trilateration method w/ distance

distance.py

# All of these should be installed with pip:
from geopy.distance import great_circle
import pandas as pd
import numpy as np
import statsmodels.formula.api as smf
import scipy

# Location of each WAP and distance to each (RSSI should be used to calculate the approximate distances)
# This is all just sample data, and should be replaced with actual data.
locations = {
    'latitude': [40.208606, 40.208760, 40.208605, 40.208432, 40.208343, 40.208329], # each latitude value
    'longitude': [-74.040819, -74.041015, -74.040785, -74.040731, -74.041041, -74.040804], # each longitude value
    'distance': [38.45, 25.61, 41.34, 51.13, 38.04, 52.33] # each distance from device to each lat,long value
}
locations_df = pd.DataFrame(data=locations)

# haversine distance formula
def haversine(lon1, lat1, lon2, lat2):
    lon1, lat1, lon2, lat2 = map(np.radians, [lon1, lat1, lon2, lat2])

    dlon = lon2 - lon1
    dlat = lat2 - lat1

    a = np.sin(dlat/2.0)**2 + np.cos(lat1) * np.cos(lat2) * np.sin(dlon/2.0)**2

    c = 2 * np.arcsin(np.sqrt(a))
    km = 6367 * c
    m = km*1000
    return m

# mean squared error 
def mse(x, locations, distances):
    mse = 0.0
    for location, distance in zip(locations, distances):
        distance_calculated = haversine(x[0], x[1], location[0], location[1])
    mse += np.power(distance_calculated - distance, 2.0)
    return mse / len(locations)

loc = []
for lat, lon in zip(locations_df['latitude'], locations_df['longitude']):
    loc.append([lat,lon])

dis = locations_df['distance']

# calculate the coordinate estimate
result = scipy.optimize.minimize(
    mse,
    [np.mean(locations_df['latitude']),np.mean(locations_df['longitude'])],
    args=(loc,dis),
    method='L-BFGS-B',
    options={
        'ftol':1e-02,
        'maxiter':1000
    }
)
print(result.x)