Talk:Pseudo-range multilateration

message: National labs for metrology in Germany (PTB), UK (NPL), US (NIST) and Japan (AIST) refer to multilateration as determining target coordinates by measuring the distance to the target from multiple locations (by whatever curvilinear line-of-measurement method that works within the geometry of the problem). While multilateration may have originated regarding one measurement technique (TDOA) and may still be considered to hold to that narrow definition within specialized disciplines, it is now being used in the broader sense above worldwide. The common use of the term multilateration for interferometers and other distance measurement devices should be covered in the article. What I think makes most sense is that trilateration refers to 3 stations and multilateration refers to an ambiguous number (3 or more), so I think that is where the terms have headed towards.
Here are just a few of many articles from work by the national labs and others using the term multilateration for laser interferometry, which is distance measurement, and NOT a TDOA method.
http://secure.theengineer.co.uk/Articles/305424/Laser+TRACER+calibration.htm
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V4K-4F490P6-1&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=d97133bda6f334a4296adcde6d667509
http://www.slac.stanford.edu/econf/C04100411/papers/054.PDF
http://www.ptb.de/de/org/5/nachrichten5/archiv/2006/wirtschaft/abteilung5_18.htm
http://www-pnp.physics.ox.ac.uk/~licas/page_talks/IWAA2008/IWAA2008_John_Dale.pdf
http://www.ptb.de/en/publikationen/jahresberichte/jb2000/jb5e.pdf  —Preceding unsigned comment added by 70.102.119.35 (talk) 22:42, 12 February 2009 (UTC)
replies: text: I agree. The article about TDOA / Multilateration, need to incorporate the wider use of the term. I also think it should be noted that Trilateration is basically a special case of Multilateration. I hope someone with enough knowledge, time and wiki-experience could rewrite this article. Haakoo (talk) 11:10, 29 July 2009 (UTC)
thread_title: Multilateration vs Trilateration

message: Multilateration uses spheres, as trilateration uses circles.
DTOA uses hyperboloids and is hyperbolic positioning and is an completely different thing, not the same as multilateration.
In http://www.aviationtoday.com/av/issue/cover/9891.html  is described how multilaterition uses spheres and NOT hyperboloids.
For the multilateration calculations it is not important how the size of the spheres is acquired.  —Preceding unsigned comment added by 92.66.245.162 (talk) 16:22, 25 June 2008 (UTC)
replies: text: This comment is somewhat anachronistic, the usage of the terms had widenen in the last decade. The restricting of multilateration to spheres is wrong. Multilateration applies, wherever the number of measurements is over determined compared to the minimum requirements. Hence multilateration is also state of the art for planar or cubic problems, not just for spheres. Using DTOA from the viewpoint of measurement applies as well to phase measurements. There is no exclusive restriction of the term to hyperbolic locating. Finally, the common term 'positioning' is misleading, as no position change is effected, all topics discussed touch 'locating' which is determining a location in a known system of coordinates or under equal entities which no fixed systemof coordinates.Wireless friend (talk) 07:04, 12 November 2008 (UTC)
replies: text: the article currently seems to put too much emmphasis on the hyperbolic thing and doesn't make any mentions of spheres or circles --TiagoTiago (talk) 07:01, 30 May 2009 (UTC)
thread_title: Multilateration VS hyperbolic positioning

message: I think that the math in the basic formula is a bit confused.  (x, y, z) is given as the unknown location of the emitter, but then also as the location of the central transmitter.  Different variable names should be used.
While I mention this, I would also suggest that the mathematical discussion be fleshed out a bit more by listing what should be minimized in the optimization.
Mark (talk) 19:46, 29 April 2008 (UTC)
thread_title: Math errors

message: 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)
thread_title:  Clarification 

message: 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,  or ).  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)
thread_title:  the above is mixed up! 

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

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

message: This article with it's redirects really needs a major clean up. The Multilateration article should either be similar to the Trilateration article, without the strong connection to Time difference of arrival / TDOA or Hyperbolic positioning should not redirect here. I do not have any good references for the present norm in literature. My opinion is that the Trilateration article is better than this one, causing less confusion. It basically ends up with a discussion of the meaning of "Multilateration", and how it should be used.
If multilateration is considered to be the process of doing a TDOA and the estimate the position, Hyperbolic positioning should not be redirected here. If multilateration on the other hand is the process of estimating a position based on a given set of data (difference in distance to reference points of known position) then TDOA should not redirect here and the article rewritten.
TODA deserves it's own article just as Time of arrival, and this article should be rewritten without the strong connection to TDOA. As I've said earlier, multilateration does not need TDOA data to estimate a position.
Haakoo 02:56, 26 September 2007 (UTC)
thread_title: Major clean up

message: The article describes 3D-space case, where distances are straight lines, but no words are said about spherical case of terrestrial radionavigation (e.g. Loran-C), where distances are calculated using haversine formula. Unomano 07:06, 11 October 2007 (UTC)
thread_title:  Terrestrial radionavigation  

message: : "Multilateration is a proven technology that has been in use for many decades" ... "Using advanced computer processing techniques" ... "Multilateration requires no additional avionics equipment" 
That's not a maths page, that's a sales page.  Hardly relevant in an encyclopedia article describing the technology?  Ojw (talk) 14:34, 15 October 2009 (UTC)
thread_title:  That external link 

message: I have expanded the 3-D solution section and added sections defining the geometry and some stuff on TDOA measurement.  In general - lots of additional math that should lead to a solution.  The "Intro" and "Principal" section were not changed.  It will take some thinking and homework to sort-out the swirling questions of the various relations (or lack of relations) between TOA, TDOA, trilateration, the assorted meanings applied to the word multilateration and the example systems mentioned in the article.  —Preceding unsigned comment added by TinyPebble (talk • contribs) 01:30, 20 March 2010 (UTC)
thread_title:  More Math 

message: I think there's a typo in the article.  Under "3-D Solution" in the 4th paragraph: "Improving accuracy with a large number of receivers can be a problem for devices with small embedded processors because of the time required to solve several simulatious..."  What does the author mean by "simulatious"?  Did he mean "simultaneous?" Krenzo (talk) 00:07, 19 December 2010 (UTC)
thread_title:  Typo? 

message: None of the other articles that I've found seemed to include the trick for removing the 2 R0 term.  Is this somewhere in the Bucher/Misra paper that I just missing, was it your own work, or some other source?  It's a very nice trick and I want to ensure that I'm referencing it correctly in the biblography for my thesis.  — Preceding unsigned comment added by 205.167.170.20 (talk) 19:45, 22 June 2011 (UTC)
thread_title:  Reference for 3-D Solution section 

message: Please examine figures 3a, 3b, and 3c. The two signals in each figure appear to be separated by about 2 time units, but the cross-correlation plot indicates a separation of 5 time units. I feel the peaks on the cross-correlation plots should be closer to 2. Please let me know if I am wrong on this issue.146.165.84.65 (talk) 18:12, 25 July 2011 (UTC)
replies: text: I Agree! I also came here to point that out. Things like this bother me. Unfortunately I currently don't have software to create such a plot. 84.137.186.78 (talk) 21:20, 20 September 2012 (UTC)

text: Yep. I came here to report exactly the same error. --ps  — Preceding unsigned comment added by 99.109.150.114 (talk) 05:11, 23 July 2013 (UTC)
thread_title:  Inaccurate Cross-Correlation Plots 

message: The article states: "Use equation 7 to generate the four constants Am,Bm,Cm,Dm from measured distances and time for each receiver 2 ≤ m ≤ N. This will be a set of N homogeneous linear equations."
That would actually leave us with N-1 equations.  For example, say you have 4 receivers (P0, P1, P2, P3), we would have N=3.  If we generate an equation for each receiver 2 ≤ m ≤ N, this would leave us with 2 equations (m=2, m=3).  Unless there is another equation that I missed.  — Preceding unsigned comment added by 192.48.242.22 (talk) 21:41, 8 September 2011 (UTC)
thread_title:  Inconsistencies in the number of linear equations  

message: I made some moderate (not major, but not typo corrections either) to the article Oct. 25-26, 2014. Comments/corrections/critiques are welcome.  
I fixed some issues (IMHO, of course), but others remain. These are
1. Article title:  In this situation, we're not dealing with a pure mathematics text, where every word of a definition is scrutinized, edited, and re-edited, and then re-edited again, etc.  Engineering terminology and documents are inherently sloppier.  I'd prefer "Differential Multilateration" to just "Multilateration".  But I could live with the latter, provided the terminology confusion is explained early in the article.   
2. "Trilateration".  This is related to #1.  Differential Multilateration can be done with many ("multi") stations, but Absolute Multilateration can only be done with three stations ("tri")?  Really -- can anyone cite a source?  I'll acknowledge that Differential Multilateration implementations are more common than Absolute Multilateration implementations in the aerospace application domain.  But this terminology is wrong "on its face".  For example, an aircraft (at sufficient altitude) can measure (a) its distance to more that two DME ground stations, plus (b) its altitude with a barometric or radio altimeter, and then (c) compute is position.  The position solution can either "clamp" the altitude to the altimeter reading or be a full three-dimensional solution.
3. "GPS is not a Differential Multilateration system".  This statement/position is factually incorrect.  GPS *IS -- repeat, IS*, repeat ... -- a Differential Multilateration system.  To not understand this calls into question every statement by the originator.  — Preceding unsigned comment added by NavigationGuy (talk • contribs) 00:38, 28 October 2014 (UTC)
thread_title:  Made Revisions / Comments Welcome / Opinions Offered 

message: When going from 2 to 3 receivers there is only one extra independ TDOA available. Often it is mentioned that there are two extra TDOAs available and this is completely true but there is only one independend extra TDOA avalable. Consider the three timing signals a, b, c. The TDOA of these signals are (a-b), (b-c) and (a-c). But the (a-c) TDOA is equivalent to (a-b)+(b-c) and does not give extra information.
For each extra receiver (or transmitter/satellite) there is only one extra TDOA. Using the other dependend TDOA's will not reduce the possible locations. So the curve stays the same because the extra hyperboloids intersect with the curve. Or when there are two points these dependend TDOA's do not eliminate one of the points.
# One transmitter/receiver/satellite does not restrict the location at all.
# Two transmitters/receivers/satellites does gives a location on a hyperboloid.
# Three transmitters/receivers/satellites does give a location on a curve. (Intersection of two hyperboloids)
# Four transmitters/receivers/satellites gives one or two mathematical points in 3D space. (The intersection of a curve with a hyperboloid. Dependend on the constellation this gives one or two points. For GPS this is very often two points, but only one of those points is stable over time.)
# 
Crazy Software Productions (talk) 16:45, 7 November 2016 (UTC)
thread_title:  An extra transmitter/reciever/satellite 

message: The second sentence: "Unlike measurements of absolute distance or angle, measuring the difference in distance between two stations results in an infinite number of locations that satisfy the measurement." - is terrible.  I don't know what this means, except that when I have to re-read something 3 times and it still makes no sense, I leave.
This entire article is poorly written.  I browsed it and quickly gave up.  And I'm in the GPS business.  That tells you something.  Someone REALLY needs to rewrite this article in proper English, so that the Average Joe doesn't give up or throw up.  Either way, it's bad. 98.194.39.86 (talk) 07:39, 26 June 2017 (UTC)
thread_title:  Poorly Written.  Second sentence was as far as I got... 

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thread_title:  External links modified (January 2018) 

message: 1. Added a section entitled Advantages and Disadvantages
2. Added GPS, Glonass and Galileo as the most prominent examples of GNSS multilateration systems.  
There's some confusion on this point. Because the stations (satellites) are moving, it's less obvious that GNSSs are multilateration systems.
3. Added a section entitled Station synchronization
4. Added a section entitled User-station geometry
5. Multiple edits.
A theme was to change measured TDOAs to measured TOAs and calculated TDOAs or something similar.
* That actually what's done (how can a surveillance system with multiple remote receivers "measure" a TDOA?)
* When the stations are fixed to the earth and the transmission are synchronized with UTC, forming TDOAs eliminates the unknown/unneeded time of transmission (TOT). However, in satellite systems are synchronized with UTC and the TOT is needed.
NavigationGuy (talk) 13:29, 16 December 2018 (UTC)
thread_title:  Edits Dec. 2018 

message: I attempted to shorten the Intro section, per the note.
NavigationGuy (talk) 12:20, 8 April 2022 (UTC)
thread_title:  Shorten Intro Section