Trajectory Approximation starting from multiple ones

How do I get to a single "nominal" trajectory giving multiples ones with associated different weights of goodness ?

Thks

Answer 1

[Raunak Gupta]

Hi,

There is a similar question which may be of relevance to you:

https://www.mathworks.com/matlabcentral/answers/482810-cubic-smoothing-sline-for-trajectory-approximation

Here for 'goodness' you may need to attach some other statistical metric instead of taking mean of all trajectory points.

[Mauro Magni]

Hi Mr Gupta,

for 'goodness' I mean that if the scalar p could be refer to different weights (so becomes a vector) respect to different trajectory hierarchy.

Is it possible ?

[Raunak Gupta]

Hi,

p is only valid for a single trajectory and it controls how the coefficient of the fitted cubic polynomial turns out (Based on smoothness and error parameter). So for adding wieght sense to p value for different trajectories will require to make the additional constraint of keeping the data-points same in each trajectory, otherwise if datapoints are different in each trajectories (which definitely will be) adding the polynomials together will not make sense and the process will end up having a set of polynomials for each trajectory. So, I suggest try making single set of data-points from multiple trajectories (This is mentioned in the last line of above answer) and then using Cubic Smoothing Spline for estimating the set of polynomials for successive pair of points.

You may try out with different p values for final data-point set to check if the generated path is upto the expectation or not.

[Mauro Magni]

Thank you for your guidance.