Convert Latitude and Longitude to point in 3D space

I’ve reformatted the code that was previously mentioned here, but more importantly you have left out some of the equations mentioned in the link provided by Niklas R

def LLHtoECEF(lat, lon, alt):
    # see http://www.mathworks.de/help/toolbox/aeroblks/llatoecefposition.html

    rad = np.float64(6378137.0)        # Radius of the Earth (in meters)
    f = np.float64(1.0/298.257223563)  # Flattening factor WGS84 Model
    cosLat = np.cos(lat)
    sinLat = np.sin(lat)
    FF     = (1.0-f)**2
    C      = 1/np.sqrt(cosLat**2 + FF * sinLat**2)
    S      = C * FF

    x = (rad * C + alt)*cosLat * np.cos(lon)
    y = (rad * C + alt)*cosLat * np.sin(lon)
    z = (rad * S + alt)*sinLat

    return (x, y, z)

Comparison output: finding ECEF for Los Angeles, CA (34.0522, -118.40806, 0 elevation)
My code:
X = -2516715.36114 meters or -2516.715 km
Y = -4653003.08089 meters or -4653.003 km
Z = 3551245.35929 meters or 3551.245 km

Your Code:
X = -2514072.72181 meters or -2514.072 km
Y = -4648117.26458 meters or -4648.117 km
Z = 3571424.90261 meters or 3571.424 km

Although in your earth rotation environment your function will produce right geographic region for display, it will NOT give the right ECEF equivalent coordinates. As you can see some of the parameters vary by as much as 20 KM which is rather a large error.

Flattening factor, f depends on the model you assume for your conversion. Typical, model is WGS 84; however, there are other models.

Personally, I like to use this link to Naval Postgraduate School for sanity checks on my conversions.

Leave a Comment