Determine vector components based on vector scaling and change of origin

Question

Ole Hermansen 2022-7-13

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https://ww2.mathworks.cn/matlabcentral/answers/1758715-determine-vector-components-based-on-vector-scaling-and-change-of-origin

回答： Ganapathi Subramanian R 2023-10-6

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.

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Answer 1

Ganapathi Subramanian R 2023-10-6

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此回答的直接链接

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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