Four Bearing method into a formula/equation?
 

So I need some advice from the trig/geometry brains here.

I have been practicing the 4 bearings method a lot lately and want to develop a quick tool to use to calculate course of a target. I love the Hydrophone tracker tool by Gutted but it isn't available in an app and I don't want to alt-tab out of the game to use it.

So my next option is to use a trig/geo app that allows me to build a formula for the 4 bearings method that I can just plug in values. Do any of the "10 pound brains" on this forum know what the equation for the four bearings method would look like? For example, if your values are as follows;

A= bearing 1
B= bearing 2
C= bearing 3
T= time intervals between bearing readings

What would the formula/equation look like on paper that would spit out a target's course? I realize I still need to take the 4th bearing from a different location to triangulate a location but 3 bearings into a formula would be a good start.

Are you basically trying to do TMA?
As in you take a line of bearing at regular intervals (say 2 mins), and use that to calc range, course and speed?

That's pretty much it. The first 3 bearings are taken at regular timed intervals from a stationary position. From this you can get a target's course, but not exact position or range. You need to move and then take a 4th bearing to triangulate.

I'm trying to figure out what the equation/formula would be on paper for estimating teh coruse based on the first three bearings.

I used the formulas on the first 4 or so pages:

http://www.gamefront.com/files/23015...s_Only_TMA.rar

to calculate the AOB at the first bearing (of 3) to make this slideruler/disk:

http://www.subsim.com/radioroom/showthread.php?t=147719

The DRM or Direction of Relative Movement, aka target course IF you yourself are not moving, is then just a matter of adding/subtracting some angles.

I think your best bet is to construct everything with vector-magic.

Pisces, I am very interested in exporing this method. Unfortunately, both of the links you posted lead to dead ends. Do you know of any working download sites for these?

I just uploaded the first one. Maybe it needs some time to settle in. Sailor Steve also had some problems with a different upload through Gamefront, but eventually was able to get it.

The second link is just a thread here on subsim. If you can't open it, but can read this one, then I don't know what's wrong. It works for both on my end. And I'm using Opera as a browser, so that might make things different also.

[EDIT]But I'll try to find a hosting place of my own that I can trust, in the near future.

Thanks, Pisces. The first link is working fine now. Downloaded the PDF and I am digesting it. Believe it has all I need to set up a calculator to do TMA.

I apologize for being unclear about the second link. I get to the SubSim thread just fine. It is the link to the AOB calculator that gives me a 403. I'm googling to see if there is anything similar out there. I'll post if I find anything interesting.

I would be very interested in anything you develop on this. I am at work but will look at the PDF when I get home

You can download it, and the formula document, now from here.

Thanks, Pisces! The slide rule is great! Now I won't have to try to teach the 11C to do the calculations. A nice piece of work. :yeah:

Did find a nice introductory piece on TMA from a DW support site. Someone may find it useful.

http://www.subguru.com/DW_missions/TMA.zip

TMA in SH4 is amazingly retarded to do, at least when I have tried anyway. The problem I have is that isn't dot stack and TMA ruler to work with in the same way as you do with DW. Then there is the fact that plotting relative motion on SH4's map is a pain in the...

There is an alternative however. If you search the forums, you'll find a nifty thing called MOBO. Get your sonar guy to track your target, as he calls the bearings, mark your subs position on the map (as instantly as possible is best).
Between marks, make a note of the mark number and the bearing called out and time called. I tend to be a bit sneaky and have my finger on the pause button so that I have all the time I need to mark the sub accurately + I have the time accurate to within seconds. After a few TMA legs, you can screenshot and pass the image to MOBO where there is a TMA tool. Don't forget to set the correct pixel to range scale (as I have done before).

Dunno if you still need this anymore, but I just open sourced my TMA calculator written in C++ (http://www.subsim.com/radioroom/showthread.php?t=240508).

The formula/equation is pretty straight forward.

First I set three unknown variables:
1. target distance at first bearing as "L1_distance"
2. target course as "crs"
3. target speed as "spd"

And I let ownship coordinate (m,n) initiate at (0,0). Y axis points to north (0 deg), and X axis points to east (90 deg). All angles start at Y axis and rotate in clockwise direction. So we can get:

1. target speed component on x axis "u" = spd * sin(crs)
2. target speed component on y axis "v" = spd * cos(crs)
3. target coordinate (a,b) at first bearing = L1_distance * sin(brg1), L1_distance * cos(brg1)
4. target coordinate (x,y) at each time = (a + u * t, b + v * t)
5. the vector pointing from ownship to target = (x-m, y-n)

By knowing the bearing of this vector, we can get the bearing vector equation:
(y-n)*sin(brg) = (x-m)*cos(brg)

Since we have three unknown variables to solve, in order to make sure the left hand side of the equation is really close to the right hand side, we can use the least square method:

Let formula f(t) = (y-n)*sin(brg) - (x-m)*cos(brg)
So we need to minimise the sum of squared f(t) for all bearing vectors. I used BFGS algorithm to solve this utilising C++ Dlib library.

With this, you can do TMA with any time interval, or moving submarine to any position.