Trilateration different approaches and issues
Although there exists several posts about (multi)lateration, i would like to summarize some approaches and present some issues/questions to better clarify the approach.
It seems that are two ways to detect the target location; using geometric/analytic approach (solving directly the equations with some trick) and fitting approach converting from non-linear to linear system.
With respect to the first one i would like to ask few questions.
The same solution can be extracted using the second approach Ax=b and latter recovering x = A^-1b or using MLS (x = A^TA)^-1 A^T b.
Please see http://www3.nd.edu/~cpoellab/teaching/cse40815/Chapter10.pdf
What about the case when the three circles have no intersection. It seems that the second approach still finds a solution. Is this normal? How can be explained?
What about the first approach when the range measurements are noisy. Does it find an approximate solution or it fails?
Considering the 3D, it seems that it needs at least 4 anchors to provide a unique solution. However, considering 3 anchors it can provide 2 solutions. I am asking if anyone of u guys can provide such equations to find the two solutions. This can be good even we have two solutions we may discard one by checking the values if they agree with our scenario. Eg, the GPS case where we pick the solution located in the earth. Instead the second approach of LMS would provide always one solution, wrong one.
Do u know any existing library C/C++ which would implement some of this techniques and maybe some more complex fitting functions such as non-linear etc.
Thank you Regards
链接地址: http://www.djcxy.com/p/84950.html上一篇: 二维三角测量