with, and m the amount of receivers). To put it simply a TDOA solution in a 2d environment requires 3 receivers and a 3d environment requires 4 receivers.

In passive equipment (yes there are exceptions but only in a cooperative environment) a single station, when receiving an emission, can only establish that an emitter exists. It can’t determine range or location for that matter (by using directional antenna’s you would be able to determine direction). A single TDOA requires at least two Times of Arrival (TOA). In other words, a single TDOA requires a minimum of two receivers. With a single TDOA a pseudo range can be determined which can be plotted on a half of a 2-sheeted hyperboloid (either the top or bottom in the picture). 
 

 

Adding a third receiver adds a second TDOA and hyperboloid. The location of the emitter in this case is on the curve (in red in the picture below) that intersects two hyperboloids.
 

Adding a fourth receiver will have the previous curve intersect with the hyperboloid on a single point (most of the time as I understand it but apparently it sometimes can intersect in two points. I might be wrong here as I don’t fully understand this part). The point is the location of the emitter.

 

With the visual examples as well as the formula I hope to demonstrate that locating an emitter with TDOA in a 3d situation requires 4 receivers. In the video by Matt, it is mentioned that at least 3 Vipers with HTS pods are required. To come back to my original question; how does ED tackle the TDOA equation with only 3 receivers?

 

On 11/19/2023 at 12:28 AM, KlarSnow said:

Each station is receiving and synchronizing the time of arrival of a particular signal and using that time sync to generate a location. With 1 station all you get is a range, thus a circle around your aircraft. 2 stations would give you a pair of potential locations, and 3 stations gives you a very accurate location.

In the above quoted part it’s clear that KlarSnow is referring to 3d true-range multilateration and not pseudo-range multilateration. The picture provided references a 2d (on a single plane) TDOA which also only requires (2+1=) 3 receivers. The TDOA problem in DCS is a 3d pseudo-range multilateration so both the written as well as graphic representation provided in the solution don't apply.

 

Further reading:

https://en.wikipedia.org/wiki/Trilateration
https://en.wikipedia.org/wiki/Pseudo-range_multilateration

Graphics:

https://en.wikipedia.org/wiki/Hyperboloid
https://math.stackexchange.com/questions/2629499/intersection-between-two-hyperboloids
https://math.stackexchange.com/questions/3379193/intersections-of-3-hyperboloids

Edited November 20, 2023 by Sinclair_76

[toilet2000]

On 11/20/2023 at 4:51 AM, Sinclair_76 said:

The solution provided does not answer my question and is incorrect.

 

TL;DR

There are multiple variations on solving emitter locations with multilateration. In this case KlarSnow conflates 3d true-range multilateration, in the text and 2d TDOA/ pseudo-range multilateration with the visual example (both 3 receivers). But the problem in localizing a hostile emitter in DCS is a 3d TDOA (not a true-range 3d or a pseudo-range 2d) problem which according to the formula for pseudo-range multilateration, m≥d+1 (m=receivers, d=dimensions) requires at least (3+1=) 4 receivers. Hence my question; how does ED solve the 3d TDOA problem with 3 HTS equipped Vipers when technically 4 receivers are required?  

 

Now for my lengthy/nerdy explanation. 

Multilateration is difficult subject. To begin there are two distinct problem sets. Multilateration with known ranges, true-range multilateration, with unknown or biased ranges, known as pseudo-range multilateration. True-range multilateration can be done with radars for example. With just range 2 emitters can locate a target in a 2d situation. With 3 emitters a target can be defined in a 3d environment.

With the HTS and passive equipment in general, ranges cannot easily be obtained. Time Differences of Arrival (TDOA) can be used to overcome the ranging problem. TDOA is typical for pseudo-range multilateration. The formula used to determine the amount of receivers to determine the location of the emitter is: m≥d+1  (d are the amount of dimensions being dealt with, and m the amount of receivers). To put it simply a TDOA solution in a 2d environment requires 3 receivers and a 3d environment requires 4 receivers.

In passive equipment (yes there are exceptions but only in a cooperative environment) a single station, when receiving an emission, can only establish that an emitter exists. It can’t determine range or location for that matter (by using directional antenna’s you would be able to determine direction). A single TDOA requires at least two Times of Arrival (TOA). In other words, a single TDOA requires a minimum of two receivers. With a single TDOA a pseudo range can be determined which can be plotted on a half of a 2-sheeted hyperboloid (either the top or bottom in the picture). 
 

 

Adding a third receiver adds a second TDOA and hyperboloid. The location of the emitter in this case is on the curve (in red in the picture below) that intersects two hyperboloids.
 

Adding a fourth receiver will have the previous curve intersect with the hyperboloid on a single point (most of the time as I understand it but apparently it sometimes can intersect in two points. I might be wrong here as I don’t fully understand this part). The point is the location of the emitter.

 

With the visual examples as well as the formula I hope to demonstrate that locating an emitter with TDOA in a 3d situation requires 4 receivers. In the video by Matt, it is mentioned that at least 3 Vipers with HTS pods are required. To come back to my original question; how does ED tackle the TDOA equation with only 3 receivers?

 

In the above quoted part it’s clear that KlarSnow is referring to 3d true-range multilateration and not pseudo-range multilateration. The picture provided references a 2d (on a single plane) TDOA which also only requires (2+1=) 3 receivers. The TDOA problem in DCS is a 3d pseudo-range multilateration so both the written as well as graphic representation provided in the solution don't apply.

 

Further reading:

https://en.wikipedia.org/wiki/Trilateration
https://en.wikipedia.org/wiki/Pseudo-range_multilateration

Graphics:

https://en.wikipedia.org/wiki/Hyperboloid
https://math.stackexchange.com/questions/2629499/intersection-between-two-hyperboloids
https://math.stackexchange.com/questions/3379193/intersections-of-3-hyperboloids

 

AFAIK, the problem doesn't need to be a full 3D problem at all. Either through a digital terrain elevation database or simply a sync'd target altitude between the different receivers (F-16s in this case), this adds a constraint to the height dimension which could be used to solve the problem. There would be a positional error associated with that, but that error could very well be within the accuracy of other parts of the measurement system.

Also, there is no requirements for a single measurement. Assuming a certain "target" or emitter model, such as a static one, we can take multiple measurements where the different position solutions for each combined (over all receivers) measurement can be filtered by their state properties. For example, a target assumed static (as would be the case for an SA-10 search radar for example) should move very little over multiple combined measurements and that movement should be somewhat random since it would be linked to measurement errors and noise.

Using @KlarSnow's example, even with 2 receivers, only one of the 2 position solutions for the emitter would stay static over time, the other position solutions (intersections of the circles) would move w.r.t. the position of the receivers, not w.r.t. the position of the emitter only.

I might definitely be missing something though, so feel free to correct me.

[BIGNEWY]

Available references are very clear that three receivers are needed. 

thank you

[TobiasA]

Am 22.11.2023 um 03:02 schrieb toilet2000:

AFAIK, the problem doesn't need to be a full 3D problem at all. Either through a digital terrain elevation database or simply a sync'd target altitude between the different receivers (F-16s in this case), this adds a constraint to the height dimension which could be used to solve the problem. There would be a positional error associated with that, but that error could very well be within the accuracy of other parts of the measurement system.

Also, there is no requirements for a single measurement. Assuming a certain "target" or emitter model, such as a static one, we can take multiple measurements where the different position solutions for each combined (over all receivers) measurement can be filtered by their state properties. For example, a target assumed static (as would be the case for an SA-10 search radar for example) should move very little over multiple combined measurements and that movement should be somewhat random since it would be linked to measurement errors and noise.

Using @KlarSnow's example, even with 2 receivers, only one of the 2 position solutions for the emitter would stay static over time, the other position solutions (intersections of the circles) would move w.r.t. the position of the receivers, not w.r.t. the position of the emitter only.

I might definitely be missing something though, so feel free to correct me.

You always need 3D because the radar beam travels in a straight line and you have to take your own height into account.

Everything else would have a degraded accuracy. Your triangle is somewhere in space, not even in the horizontal plane. And all those problems with having two receivers leave much room for error. The HTS pod does use triangulation but it is simply not as accurate. You also have to take sensor inaccuracies into account. It is hard to measure the exact angle, but the time of a signal arriving does easily have a high accuracy when clocks are synchronized. 

The thing with TDOA is that it does not rely on ownship movement and directional measurement as without TDOA but does extrapolate within only seconds with extreme accuracy. 

Other methods are possible, but require more time or are less accurate. 

[toilet2000]

10 hours ago, TobiasA said:

You always need 3D because the radar beam travels in a straight line and you have to take your own height into account.

Everything else would have a degraded accuracy. Your triangle is somewhere in space, not even in the horizontal plane. And all those problems with having two receivers leave much room for error. The HTS pod does use triangulation but it is simply not as accurate. You also have to take sensor inaccuracies into account. It is hard to measure the exact angle, but the time of a signal arriving does easily have a high accuracy when clocks are synchronized. 

The thing with TDOA is that it does not rely on ownship movement and directional measurement as without TDOA but does extrapolate within only seconds with extreme accuracy. 

Other methods are possible, but require more time or are less accurate. 

What I'm saying is not that it is not a 3D problem, just that making some hypothesis or constraining the problem to "the target has to be on the ground given a certain DTED" or "the target has to be at system altitude 0", it can be solved as either a 2D or 2.5D problem, meaning there exist additional equations to solve the problem.

Also, as I hinted at, using multiple measurements can also solve the problem without additional receivers. I'm not talking about what it's currently doing in DCS (we don't know that) or what it's doing IRL (I and probably no one here knows, and if they do, they probably can't talk about it here).

An under-constrained problem can be solved with multiple measurements under some state constraints. That's a possible answer to OP's question.

[TobiasA]

vor 3 Stunden schrieb toilet2000:

What I'm saying is not that it is not a 3D problem, just that making some hypothesis or constraining the problem to "the target has to be on the ground given a certain DTED" or "the target has to be at system altitude 0", it can be solved as either a 2D or 2.5D problem, meaning there exist additional equations to solve the problem.

Also, as I hinted at, using multiple measurements can also solve the problem without additional receivers. I'm not talking about what it's currently doing in DCS (we don't know that) or what it's doing IRL (I and probably no one here knows, and if they do, they probably can't talk about it here).

An under-constrained problem can be solved with multiple measurements under some state constraints. That's a possible answer to OP's question.

But that would require multiple measurements over a longer period of time.

The original question was why TDOA requires three emitters, and that question has been answered. 

And there might be different solutions to that mathematical problem, but it seems that the engineers of the HTS did not use these due to reasons being classified. Probably poor sensor angle resolution, not reaching the resolution of what you get by TDOA. Or the need to have a pretty wide spread or multiple locations over time, which can quickly be rendered useless when SAMs start blinking (which they never do in DCS, only in another sim or with the Skynet script).

We tried it as a squad and pinpointed a SA-15 in only a few seconds, 20 - 25nm out, 15ft resolution. Enough to employ ordnance without ever seeing it. Doesn't matter if they blink or not.

Of course, you can circle the site to find the emitter (the Viggen does that with a single airframe) but you need different angles and more time.

The whole point of TDOA is to improve the inaccuracies of other methods that do work, even with fewer receivers, but with less accuracy and in a longer time.

[Sinclair_76]

On 11/25/2023 at 12:04 AM, TobiasA said:

The original question was why TDOA requires three emitters, and that question has been answered. 

I don't consider BN's reply a real answer. He only stated documents reference they need 3x emitters. I asked for a reason why. Of course it's possible he can't give a reason, which is fine. 

 

At least three receivers is neither fish nor fowl. A true TDOA solution requires 4x receivers (=3x TDOA). If a solution only requires 3x receivers, my bet is the system uses a Kalman filter to get a fused location using ,3x receiver TDOA ( a curve) and multiple triangulation ellipses (the location is where the curve touches the ellipse or DTED as suggested by @toilet2000). But then this system would also work with 2x receivers (the location is where the hyperboloid touches the ellipse, if there is overlap there is a significant reduction of the area where the true location is at). The beauty of a full TDOA location it's that it is near instant high accuracy. Any location fusion with less than 4x receivers just requires (a lot of?) more time to get proper measurements and have the Kalman filter come up with a precise location. 

or

ED interpreted the 3x TDOA as 3x receivers.

Edited November 26, 2023 by Sinclair_76

[TobiasA]

vor 21 Minuten schrieb Sinclair_76:

I don't consider BN's reply a real answer. He only stated documents reference they need 3x emitters. I asked for a reason why. Of course it's possible he can't give a reason, which is fine. 

 

At least three receivers is neither fish nor fowl. A true TDOA solution requires 4x receivers (=3x TDOA). If a solution only requires 3x receivers, my bet is the system uses a Kalman filter to get a fused location using ,3x receiver TDOA ( a curve) and multiple triangulation ellipses (the location is where the curve touches the ellipse or DTED as suggested by @toilet2000). But then this system would also work with 2x receivers (the location is where the hyperboloid touches the ellipse, if there is overlap there is a significant reduction of the area where the true location is at). The beauty of a full TDOA location it's that it is near instant high accuracy. Any location fusion with less than 4x receivers just requires (a lot of?) more time to get proper measurements and have the Kalman filter come up with a precise location. 

or

ED interpreted the 3x TDOA as 3x receivers.

 

Nobody will have an unclassified documentation about HOW this works in detail.

My guess is that they use triangulation as a base and then use TDOA to get a more accurate position on that point in space.

[Sinclair_76]

42 minutes ago, TobiasA said:

Nobody will have an unclassified documentation about HOW this works in detail.

My guess is that they use triangulation as a base and then use TDOA to get a more accurate position on that point in space.

That could be very well be but in that case it should also work with 2x receivers imo, just need extra time to compensate.

Edited November 26, 2023 by Sinclair_76

[TobiasA]

vor 38 Minuten schrieb Sinclair_76:

That could be very well be but in that case it should also work with 2x receivers imo, just need extra time to compensate.

 

Given time, it probably does.

Not all publicly available information does mention all the capabilities.