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+#!/usr/bin/nickle -f
+/*
+ * Pressure Sensor Model, version 1.1
+ *
+ * written by Holly Grimes
+ *
+ * Uses the International Standard Atmosphere as described in
+ * "A Quick Derivation relating altitude to air pressure" (version 1.03)
+ * from the Portland State Aerospace Society, except that the atmosphere
+ * is divided into layers with each layer having a different lapse rate.
+ *
+ * Lapse rate data for each layer was obtained from Wikipedia on Sept. 1, 2007
+ * at site <http://en.wikipedia.org/wiki/International_Standard_Atmosphere
+ *
+ * Height measurements use the local tangent plane. The postive z-direction is up.
+ *
+ * All measurements are given in SI units (Kelvin, Pascal, meter, meters/second^2).
+ * The lapse rate is given in Kelvin/meter, the gas constant for air is given
+ * in Joules/(kilogram-Kelvin).
+ */
+
+const real GRAVITATIONAL_ACCELERATION = -9.80665;
+const real AIR_GAS_CONSTANT = 287.053;
+const int NUMBER_OF_LAYERS = 7;
+const real MAXIMUM_ALTITUDE = 84852;
+const real MINIMUM_PRESSURE = 0.3734;
+const real LAYER0_BASE_TEMPERATURE = 288.15;
+const real LAYER0_BASE_PRESSURE = 101325;
+
+/* lapse rate and base altitude for each layer in the atmosphere */
+const real[NUMBER_OF_LAYERS] lapse_rate = {
+ -0.0065, 0.0, 0.001, 0.0028, 0.0, -0.0028, -0.002
+};
+const int[NUMBER_OF_LAYERS] base_altitude = {
+ 0, 11000, 20000, 32000, 47000, 51000, 71000
+};
+
+
+/* outputs atmospheric pressure associated with the given altitude. altitudes
+ are measured with respect to the mean sea level */
+real altitude_to_pressure(real altitude) {
+
+ real base_temperature = LAYER0_BASE_TEMPERATURE;
+ real base_pressure = LAYER0_BASE_PRESSURE;
+
+ real pressure;
+ real base; /* base for function to determine pressure */
+ real exponent; /* exponent for function to determine pressure */
+ int layer_number; /* identifies layer in the atmosphere */
+ int delta_z; /* difference between two altitudes */
+
+ if (altitude > MAXIMUM_ALTITUDE) /* FIX ME: use sensor data to improve model */
+ return 0;
+
+ /* calculate the base temperature and pressure for the atmospheric layer
+ associated with the inputted altitude */
+ for(layer_number = 0; layer_number < NUMBER_OF_LAYERS - 1 && altitude > base_altitude[layer_number + 1]; layer_number++) {
+ delta_z = base_altitude[layer_number + 1] - base_altitude[layer_number];
+ if (lapse_rate[layer_number] == 0.0) {
+ exponent = GRAVITATIONAL_ACCELERATION * delta_z
+ / AIR_GAS_CONSTANT / base_temperature;
+ base_pressure *= exp(exponent);
+ }
+ else {
+ base = (lapse_rate[layer_number] * delta_z / base_temperature) + 1.0;
+ exponent = GRAVITATIONAL_ACCELERATION /
+ (AIR_GAS_CONSTANT * lapse_rate[layer_number]);
+ base_pressure *= pow(base, exponent);
+ }
+ base_temperature += delta_z * lapse_rate[layer_number];
+ }
+
+ /* calculate the pressure at the inputted altitude */
+ delta_z = altitude - base_altitude[layer_number];
+ if (lapse_rate[layer_number] == 0.0) {
+ exponent = GRAVITATIONAL_ACCELERATION * delta_z
+ / AIR_GAS_CONSTANT / base_temperature;
+ pressure = base_pressure * exp(exponent);
+ }
+ else {
+ base = (lapse_rate[layer_number] * delta_z / base_temperature) + 1.0;
+ exponent = GRAVITATIONAL_ACCELERATION /
+ (AIR_GAS_CONSTANT * lapse_rate[layer_number]);
+ pressure = base_pressure * pow(base, exponent);
+ }
+
+ return pressure;
+}
+
+
+/* outputs the altitude associated with the given pressure. the altitude
+ returned is measured with respect to the mean sea level */
+real pressure_to_altitude(real pressure) {
+
+ real next_base_temperature = LAYER0_BASE_TEMPERATURE;
+ real next_base_pressure = LAYER0_BASE_PRESSURE;
+
+ real altitude;
+ real base_pressure;
+ real base_temperature;
+ real base; /* base for function to determine base pressure of next layer */
+ real exponent; /* exponent for function to determine base pressure
+ of next layer */
+ real coefficient;
+ int layer_number; /* identifies layer in the atmosphere */
+ int delta_z; /* difference between two altitudes */
+
+ if (pressure < 0) /* illegal pressure */
+ return -1;
+ if (pressure < MINIMUM_PRESSURE) /* FIX ME: use sensor data to improve model */
+ return MAXIMUM_ALTITUDE;
+
+ /* calculate the base temperature and pressure for the atmospheric layer
+ associated with the inputted pressure. */
+ layer_number = -1;
+ do {
+ layer_number++;
+ base_pressure = next_base_pressure;
+ base_temperature = next_base_temperature;
+ delta_z = base_altitude[layer_number + 1] - base_altitude[layer_number];
+ if (lapse_rate[layer_number] == 0.0) {
+ exponent = GRAVITATIONAL_ACCELERATION * delta_z
+ / AIR_GAS_CONSTANT / base_temperature;
+ next_base_pressure *= exp(exponent);
+ }
+ else {
+ base = (lapse_rate[layer_number] * delta_z / base_temperature) + 1.0;
+ exponent = GRAVITATIONAL_ACCELERATION /
+ (AIR_GAS_CONSTANT * lapse_rate[layer_number]);
+ next_base_pressure *= pow(base, exponent);
+ }
+ next_base_temperature += delta_z * lapse_rate[layer_number];
+ }
+ while(layer_number < NUMBER_OF_LAYERS - 1 && pressure < next_base_pressure);
+
+ /* calculate the altitude associated with the inputted pressure */
+ if (lapse_rate[layer_number] == 0.0) {
+ coefficient = (AIR_GAS_CONSTANT / GRAVITATIONAL_ACCELERATION)
+ * base_temperature;
+ altitude = base_altitude[layer_number]
+ + coefficient * log(pressure / base_pressure);
+ }
+ else {
+ base = pressure / base_pressure;
+ exponent = AIR_GAS_CONSTANT * lapse_rate[layer_number]
+ / GRAVITATIONAL_ACCELERATION;
+ coefficient = base_temperature / lapse_rate[layer_number];
+ altitude = base_altitude[layer_number]
+ + coefficient * (pow(base, exponent) - 1);
+ }
+
+ return altitude;
+}
+
+real feet_to_meters(real feet)
+{
+ return feet * (12 * 2.54 / 100);
+}
+
+real meters_to_feet(real meters)
+{
+ return meters / (12 * 2.54 / 100);
+}
+
+/*
+ * Values for our MP3H6115A pressure sensor
+ *
+ * From the data sheet:
+ *
+ * Pressure range: 15-115 kPa
+ * Voltage at 115kPa: 2.82
+ * Output scale: 27mV/kPa
+ *
+ *
+ * 27 mV/kPa * 2047 / 3300 counts/mV = 16.75 counts/kPa
+ * 2.82V * 2047 / 3.3 counts/V = 1749 counts/115 kPa
+ */
+
+real counts_per_kPa = 27 * 2047 / 3300;
+real counts_at_101_3kPa = 1674;
+
+real fraction_to_kPa(real fraction)
+{
+ return (fraction + 0.095) / 0.009;
+}
+
+
+real count_to_kPa(real count) = fraction_to_kPa(count / 2047);
+
+typedef struct {
+ real m, b;
+ int m_i, b_i;
+} line_t;
+
+line_t best_fit(real[] values, int first, int last) {
+ real sum_x = 0, sum_x2 = 0, sum_y = 0, sum_xy = 0;
+ int n = last - first + 1;
+ real m, b;
+ int m_i, b_i;
+
+ for (int i = first; i <= last; i++) {
+ sum_x += i;
+ sum_x2 += i**2;
+ sum_y += values[i];
+ sum_xy += values[i] * i;
+ }
+ m = (n*sum_xy - sum_y*sum_x) / (n*sum_x2 - sum_x**2);
+ b = sum_y/n - m*(sum_x/n);
+ return (line_t) { m = m, b = b };
+}
+
+real count_to_altitude(real count) {
+ return pressure_to_altitude(count_to_kPa(count) * 1000);
+}
+
+real fraction_to_altitude(real frac) = pressure_to_altitude(fraction_to_kPa(frac) * 1000);
+
+int num_samples = 1024;
+
+real[num_samples] alt = { [n] = fraction_to_altitude(n/(num_samples - 1)) };
+
+int num_part = 128;
+int seg_len = num_samples / num_part;
+
+line_t [dim(alt) / seg_len] fit = {
+ [n] = best_fit(alt, n * seg_len, n * seg_len + seg_len - 1)
+};
+
+int[num_samples/seg_len + 1] alt_part;
+
+alt_part[0] = floor (fit[0].b + 0.5);
+alt_part[dim(fit)] = floor(fit[dim(fit)-1].m * dim(fit) * seg_len + fit[dim(fit)-1].b + 0.5);
+
+for (int i = 0; i < dim(fit) - 1; i++) {
+ real here, there;
+ here = fit[i].m * (i+1) * seg_len + fit[i].b;
+ there = fit[i+1].m * (i+1) * seg_len + fit[i+1].b;
+ alt_part[i+1] = floor ((here + there) / 2 + 0.5);
+}
+
+real count_to_fit_altitude(int count) {
+ int sub = count // seg_len;
+ int off = count % seg_len;
+ line_t l = fit[sub];
+ real r_v;
+ real i_v;
+
+ r_v = count * l.m + l.b;
+ i_v = (alt_part[sub] * (seg_len - off) + alt_part[sub+1] * off) / seg_len;
+ return i_v;
+}
+
+real max_error = 0;
+int max_error_count = 0;
+real total_error = 0;
+
+for (int count = 0; count < num_samples; count++) {
+ real kPa = fraction_to_kPa(count / (num_samples - 1));
+ real meters = pressure_to_altitude(kPa * 1000);
+
+ real meters_approx = count_to_fit_altitude(count);
+ real error = abs(meters - meters_approx);
+
+ total_error += error;
+ if (error > max_error) {
+ max_error = error;
+ max_error_count = count;
+ }
+# printf (" %7d, /* %6.2g kPa %5d count approx %d */\n",
+# floor (meters + 0.5), kPa, count, floor(count_to_fit_altitude(count) + 0.5));
+}
+
+printf ("/*max error %f at %7.3f%%. Average error %f*/\n", max_error, max_error_count / (num_samples - 1) * 100, total_error / num_samples);
+
+printf ("#define NALT %d\n", dim(alt_part));
+printf ("#define ALT_FRAC_BITS %d\n", floor (log2(32768/(dim(alt_part)-1)) + 0.1));
+
+for (int i = 0; i < dim(alt_part); i++) {
+ real fraction = i / (dim(alt_part) - 1);
+ real kPa = fraction_to_kPa(fraction);
+ printf ("%9d, /* %6.2f kPa %7.3f%% */\n",
+ alt_part[i], kPa, fraction * 100);
+}
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