Determine vector components based on vector scaling and change of origin

Consider a known vector k and an unknown vector L. L is positioned between vector k and an unknown fixed point in space. The vector L is comprised of two components, but is subject to change over time, hence a scaling factor delta(t).

I would like to determine the vector components of L, such that w can be determined.

I am able to translate and rotate the coordinate origin and sample the data of x(t), y(t), and theta(t), while also sampling the change of vector L collected in delta(t).

I am figuring that a least-square optimisation is needed to determine L's components, where an error based on the sampling data is minimised. However, so far I have been unable to setup the scheme.

Thanks.

Answer 1

[Ganapathi Subramanian R]

Hi Ole,

I understand that you are working on vector components and would like to know the implementation of least-square optimization. Please refer the below documentation to learn more about least square optimization algorithms and the solvers present in Optimization Toolbox to implement it.

https://www.mathworks.com/help/optim/ug/least-squares-model-fitting-algorithms.html

Kindly refer the below example for further information on how to utilize the solvers in Optimization Toolbox.

https://www.mathworks.com/help/optim/ug/nonlinear-data-fitting-example.html