diff --git a/engine.py b/engine.py
index 7fe3cfc..14b167a 100755
--- a/engine.py
+++ b/engine.py
@@ -5,6 +5,7 @@ import os
 import overpy
 import numpy as np
 import pandas as pd
+import scipy
 
 from pathlib import Path
 
@@ -66,7 +67,11 @@ def fetch_data(brand: str, cache: bool = True) -> list[tuple[float, float]]:
 
 
 def spherical_dist(pos1, pos2, r=6378137):
-    """Calculate sperical distances between two arrays of coordinates."""
+    """Calculate sperical distances between two arrays of coordinates.
+
+    Return value is the same unit as `r`.
+    `r` defaults to the radius of the earth, in meters.
+    """
     pos1 = pos1 * np.pi / 180
     pos2 = pos2 * np.pi / 180
 
@@ -77,6 +82,7 @@ def spherical_dist(pos1, pos2, r=6378137):
     return r * np.arccos(cos_lat_d - cos_lat1 * cos_lat2 * (1 - cos_lon_d))
 
 
+# (lat, lon), dist
 StationT = tuple[tuple[float, float], float]
 
 
@@ -93,9 +99,7 @@ def trilaterate(stations: list[StationT]) -> tuple[float, float]:
     Each station is of the format ((lat, lon), distance).
     """
 
-    # TODO scipy optimise using trilat_error
-
-    return (0., 0.)
+    return scipy.optimize.fmin(lambda pos: trilat_error(stations, pos), (0., 0.))
 
 
 def encode(location: tuple[float, float]) -> EncodedLocation:
@@ -113,8 +117,6 @@ def encode(location: tuple[float, float]) -> EncodedLocation:
     distances = distances.sort_values()
 
     closest = distances.head(LOCS_COUNT)
-    closest_dist = list(closest.values)
-    closest_ind  = list(closest.index)
 
     result: EncodedLocation = []
     for v, i in zip(closest.values, closest.index):
@@ -129,38 +131,34 @@ def encode(location: tuple[float, float]) -> EncodedLocation:
 def decode(location: EncodedLocation) -> tuple[float, float]:
     """Decode into a location."""
 
-    #form the distances matrix
-    greggs = np.array(fetch_data("greggs"))
+    # form the distances matrix
+    greggs_raw = fetch_data("greggs")
+    greggs = np.array(greggs_raw)
     repeat_rows = np.tile(greggs, (len(greggs), 1, 1))
     repeat_cols = np.transpose(repeat_rows, (1, 0, 2))
     dist_matrix = spherical_dist(repeat_rows, repeat_cols)
 
-    #split the distances matrix into a list of series, which allows us to sort each row
+    # split the distances matrix into a list of series, which allows us to sort each row
     dist_series_list = []
     for i in dist_matrix:
         dist_series_list.append(pd.Series(i).sort_values().head(len(location[0][1])+1)[1:])
 
-    #part 1: find the ID of each gregg's
+    # part 1: find the ID of each gregg's
     closest_greggs = []
-    for i in range(len(location)):
-        dists = location[i][1]
+    for loc in location:
+        dists = loc[1]
+
+        errors = [sum((j - dists) ** 2) for j in dist_series_list]
 
-        errors = []
-        for j in dist_series_list:
-                errors.append(sum((j-dists)**2))
         minerr = min(errors)
         if minerr > 1:
             print(f"warning: high error value of {minerr}")
 
-        closest_greggs = [errors.index(min(errors))]
+        closest_greggs.append(errors.index(min(errors)))
 
-
-
-
-    #part 2: trilaterate
-
-    # Stub
-    return (0.091659, 52.210796)
+    # part 2: trilaterate
+    stations: list[StationT] = [(greggs_raw[g], location[i][0]) for i, g in enumerate(closest_greggs)]
+    return trilaterate(stations)
 
 
 def format_dist(dist: float) -> str:
@@ -188,12 +186,17 @@ def parse_location(location: str) -> EncodedLocation:
 
 def main():
     """Testing."""
-    #print("Running query...")
-    #greggs = fetch_data("greggs")
-    #print(f"Query done - got {len(greggs)} Greggs!")
+    coords = (52.210796, 0.091659)
+    print("Original:", coords)
 
-    outcome = encode((52.210796, 0.091659))
-    decode(outcome)
+    outcome = encode(coords)
+    print("Encoded:", outcome)
+
+    decoded = decode(outcome)
+    print("Decoded:", decoded)
+
+    error = spherical_dist(np.array(coords), np.array(decoded))
+    print(f"Error: {error:.10f}m")
 
 
 if __name__ == "__main__":
diff --git a/requirements.txt b/requirements.txt
index 6a824c1..b6e53de 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -2,3 +2,4 @@ overpy
 django
 numpy
 pandas
+scipy