I think I can sort of see what's going on, we're trying to fit the data of some GPS position taken from a walk around the park or something similar, and fit it to some linear combination of basis of some "street functions" to minimize its two-norm, where the "street function" corresponding to each street for some point (x,y) is some measure of how far away from the street that point is.

For example, in the subproblem of only one-way streets that we can assume to be composed of one or more segments of straight lines per street, we take a simple street-function $\phi_i(x,y)$ corresponding to street i to be the norm of the projection of <x,y> onto that street. Furthermore we also add into the system some "smoothing-function" to ensure that the overall shape of the final path is doable, for example constraining the distance between successive points. Next, we solve the argmin of the norm equation for each point so that each point is now moved to some linear combination of the streets, and truncate all but the most significant street basis, and rerun until we get to some acceptable tolerance.

Maybe?