How is the calibration algorithm working?

[TebbeUbben]

Hello,

can anyone explain the mathematical process of the calibration algorithm to me?

[tzachi-dar]

At a very high level, for each calibration there is a bg and raw value. We try to find the parameters of a straight line that will be as close as possible to this points.

In a little bit more details, each point gets a weight that is based on a few factors, such as how high it is, or how fast bg was changing.

[TebbeUbben]

I would like to know exactly how a calibration is calculated. I'm pretty young, so I'm curious about such things. Would be pretty nice if you could answer my question :)

[tzachi-dar]

Here is how slope and intercept are being calculated:
private static void calculate_w_l_s(boolean extended) {
if (Sensor.isActive()) {
double l = 0;
double m = 0;
double n = 0;
double p = 0;
double q = 0;
double w;

        final SlopeParameters sParams = getSlopeParameters();

        List<Calibration> calibrations = allForSensorInLastFourDays(); //5 days was a bit much, dropped this to 4

        if (calibrations == null) {
            Log.e(TAG, "Somehow ended up with null calibration list!");
            Home.toaststatic("Somehow ended up with null calibration list!");
            return;
        }

        // less than 5 calibrations in last 4 days? cast the net wider if in extended mode
        final int ccount = calibrations.size();
        if ((ccount < 5) && extended) {
            calibrations = allForSensorLimited(5);
            if (calibrations.size() > ccount) {
                Home.toaststaticnext("Calibrated using data beyond last 4 days");
            }
        }

        if (calibrations.size() <= 1) {
            Calibration calibration = Calibration.last();
            calibration.slope = 1;
            calibration.intercept = calibration.bg - (calibration.raw_value * calibration.slope);
            calibration.save();
            CalibrationRequest.createOffset(calibration.bg, 25);
            newFingerStickData();
        } else {
            for (Calibration calibration : calibrations) {
                w = calibration.calculateWeight();
                l += (w);
                m += (w * calibration.estimate_raw_at_time_of_calibration);
                n += (w * calibration.estimate_raw_at_time_of_calibration * calibration.estimate_raw_at_time_of_calibration);
                p += (w * calibration.bg);
                q += (w * calibration.estimate_raw_at_time_of_calibration * calibration.bg);
            }

            Calibration last_calibration = Calibration.last();
            w = (last_calibration.calculateWeight() * (calibrations.size() * 0.14));
            l += (w);
            m += (w * last_calibration.estimate_raw_at_time_of_calibration);
            n += (w * last_calibration.estimate_raw_at_time_of_calibration * last_calibration.estimate_raw_at_time_of_calibration);
            p += (w * last_calibration.bg);
            q += (w * last_calibration.estimate_raw_at_time_of_calibration * last_calibration.bg);

            double d = (l * n) - (m * m);
            Calibration calibration = Calibration.last();
            calibration.intercept = ((n * p) - (m * q)) / d;
            calibration.slope = ((l * q) - (m * p)) / d;
            if ((calibrations.size() == 2 && calibration.slope < sParams.getLowSlope1()) || (calibration.slope < sParams.getLowSlope2())) { // I have not seen a case where a value below 7.5 proved to be accurate but we should keep an eye on this
                calibration.slope = calibration.slopeOOBHandler(0);
                if (calibrations.size() > 2) {
                    calibration.possible_bad = true;
                }
                calibration.intercept = calibration.bg - (calibration.estimate_raw_at_time_of_calibration * calibration.slope);
                CalibrationRequest.createOffset(calibration.bg, 25);
            }
            if ((calibrations.size() == 2 && calibration.slope > sParams.getHighSlope1()) || (calibration.slope > sParams.getHighSlope2())) {
                calibration.slope = calibration.slopeOOBHandler(1);
                if (calibrations.size() > 2) {
                    calibration.possible_bad = true;
                }
                calibration.intercept = calibration.bg - (calibration.estimate_raw_at_time_of_calibration * calibration.slope);
                CalibrationRequest.createOffset(calibration.bg, 25);
            }
            Log.d(TAG, "Calculated Calibration Slope: " + calibration.slope);
            Log.d(TAG, "Calculated Calibration intercept: " + calibration.intercept);

            if ((calibration.slope == 0) && (calibration.intercept == 0)) {
                calibration.sensor_confidence = 0;
                calibration.slope_confidence = 0;
                Home.toaststaticnext("Got invalid zero slope calibration!");
                calibration.save(); // Save nulled record, lastValid should protect from bad calibrations
                newFingerStickData();

            } else {
                calibration.save();
                newFingerStickData();
            }
        }
    } else {
        Log.d(TAG, "NO Current active sensor found!!");
    }
}

you can see more in the file:
https://github.com/NightscoutFoundation/xDrip/blob/master/app/src/main/java/com/eveningoutpost/dexdrip/Models/Calibration.java

[TebbeUbben]

Okay, and what's the meaning and purpose of the variables you mentioned above?