Talk:Multilateration

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Contents 1 Decca 1.1 Response 1.2 Clarification 2 It's mixed up 2.1 the above is mixed up! 3 Merge 4 Loose ends? 5 GPS

[edit] Decca

I am no expert in this field. But I would like clarify a small matter.

My understanding of the situation (and its 20 years since I did my exams) is that the LORAN hyperbolae were based on time differences, but that Decca and Omega were both based on phase differences and NOT time differences.

If this is the case then one of the following actions should be taken:

1. The reference to multilateration should be removed from the decca article; or 2. The definition on the multilateration page should be changed to include phase or time difference

[edit] Response

I have modified the article to include mention of the phase approach, and also modified the DECCA article to say "approach similar to multilateration". In fact, as the DECCA transmissions are continous wave, I think it is correct to describe the approach as multilateration. Phase-difference and time-difference are essentially the same thing with a narrow band source. Paul 06:42, 26 December 2005 (UTC)

This does not make sense to me. Either Multilateration includes phase difference, in which case the description "approach similar to multilateration" is incorrect for Decca, or it excludes phase difference, in which case Decca is not multilateration. The NPL describes it as "Multi-lateration is a way of measuring the position of a target, or targets, relative to several fixed measuring stations" at http://www.npl.co.uk/length/dmet/science/multilateration.html. This appears to include phase difference. --SC 22:17, 29 December 2005 (UTC)

I think that the confusion originates from the fact that this entry describes Multilateration as "the process of locating an object by accurately computing the time difference of arrival of signals from three or more locations to that point". Having read around a bit more it appears to me that Multilateration measurements do not have to be by TDOA (although they presumably are usually). This article also duplicates the principles already covered in the trilateration article. I propose the following actions:

• Rewrite multilateration removing dependence on TDOAs, whilst recognising that TDOAs are often used.
• Remove duplication between multilateration and trilateration. (The Trilateration article is probably a better place to describe the principles, since it is an easier concept to grasp.)
• Reduce emphasis on Decca in both articles, since it is obsolete and (I think) that GPS is hyperbolic also, so that would be a better reference
• Add description of what multilateration adds to trilateration. This is unclear to me.

--SC 08:19, 30 December 2005 (UTC)

The problem with using GPS as an example is that it is very difficult to plot GPS hyperbolae on a chart or map. For a start they are 3-dimensional. They are time-difference based and the stations are in orbit above us.

The nice thing about Decca and/or Loran is that the hyperbolae can be (and often are) overlayed on a navigational chart and the readings plotted as lines of position to give a position fix. It was certainly seeing overlayed hyperbolae printed on charts that made it all "click" for me all those years ago. I seem to remember our Electronic Nav lecturer using a North Sea chart with the lattices from 3 different Decca chains printed thereon and the positions of at least 2 master stations and numberous slave stations highlighted along with the baselines. It just all fell into place.

Now trying to do something similar with GPS LOP's, that would be fun.Frelke 09:44, 30 December 2005 (UTC)

Again I am not claiming expert status here, but isn't multilateration just a generic form of trilateration, i.e tri = 3 and multi = >1. I am guessing now, but I think we are headed for merge here.

Frelke 09:49, 30 December 2005 (UTC)

[edit] Clarification

I'm struggling to understand the confusions here. Multilateration is the determination of location using multiple receivers. Trilateration is with exactly three. Both use TDOA to determine the intersection of 2 (with trilateration) or N-1 (with multilateration using N receivers) hyperboloids. Hence the term hyperbolic positioning.

TDOA is usually measured by measuring time of arrival directly, but equivalently can be determined by measuring phase difference - but only if the signal is narrowband.

If anything needs to be merged, then trilateration should be merged into this article, as trilateration is just a special case of multilateration.

The article already says all of this. Paul 21:37, 18 January 2006 (UTC)

[edit] It's mixed up

Quote «Multilateration, also known as hyperbolic positioning...»

1. Multilateration (including trilateration) is based on estimation of the time of arrival (TOA).
2. Hyperbolic positioning is based on estimating the time difference of arrial (TDOA).
3. Dopler positioning is based on estimating the dopler shift of the satellite signal.

These are three (3) main (and different) types of radionavigation. See, for example, book Global Positioning System by Pratap Misra and Per Enge (page 12, chapter 1.2 "Methods of Radionavigation").

Kender 05:37, 18 January 2006 (UTC) Stanford, CA

Now I'm totally confused. So what is the difference between types 1 and 2 above ?

Is there a difference between is based on estimation of the time of arrival and is based on estimating the time difference of arrial. I think we have already agreed here that Hyperbolic positioning can be based on more than just time difference. It can be based on phase difference (as in the case of Decca and Omega). So can we clarify what Misra and Enge mean (presumably these definitions are theirs).

My biggest problem with all this is that I still believe that whatever multilateration is, the only difference between it and trilateration is the number of position lines used, tri having 3 p/l's and multi having an unspecified number.

Frelke 07:35, 18 January 2006 (UTC)

It's all based on the difference between TDOA and TOA.

Since historically TDOA was used for navigation before TOA, let's start with TDOA. Consider two transmitters spaced far apart and one receiver (or user). Each of the transmitters sends a pulse at the same time – they are synchronized. A user first receives a pulse from transmitter 1 then from transmitter 2. The delay between the pulsed is TDOA. TDOA=TOA1-TOA2 (Because of the clock bias, user doesn’t even know the TOAs.) In 2D TDOA from one pair of transmitters puts a user on the hyperbola; hence TDOA systems are also known as hyperbolic systems. To estimate the position the user needs at least two pairs of transmitters (two TDOAs). Each of the pairs will produce a hyperbola and the user position is at the intersection of these hyperbolas.

Next, consider one transmitter and one receiver. One pulse arrives to the receiver. There is no TDOA, because you need two pulses to produce the difference. However, if both receiver and transmitter are somehow synchronized to common time, TOA can be estimated. In 2D TOA from one receiver puts a user on a circle. To estimate the position the user needs at least two transmitters (two TOAs).

Quote «The problem with using GPS as an example is that it is very difficult to plot GPS hyperbolae on a chart or map.»

GPS doesn't produce hyperbolas, because it's not a TDOA system. It's a TOA systen, and the LOP in 3D is a sphere.

Kender 08:17, 18 January 2006 (UTC) Stanford, CA

[edit] the above is mixed up!

The statement "multilateration is based on estimation of the time of arrival (TOA)" above is incorrect. Multilateration uses the time-difference of arrival of a pulse between two sites (see, for instance, [1] or [2]). Absolute time of arrival is not required, and not even measured in systems such as VERA. The explanation above of two transmitters and one receiver is correct - but just the reciprocal case of what I just described. Both are TDOA. So, in terms of the list above, both 1) and 2) use TDOA, and both can be called multilateration or hyperbolic positioning. Incidentally, in my professional life I work on this technology, and the term multilateration is commonly used in the way described in this article.

Paul 06:16, 19 January 2006 (UTC)

[edit] Merge

I am proposing to merge this page with trilateration, this being the more general case. I think that the other article is actually the better article and so would intend to keep the vast majority of it.

See discussion page for vote.

Frelke 07:42, 19 January 2006 (UTC)

I would agree - but see my more detailed comments on discussion page. Care is required. Paul 11:32, 19 January 2006 (UTC)

Frelke, do you think that trilateration is a particular case of multilateration? Kender 04:15, 23 January 2006 (UTC) Stanford, CA

I think that it is, but I am not an expert. I just studied hyperbolic navigation many years ago and my brain still works. Frelke 11:18, 23 January 2006 (UTC)

[edit] Loose ends?

The article is much improved after the recent activity. I presume it is correct now ;-) If so, there appear to be a few loose ends to tidy up as the Multilateration article says that Decca used Multilateration but the Decca article says that is used "an approach similar to multilateration". Does this mean now that the Decca article (and others) needs updating? --SC 22:43, 27 January 2006 (UTC)

Again, I am not the expert, rather the person who stirs the bucket to get a reaction. I remember that comment going into the Decca article and thinking myself at the time that it sounded 'uncomfortable'.

I suggest that it be changed to "...a multilateration-based approach..." unless anyone has a better alternative. Frelke 23:25, 27 January 2006 (UTC)

I just updated the DECCA article seeing as it was my unfortunate wording in the first place. I simply changed it to "also known as multilateration". --Paul 12:29, 30 January 2006 (UTC)

[edit] GPS

GPS works by receiving several known signals in 1 location, not by sending one signal, and receiving in several locations. So I'd say that GPS is not a valid example (but location determining in cellphone networks can be). Am I right?

I would rather say that where you do the measurement is of no important. The basic principle is the same. You measure the difference in distances between several references and an unknown position. If the references or the "locator" sends the signals is irrelevant. (Håkon K. Olafsen) 193.157.188.206 14:31, 25 March 2007 (UTC)