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I found this question linked on another question. I actually did academic research on this kind of problem. Please check my answer "Least square root" fitting? A fitting method with multiple minima for more details.

whuber's Hough transform based approach is a very good solution for simple scenarios as the one you gave. I worked on scenarios with more complex data, such as this:

My co-authors and I denoted this a "data association" problem. When you try to solve it, the main problem is typically combinatorial due to the exponential amount of possible data combinations.

We have a publication "Overlapping Mixtures of Gaussian Processes for the data association problem" where we approached the general problem of N curves with an iterative technique, giving very good results. You can find Matlab code linked in the paper (sorry, no R nor Python).

I have another paper where we relaxed the problem to obtain a convex optimization problem, but it has not been accepted for publication yet. It is specific for 2 curves, so it would work perfectly on your data. Let me know if you are interested.

I found this question linked on another question. I actually did academic research on this kind of problem. Please check my answer "Least square root" fitting? A fitting method with multiple minima for more details.

whuber's Hough transform based approach is a very good solution for simple scenarios as the one you gave. I worked on scenarios with more complex data, such as this:

My co-authors and I denoted this a "data association" problem. When you try to solve it, the main problem is typically combinatorial due to the exponential amount of possible data combinations.

We have a publication "Overlapping Mixtures of Gaussian Processes for the data association problem" where we approached the general problem of N curves with an iterative technique, giving very good results. You can find Matlab code linked in the paper.

[Update] A Python implementation of the OMGP technique can be found in the GPClust library.

I have another paper where we relaxed the problem to obtain a convex optimization problem, but it has not been accepted for publication yet. It is specific for 2 curves, so it would work perfectly on your data. Let me know if you are interested.

I found this question linked on another question. I actually did academic research on this kind of problem. Please check my answer "Least square root" fitting? A fitting method with multiple minima for more details.

whuber's Hough transform based approach is a very good solution for simple scenarios as the one you gave. I worked on scenarios with more complex data, such as this:

My co-authors and I denoted this a "data association" problem. When you try to solve it, the main problem is typically combinatorial due to the exponential amount of possible data combinations.

We have a publication "Overlapping Mixtures of Gaussian Processes for the data association problem" where we approached the general problem of N curves with an iterative technique, giving very good results. You can find Matlab code linked in the paper (sorry, no R nor Python).

I have another paper where we relaxed the problem to obtain a convex optimization problem, but it has not been accepted for publication yet. It is specific for 2 curves, so it would work perfectly on your data. Let me know if you are interested.

I found this question linked on another question. I actually did academic research on this kind of problem. Please check my answer "Least square root" fitting? A fitting method with multiple minima for more details.

whuber's Hough transform based approach is a very good solution for simple scenarios as the one you gave. I worked on scenarios with more complex data, such as this:

My co-authors and I denoted this a "data association" problem. When you try to solve it, the main problem is typically combinatorial due to the exponential amount of possible data combinations.

We have a publication "Overlapping Mixtures of Gaussian Processes for the data association problem" where we approached the general problem of N curves with an iterative technique, giving very good results. You can find Matlab code linked in the paper (sorry, no R nor Python).

I have another paper where we relaxed the problem to obtain a convex optimization problem, but it has not been accepted for publication yet. It is specific for 2 curves, so it would work perfectly on your data. Let me know if you are interested.

I found this question linked on another question. I actually did academic research on this kind of problem. Please check my answer "Least square root" fitting? A fitting method with multiple minima for more details.

whuber's Hough transform based approach is a very good solution for simple scenarios as the one you gave. I worked on scenarios with more complex data, such as this:

My co-authors and I denoted this a "data association" problem. When you try to solve it, the main problem is typically combinatorial due to the exponential amount of possible data combinations.

We have a publication "Overlapping Mixtures of Gaussian Processes for the data association problem" where we approached the general problem of N curves with an iterative technique, giving very good results. You can find Matlab code linked in the paper (sorry, no R nor Python).

I have another paper where we relaxed the problem to obtain a convex optimization problem, but it has not been accepted for publication yet. It is specific for 2 curves, so it would work perfectly on your data. Let me know if you are interested.

I found this question linked on another question. I actually did academic research on this kind of problem. Please check my answer "Least square root" fitting? A fitting method with multiple minima for more details.

whuber's Hough transform based approach is a very good solution for simple scenarios as the one you gave. I worked on scenarios with more complex data, such as this:

My co-authors and I denoted this a "data association" problem. When you try to solve it, the main problem is typically combinatorial due to the exponential amount of possible data combinations.

We have a publication "Overlapping Mixtures of Gaussian Processes for the data association problem" where we approached the general problem of N curves with an iterative technique, giving very good results. You can find Matlab code linked in the paper (sorry, no R nor Python).

I have another paper where we relaxed the problem to obtain a convex optimization problem, but it has not been accepted for publication yet. It is specific for 2 curves, so it would work perfectly on your data. Let me know if you are interested.