Open sourced automatic TMA calculator

[ljqcn101]

Thanks Pisces for the analysis on 3-bearing AOB method!

I've just released v0.3 and added probability calculation for positional/course error distributions, assuming a random inaccuracy of bearing input within a range of -0.5 to 0.5 deg. The probability is computed over 1000 iterations.

Since this tool uses least squares optimisation to interpolate an solution, I can keep the original time interval and take one more bearing to further reduce the impact from bearing inaccuracies.

An example of recording a 5 deg/min bearing rate target when stationary:

time t1 = 0 (sec)
ownship heading at t1 (deg): 0

target bearing at t1 (deg): 350

ownship straight direction from last position = 0 (deg)
ownship straight distance from last position = 0 (meter)
*******************************
time t2 (sec): 120

ownship heading at t2: 0

target bearing at t2 (deg): 0

ownship straight direction from last position (deg): 0

ownship straight distance from last position (meter): 0

*******************************
time t3 (sec): 240

ownship heading at t3: 0

target bearing at t3 (deg): 10

ownship straight direction from last position (deg): 0

ownship straight distance from last position (meter): 0


target course: 90deg

probability of target course error within 5deg: 29.5868 %
probability of target course error within 10deg: 54.7107
probability of target course error within 20deg: 89.9174

3 bearings when stationary can only get course solution.

*******************************
time t4 (sec): 360

ownship heading at t4: 0

target bearing at t4 (deg): 19.4

ownship straight direction from last position (deg): 0

ownship straight distance from last position (meter): 0


target course: 89.78deg

probability of target course error within 5deg: 55.1948 %
probability of target course error within 10deg: 87.6623
probability of target course error within 20deg: 100 %

4 bearings when stationary can only get course solution.

*******************************
time t5 (sec): 480

ownship heading at t5: 0

target bearing at t5 (deg): 27.8

ownship straight direction from last position (deg): 0

ownship straight distance from last position (meter): 0


target course: 89.64deg

probability of target course error within 5deg: 85.7143 %
probability of target course error within 10deg: 100 %
probability of target course error within 20deg: 100 %

5 bearings when stationary can only get course solution.

*******************************
time t6 (sec): 600

ownship heading at t6: 0

target bearing at t6 (deg): 35.1

ownship straight direction from last position (deg): 0

ownship straight distance from last position (meter): 0


target course: 89.71deg

probability of target course error within 5deg: 100 %
probability of target course error within 10deg: 100 %
probability of target course error within 20deg: 100 %

6 bearings when stationary can only get course solution.

As you can see the probability of target course error within 5 deg almost doubled by adding the 4th bearing into interpolation. Adding a 5th bearing can even improve it to over 85%.

But looks like simply increasing the time interval virtually achieved the same result:

time t1 = 0 (sec)
ownship heading at t1 (deg): 0

target bearing at t1 (deg): 350

ownship straight direction from last position = 0 (deg)
ownship straight distance from last position = 0 (meter)
*******************************
time t2 (sec): 240

ownship heading at t2: 0

target bearing at t2 (deg): 10

ownship straight direction from last position (deg): 0

ownship straight distance from last position (meter): 0

*******************************
time t3 (sec): 480

ownship heading at t3: 0

target bearing at t3 (deg): 27.8

ownship straight direction from last position (deg): 0

ownship straight distance from last position (meter): 0


target course: 89.6deg

probability of target course error within 5deg: 85.6198 %
probability of target course error within 10deg: 100 %
probability of target course error within 20deg: 100 %

3 bearings when stationary can only get course solution.

And I've also updated the example in the original post. Since the bearing rate is lower and the target is pretty far away, the solution is more error prone to bearing inaccuracies.

[geosub1978]

Hi!
Can you please tell me which Windows version did you use? My copy refuses to be installed an dI guess it has to do with that.

[ljqcn101]

Originally Posted by geosub1978

Hi!
Can you please tell me which Windows version did you use? My copy refuses to be installed an dI guess it has to do with that.

I tested on win8.1 and win10. Both are x64 systems. Make sure you have Visual C++ Redistributable for Visual Studio 2015 x64 installed.

[geosub1978]

I am currently working on a method based on radial speed rule
(Bearing Rate=(Target Speed*sinAOB-Ownspeed*sin(LeadingAngle))/Range)

By taking into consideration that the new AOB=PREVIOUSAOB+BEARINGCHANGE

Then if you apply the Rule of Sins for three individual bearing shootings and counting manualy the bearing rate, you can have a final equation with an unkown target speed or sinAOB. The maths are too long for the moment and require patience!

[ljqcn101]

Originally Posted by geosub1978

I am currently working on a method based on radial speed rule
(Bearing Rate=(Target Speed*sinAOB-Ownspeed*sin(LeadingAngle))/Range)

By taking into consideration that the new AOB=PREVIOUSAOB+BEARINGCHANGE

Then if you apply the Rule of Sins for three individual bearing shootings and counting manualy the bearing rate, you can have a final equation with an unkown target speed or sinAOB. The maths are too long for the moment and require patience!

Great. But be careful when computing with Ownspeed, since you need a course change in order to get a single solution, if you keep a constant ownspeed.

For computational convenience the boat is always assumed to be able to instantaneously change speed or course at each observation point, but in reality it cannot. And any departure from these idealisations introduce errors. That's why I use distance and direction between two observation points for computation.