trilateration.jl

using Flux.Tracker
using Flux.Tracker: update!
using ProgressMeter

euclidean_distance(p1, p2) = sqrt((p1[1] - p2[1]) ^ 2 + (p1[2] - p2[2]) ^ 2)

squared_error(expected, output) = (expected - output) ^ 2

function trilateration_error(r1, r2, r3, expected_distances, prediction)
    prediction_r1 = euclidean_distance(prediction, r1)
    prediction_r2 = euclidean_distance(prediction, r2)
    prediction_r3 = euclidean_distance(prediction, r3)
    error_r1 = squared_error(expected_distances[1], prediction_r1)
    error_r2 = squared_error(expected_distances[2], prediction_r2)
    error_r3 = squared_error(expected_distances[3], prediction_r3)
    return error_r1 + error_r2 + error_r3
end

d_trilateration_error(r1, r2, r3, expected_distances, prediction) = Tracker.gradient(trilateration_error, r1, r2, r3, expected_distances, prediction)[5]

ref1 = param([0, 20])
ref2 = param([-20, 0])
ref3 = param([20, 0])
g = param([5, 10])
pred = param([1, 1])

expected_distances = [euclidean_distance(ref1, g), euclidean_distance(ref2, g), euclidean_distance(ref3, g)]

for i in 1:5000
    grad = d_trilateration_error(ref1, ref2, ref3, expected_distances, pred)
    update!(pred, -0.1 * grad)
end

println(pred)