4 * Pressure Sensor Model, version 1.1
6 * written by Holly Grimes
8 * Uses the International Standard Atmosphere as described in
9 * "A Quick Derivation relating altitude to air pressure" (version 1.03)
10 * from the Portland State Aerospace Society, except that the atmosphere
11 * is divided into layers with each layer having a different lapse rate.
13 * Lapse rate data for each layer was obtained from Wikipedia on Sept. 1, 2007
14 * at site <http://en.wikipedia.org/wiki/International_Standard_Atmosphere
16 * Height measurements use the local tangent plane. The postive z-direction is up.
18 * All measurements are given in SI units (Kelvin, Pascal, meter, meters/second^2).
19 * The lapse rate is given in Kelvin/meter, the gas constant for air is given
20 * in Joules/(kilogram-Kelvin).
23 const real GRAVITATIONAL_ACCELERATION = -9.80665;
24 const real AIR_GAS_CONSTANT = 287.053;
25 const int NUMBER_OF_LAYERS = 7;
26 const real MAXIMUM_ALTITUDE = 84852;
27 const real MINIMUM_PRESSURE = 0.3734;
28 const real LAYER0_BASE_TEMPERATURE = 288.15;
29 const real LAYER0_BASE_PRESSURE = 101325;
31 /* lapse rate and base altitude for each layer in the atmosphere */
32 const real[NUMBER_OF_LAYERS] lapse_rate = {
33 -0.0065, 0.0, 0.001, 0.0028, 0.0, -0.0028, -0.002
35 const int[NUMBER_OF_LAYERS] base_altitude = {
36 0, 11000, 20000, 32000, 47000, 51000, 71000
40 /* outputs atmospheric pressure associated with the given altitude. altitudes
41 are measured with respect to the mean sea level */
42 real altitude_to_pressure(real altitude) {
44 real base_temperature = LAYER0_BASE_TEMPERATURE;
45 real base_pressure = LAYER0_BASE_PRESSURE;
48 real base; /* base for function to determine pressure */
49 real exponent; /* exponent for function to determine pressure */
50 int layer_number; /* identifies layer in the atmosphere */
51 int delta_z; /* difference between two altitudes */
53 if (altitude > MAXIMUM_ALTITUDE) /* FIX ME: use sensor data to improve model */
56 /* calculate the base temperature and pressure for the atmospheric layer
57 associated with the inputted altitude */
58 for(layer_number = 0; layer_number < NUMBER_OF_LAYERS - 1 && altitude > base_altitude[layer_number + 1]; layer_number++) {
59 delta_z = base_altitude[layer_number + 1] - base_altitude[layer_number];
60 if (lapse_rate[layer_number] == 0.0) {
61 exponent = GRAVITATIONAL_ACCELERATION * delta_z
62 / AIR_GAS_CONSTANT / base_temperature;
63 base_pressure *= exp(exponent);
66 base = (lapse_rate[layer_number] * delta_z / base_temperature) + 1.0;
67 exponent = GRAVITATIONAL_ACCELERATION /
68 (AIR_GAS_CONSTANT * lapse_rate[layer_number]);
69 base_pressure *= pow(base, exponent);
71 base_temperature += delta_z * lapse_rate[layer_number];
74 /* calculate the pressure at the inputted altitude */
75 delta_z = altitude - base_altitude[layer_number];
76 if (lapse_rate[layer_number] == 0.0) {
77 exponent = GRAVITATIONAL_ACCELERATION * delta_z
78 / AIR_GAS_CONSTANT / base_temperature;
79 pressure = base_pressure * exp(exponent);
82 base = (lapse_rate[layer_number] * delta_z / base_temperature) + 1.0;
83 exponent = GRAVITATIONAL_ACCELERATION /
84 (AIR_GAS_CONSTANT * lapse_rate[layer_number]);
85 pressure = base_pressure * pow(base, exponent);
92 /* outputs the altitude associated with the given pressure. the altitude
93 returned is measured with respect to the mean sea level */
94 real pressure_to_altitude(real pressure) {
96 real next_base_temperature = LAYER0_BASE_TEMPERATURE;
97 real next_base_pressure = LAYER0_BASE_PRESSURE;
101 real base_temperature;
102 real base; /* base for function to determine base pressure of next layer */
103 real exponent; /* exponent for function to determine base pressure
106 int layer_number; /* identifies layer in the atmosphere */
107 int delta_z; /* difference between two altitudes */
109 if (pressure < 0) /* illegal pressure */
111 if (pressure < MINIMUM_PRESSURE) /* FIX ME: use sensor data to improve model */
112 return MAXIMUM_ALTITUDE;
114 /* calculate the base temperature and pressure for the atmospheric layer
115 associated with the inputted pressure. */
119 base_pressure = next_base_pressure;
120 base_temperature = next_base_temperature;
121 delta_z = base_altitude[layer_number + 1] - base_altitude[layer_number];
122 if (lapse_rate[layer_number] == 0.0) {
123 exponent = GRAVITATIONAL_ACCELERATION * delta_z
124 / AIR_GAS_CONSTANT / base_temperature;
125 next_base_pressure *= exp(exponent);
128 base = (lapse_rate[layer_number] * delta_z / base_temperature) + 1.0;
129 exponent = GRAVITATIONAL_ACCELERATION /
130 (AIR_GAS_CONSTANT * lapse_rate[layer_number]);
131 next_base_pressure *= pow(base, exponent);
133 next_base_temperature += delta_z * lapse_rate[layer_number];
135 while(layer_number < NUMBER_OF_LAYERS - 1 && pressure < next_base_pressure);
137 /* calculate the altitude associated with the inputted pressure */
138 if (lapse_rate[layer_number] == 0.0) {
139 coefficient = (AIR_GAS_CONSTANT / GRAVITATIONAL_ACCELERATION)
141 altitude = base_altitude[layer_number]
142 + coefficient * log(pressure / base_pressure);
145 base = pressure / base_pressure;
146 exponent = AIR_GAS_CONSTANT * lapse_rate[layer_number]
147 / GRAVITATIONAL_ACCELERATION;
148 coefficient = base_temperature / lapse_rate[layer_number];
149 altitude = base_altitude[layer_number]
150 + coefficient * (pow(base, exponent) - 1);
156 real feet_to_meters(real feet)
158 return feet * (12 * 2.54 / 100);
161 real meters_to_feet(real meters)
163 return meters / (12 * 2.54 / 100);
167 * Values for our MP3H6115A pressure sensor
169 * From the data sheet:
171 * Pressure range: 15-115 kPa
172 * Voltage at 115kPa: 2.82
173 * Output scale: 27mV/kPa
176 * 27 mV/kPa * 2047 / 3300 counts/mV = 16.75 counts/kPa
177 * 2.82V * 2047 / 3.3 counts/V = 1749 counts/115 kPa
180 real counts_per_kPa = 27 * 2047 / 3300;
181 real counts_at_101_3kPa = 1674;
183 real count_to_kPa(real count)
185 return (count / 2047 + 0.095) / 0.009;
195 read_record(file in) {
197 File::fscanf(in, "%c %x %x %x\n",
198 &r.type, &r.time, &r.a, &r.b);
202 real g_count = 264.8;
208 count_to_g(real count)
210 return (g_base + g_count - count) / g_count;
222 real[...] accelerometer;
224 real sinc(real x) = x != 0 ? sin(x)/x : 1;
226 real gaussian(real x) = exp(-(x**2)/2) / sqrt(2 * pi);
230 real[...] convolve(real[...] d, real[...] e) {
231 real sample(n) = n < 0 ? d[0] : n >= dim(d) ? d[dim(d)-1] : d[n];
232 real w = (dim(e) - 1) / 2;
235 for (int o = -w; o <= w; o++)
236 v += sample(center + o) * e[o + w];
239 return (real[dim(d)]) { [n] = c(n) };
242 real sum(real[...] x) { real s = 0; for(int i = 0; i < dim(x); i++) s += x[i]; return s; }
244 real[...] kaiser_filter(real[...] d, int half_width) {
245 # real[half_width * 2 + 1] fir = { [n] = sinc(2 * pi * n / (2 * half_width)) };
246 real M = half_width * 2 + 1;
247 real[M] fir = { [n] = kaiser(n, M, 8) };
248 real fir_sum = sum(fir);
249 for (int i = 0; i < dim(fir); i++) fir[i] /= fir_sum;
250 return convolve(d, fir);
253 int[...] int_filter(int[...] d, int shift) {
254 /* Emulate the exponential IIR filter used in the TeleMetrum flight
261 for (n = 0; n < dim(d); n++) {
262 v -= (v + (1 << (shift - 1))) >> shift;
263 v += (d[n] + (1 << (shift - 1))) >> shift;
269 real gravity = 9.80665;
271 int[...] pressure_value, accelerometer_value;
274 void readsamples_log(file in) {
275 setdim(pressure_value, 0);
276 setdim(accelerometer_value, 0);
277 while (!File::end(in)) {
278 flight_record r = read_record(in);
283 clock[dim(clock)] = r.time / 100;
284 pressure_value[dim(pressure_value)] = r.b;
285 accelerometer_value[dim(accelerometer_value)] = r.a;
299 telem_record read_telem(file in) {
300 string[*] r = wordsplit(chomp(fgets(in)), " ");
305 printf ("invalid record line %d\n", line);
306 return read_telem(in);
308 return (telem_record) {
309 .time = string_to_integer(r[10]),
310 .accel = string_to_integer(r[12]),
311 .pressure = string_to_integer(r[14]),
316 void readsamples_telem(file in) {
317 telem_record[...] telem;
322 setdim(pressure_value, 0);
323 setdim(accelerometer_value, 0);
326 telem_record[...] save = {};
329 while (!File::end(in)) {
330 save[dim(save)] = read_telem(in);
331 if (save[dim(save)-1].state == "boost")
334 int start = dim(save) - 4;
337 for (int i = 0; i < start; i++)
338 accel_total += save[i].accel;
339 g_base = accel_total // start;
341 for (int i = start; i < dim(save); i++)
342 telem[dim(telem)] = save[i];
344 while (!File::end(in)) {
346 telem[n] = read_telem(in);
347 telem[n].time += clock_bias;
348 if (n > 0 && telem[n].time < telem[n-1].time) {
350 telem[n].time += 65536;
353 int clock_start = telem[0].time;
354 int clock_end = telem[dim(telem)-1].time;
355 int samples = clock_end - clock_start;
358 for (int i = 0; i < samples; i++) {
360 pressure_value[i] = telem[j].pressure;
361 accelerometer_value[i] = telem[j].accel;
362 if (j < dim(telem)-1) {
363 int cur_time = clock_start + i;
364 if (cur_time - telem[j].time > telem[j+1].time - cur_time)
370 readsamples_log(stdin);
372 int[...] int_integrate(int[...] d, int base) {
377 for (int i = 1; i < dim(d); i++)
378 ret[i] = (v += (d[i-1] + d[i] + 1) // 2);
382 int[...] int_differentiate(int[...] d) {
383 return (int[dim(d)]) { [n] = n == 0 ? 0 : d[n] - d[n-1] };
386 int average(int[...] d, int n) {
388 for (int i = 0; i < n; i++)
393 int[...] rebase(int[...] d, int m, int a) = (int[dim(d)]) { [n] = d[n] * m + a };
395 int size = dim(accelerometer_value);
397 real[...] do_low_pass(real[] data, real ωpass, real ωstop, real error) {
398 real[*] fir = low_pass_filter (ωpass, ωstop, error);
399 File::fprintf (stderr, "low pass filter is %d long\n", dim(fir));
400 return convolve(data, fir);
404 accelerometer_value = rebase(accelerometer_value, -1, g_base);
405 int accel_i0_base = average(accelerometer_value, 30);
406 int[size] pres_d0 = int_filter(pressure_value, 4);
407 int[size] accel_i0 = int_filter(accelerometer_value, 4);
408 int[size] pres_d1 = int_filter(int_differentiate(pres_d0), 4);
409 int[size] accel_i1 = int_integrate(accelerometer_value, accel_i0_base);
410 int[size] pres_d2 = int_filter(int_differentiate(pres_d1), 4);
411 int[size] accel_i2 = int_integrate(accel_i1, 0);
413 real count_to_altitude(int count) = pressure_to_altitude(count_to_kPa(count / 16) * 1000);
415 for (int i = 0; i < size; i++)
416 printf("%g %g %g %g %g %g %g %g %g\n",
418 count_to_altitude(pres_d0[i]) - count_to_altitude(pres_d0[0]), accel_i2[i] / 10000 / g_count * gravity,
419 pres_d1[i] * 100, accel_i1[i] / 100 / g_count * gravity,
420 pres_d2[i] * 10000, accel_i0[i] / g_count * gravity,
421 count_to_altitude(pressure_value[i]) -
422 count_to_altitude(pressure_value[0]), accelerometer_value[i]
423 / g_count * gravity);
426 real[size] accelerometer = { [n] = gravity * (count_to_g(accelerometer_value[n]) - 1.0) };
427 real[size] barometer = { [n] = pressure_to_altitude(count_to_kPa(pressure_value[n] / 16) * 1000) };
428 real[size] filtered_accelerometer = do_low_pass(accelerometer,
432 real[size] filtered_barometer = do_low_pass(barometer,
437 real[...] integrate(real[...] d) {
439 for (int i = 0; i < dim(ret); i++)
440 ret[i] = i == 0 ? 0 : ret[i-1] + (d[i-1] + d[i]) / 2 * (clock[i] - clock[i-1]);
444 real[...] differentiate(real[...] d) {
446 for (int i = 1; i < dim(ret); i++)
447 ret[i] = (d[i] - d[i-1]) / (clock[i] - clock[i-1]);
452 real[size] accel_speed = integrate(accelerometer);
453 real[size] accel_pos = integrate(accel_speed);
454 real[size] baro_speed = differentiate(filtered_barometer);
455 real[size] baro_accel = differentiate(baro_speed);
457 printf("%7s %12s %12s %12s %12s %12s %12s %12s %12s\n",
467 for (int i = 0; i < size; i++)
468 printf("%7.2f %12.6f %12.6f %12.6f %12.6f %12.6f %12.6f %12.6f %12.6f\n",
470 filtered_barometer[i] - filtered_barometer[0], accel_pos[i],
471 baro_speed[i], accel_speed[i],
472 baro_accel[i], filtered_accelerometer[i],
473 barometer[i] - barometer[0], accelerometer[i]);