How do I align two 3D curves that are displaced in time?

I have two 3D curves (trajectories) that are nearly identical. One curve is a subset of the other, that is, its end point coordinates are within the longer curve (I hope). The time data does not align between the two curves. How do I adjust the two curves so they overlay, so that I can update the times to match? I am dealing with latitude, longitude and altitude here.

If either endpoint of the shorter curve ends up extending outside the longer curve, I need to account for that too.

[dpb]

Without the data to play with, unlikely anybody can do much towards your specific problem...when descriptions include things like "I hope", canned answers aren't likely to help.

[Kurt]

OK, skip the hope thing. I'm dealing with two ephemeris tables with similar tracks. My first reaction is to merge the two tables and sort them by lat, long and altitude and look for adjacent rows. I will need to look above and below each short track data row to see which long track row is closer to it. This is a rather time-consuming approach. Is there a curve-fitting function that will do all this for me?

I'm not at liberty to display the data, which is rather large in any case.

[dpb]

Surely you can add some obfuscation that would make it undistinguishable but show the issues? And, it wouldn't need to be extremely long, but it's a lot to ask folks to also have to try to manufacture something to look at as well...

[Adam Danz]

If each dimension independently varies, you could use xcorr or xcorr2 to compute the cross correlation.

convn could be used for a 3D version of cross correlation.

[dpb]

Those would be my best guess of starting points as well, Adam, but I hate to do anything w/o first looking at the data...one can make gross blunders by assuming a result means something that it may not at all when looked at...

[Kurt]

I need to slide the shorter curve left or right until it overlays a section of the longer curve as a best fit. Then I extract that portion of the longer curve and update its times to match the shorter curve. I got it to work using the sort process I described. but it's a bit clunky.

This whole exercise is for the purpose of displaying simulated and actual data simultaneously, overlayed. The simulated and actual times have nothing in common.

[Umar]

Hi @Kurt,

I would use a method like cross-correlation to find the best alignment between the two curves.Once they are aligned, update the time data of the longer curve to match the time scale of the shorter curve.If the shorter curve extends beyond the longer one, trim or pad the curves accordingly to ensure they align properly. Afterwards, plot the synchronized curves to display simulated and actual data simultaneously. Hope this helps, please let me know if you have any further questions.

[Kurt]

Thanks. This sounds like the best approach. I wish I could provide more specifics, but yanno...

[dpb]

The Q? that occurred to me later is whether the two are simply different recordings/measurements of the same data but taken asynchronously, or are they two separate data streams that should be correlated to each other? If the former, then simply retime may be the easy route. I initially was thinking of the latter which would be the alternate of trying to actually align two independent datasets...

[Kurt]

The "truth" data is a simulated, ideal model. The "observations" (the smaller curve) are the actual observed track data. We need to overlay the two and measure the dispersions in order to determine how accurate our measurements are. So yes, they are very similar, but the question is just "how" similar they are statistically.

[Star Strider]

If you expect the two to be linearly related (that they are inherently nonlinear is not important), ignore the times (or adjust the times and sampling intervals to start at the same value and have the same sampling frequency) and then do a linear fit using fitlm or regress or whatever linear or nonlinear regression function is appropriate, with overlapping ranges of the independent variables and equal numbers of observations. The parameter values and related statistics should give you an idea of how (and how closely) they are related.

Without the data (or a representative data set), this is simply a guess as to an appropriate approach.

[dpb]

"Without the data (or a representative data set), this is simply a guess..."

+1/0