Sensor sample frequency

whatfreq.js

// Trying to find the formula to determine the frequency
// at which to sample GPS coordinates of a moving vehicle
// in order to have the maximum precision but not to store
// more data than necessary.

let precision = 1;                         // The precision of the GPS in meters
let max_speed = 180 / 3.6                  // 180km/h converted to m/s = 50m/s
let max_frequency = max_speed / precision;

// Nyquist–Shannon sampling theorem[1] tells us a
// sufficient sample-rate is 2B samples/second, or anything larger, thus:

let min_sample_rate = 2 * max_frequency;   // 100Hz



// As a second step, considering this data is for display
// on a digital map, figure out how you can further lower
// the requirements given screen size, pixel density and
// map zoom factor.

// From Bing Map Tiles System[2] we learn that
// the following forumla can be applied to get
// the map resolution (in px/m).

let resolution = (latitude, zoomLevel) => {
    let PI = Math.PI;
    let EARTH_CIRC = 6378137;
    return (Math.cos(latitude * PI/180) * 2 * PI * EARTH_CIRC) / (256 * Math.pow(2, zoomLevel));
} 

// This gives a ~0.5m/px resolution at my latitude and a zoom level of 18,
// which is actually more precise that a GPS resolution of 1m.
// We thus can't reduce the sample rate at that zoom level.

// Should we offer a much higher view, however,
// e.g. a zoom level of 10, which gives a resolution of ~150m/px
// then we could lower our sample rate accordingly:

let min_sample_rate_at_zoom_level_10 = 2 * (max_speed / 150); // 0.67Hz

// so just a little under 2 samples per second.

// So factoring all the variables:

let minFrequency = (maxSpeed /* m/s */, latitude, zoomLevel) {
    let PI = Math.PI;
    let EARTH_CIRC = 6378137;
    let GPS_PRECISION = 1; // 1m it's proabbly worse, actually.
    let resolution = (Math.cos(latitude * PI/180) * 2 * PI * EARTH_CIRC) / (256 * Math.pow(2, zoomLevel));
    let precision = Math.max(GPS_PRECISION, resolution);
    return 2 * (maxSpeed / precision);
}

// Still TODO: include pixel density in the equation.

// [1] https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem
// [2] https://msdn.microsoft.com/en-us/library/bb259689.aspx

/cc @rwaldron (does the above reasoning make sense?)