estimate the position of a $$x in mathbb {R} ^ 2$$ knowing its distance to four beacons $$v_i$$, $$i in {1, .., 4 }$$, by the least squares, is finding the least squares solution to $$y = Ax$$, or $$y in mathbb {R} ^ 4$$ is the vector of distances between $$x$$ and $$k_i$$ and $$A in mathbb {R} ^ {4×2}$$ is the matrix with the line vectors $$a_i ^ T = frac {v_i ^ T} { | {v_i} |}$$.
I have trouble understanding where the wording comes from $$y = Ax$$ the problem comes from intuitively. What projections under the hood correct this formulation? What's going on geometrically?