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   1 #!/usr/bin/env nickle
   2
   3 /*
   4  * Copyright © 2011 Keith Packard <keithp@keithp.com>
   5  *
   6  * This program is free software; you can redistribute it and/or modify
   7  * it under the terms of the GNU General Public License as published by
   8  * the Free Software Foundation; version 2 of the License.
   9  *
  10  * This program is distributed in the hope that it will be useful, but
  11  * WITHOUT ANY WARRANTY; without even the implied warranty of
  12  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  13  * General Public License for more details.
  14  *
  15  * You should have received a copy of the GNU General Public License along
  16  * with this program; if not, write to the Free Software Foundation, Inc.,
  17  * 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA.
  18  */
  19
  20 autoimport ParseArgs;
  21
  22 load "load_csv.5c"
  23 import load_csv;
  24
  25 load "matrix.5c"
  26 import matrix;
  27
  28 load "kalman_filter.5c"
  29 import kalman;
  30
  31 /*
  32  * AltOS keeps speed and accel scaled
  33  * by 4 bits to provide additional precision
  34  */
  35 real    height_scale = 1.0;
  36 real    accel_scale = 16.0;
  37 real    speed_scale = 16.0;
  38
  39 /*
  40  * State:
  41  *
  42  * x[0] = height
  43  * x[1] = velocity
  44  * x[2] = acceleration
  45  */
  46
  47 /*
  48  * Measurement
  49  *
  50  * z[0] = height
  51  * z[1] = acceleration
  52  */
  53
  54 real default_σ_m = 5;
  55 real default_σ_h = 20;
  56 real default_σ_a = 2;
  57
  58 real[3,3] model_error(t, Φ) = multiply_mat_val ((real[3,3]) {
  59                 { t**5 / 20, t**4 / 8, t**3 / 6 },
  60                 { t**4 /  8, t**3 / 3, t**2 / 2 },
  61                 { t**3 /  6, t**2 / 2, t }
  62         }, Φ);
  63
  64 parameters_t param_both(real t, real σ_m, real σ_h, real σ_a) {
  65         if (σ_m == 0)
  66                 σ_m = default_σ_m;
  67         if (σ_h == 0)
  68                 σ_h = default_σ_h;
  69         if (σ_a == 0)
  70                 σ_a = default_σ_a;
  71
  72         σ_m = imprecise(σ_m) * accel_scale;
  73         σ_h = imprecise(σ_h) * height_scale;
  74         σ_a = imprecise(σ_a) * accel_scale;
  75
  76         t = imprecise(t);
  77
  78         return (parameters_t) {
  79 /*
  80  * Equation computing state k from state k-1
  81  *
  82  * height = height- + velocity- * t + acceleration- * t² / 2
  83  * velocity = velocity- + acceleration- * t
  84  * acceleration = acceleration-
  85  */
  86                 .a = (real[3,3]) {
  87                         { 1,
  88                           t * height_scale / speed_scale , t**2/2 * height_scale / accel_scale },
  89                         { 0, 1, t * speed_scale / accel_scale },
  90                         { 0, 0, 1 }
  91                 },
  92 /*
  93  * Model error covariance. The only inaccuracy in the
  94  * model is the assumption that acceleration is constant
  95  */
  96                 .q = model_error (t, σ_m**2),
  97 /*
  98  * Measurement error covariance
  99  * Our sensors are independent, so
 100  * this matrix is zero off-diagonal
 101  */
 102                 .r = (real[2,2]) {
 103                         { σ_h ** 2, 0 },
 104                         { 0, σ_a ** 2 },
 105                 },
 106 /*
 107  * Extract measurements from state,
 108  * this just pulls out the height and acceleration
 109  * values.
 110  */
 111                 .h = (real[2,3]) {
 112                         { 1, 0, 0 },
 113                         { 0, 0, 1 },
 114                 },
 115          };
 116 }
 117
 118 parameters_t param_baro(real t, real σ_m, real σ_h) {
 119         if (σ_m == 0)
 120                 σ_m = default_σ_m;
 121         if (σ_h == 0)
 122                 σ_h = default_σ_h;
 123
 124         σ_m = imprecise(σ_m) * accel_scale;
 125         σ_h = imprecise(σ_h) * height_scale;
 126
 127         t = imprecise(t);
 128         return (parameters_t) {
 129 /*
 130  * Equation computing state k from state k-1
 131  *
 132  * height = height- + velocity- * t + acceleration- * t² / 2
 133  * velocity = velocity- + acceleration- * t
 134  * acceleration = acceleration-
 135  */
 136                 .a = (real[3,3]) {
 137                         { 1, t * height_scale / speed_scale , t**2/2 * height_scale / accel_scale },
 138                         { 0, 1, t * speed_scale / accel_scale },
 139                         { 0, 0, 1 }
 140                 },
 141 /*
 142  * Model error covariance. The only inaccuracy in the
 143  * model is the assumption that acceleration is constant
 144  */
 145                 .q = model_error (t, σ_m**2),
 146 /*
 147  * Measurement error covariance
 148  * Our sensors are independent, so
 149  * this matrix is zero off-diagonal
 150  */
 151                 .r = (real[1,1]) {
 152                         { σ_h ** 2 },
 153                 },
 154 /*
 155  * Extract measurements from state,
 156  * this just pulls out the height
 157  * values.
 158  */
 159                 .h = (real[1,3]) {
 160                         { 1, 0, 0 },
 161                 },
 162          };
 163 }
 164
 165 parameters_t param_accel(real t, real σ_m, real σ_a) {
 166         if (σ_m == 0)
 167                 σ_m = default_σ_m;
 168         if (σ_a == 0)
 169                 σ_a = default_σ_a;
 170
 171         σ_m = imprecise(σ_m) * accel_scale;
 172         σ_a = imprecise(σ_a) * accel_scale;
 173
 174         t = imprecise(t);
 175         return (parameters_t) {
 176 /*
 177  * Equation computing state k from state k-1
 178  *
 179  * height = height- + velocity- * t + acceleration- * t² / 2
 180  * velocity = velocity- + acceleration- * t
 181  * acceleration = acceleration-
 182  */
 183                 .a = (real[3,3]) {
 184                         { 1, t * height_scale / speed_scale , t**2/2 * height_scale / accel_scale },
 185                         { 0, 1, t * speed_scale / accel_scale },
 186                         { 0, 0, 1 }
 187                 },
 188 /*
 189  * Model error covariance. The only inaccuracy in the
 190  * model is the assumption that acceleration is constant
 191  */
 192                 .q = model_error (t, σ_m**2),
 193 /*
 194  * Measurement error covariance
 195  * Our sensors are independent, so
 196  * this matrix is zero off-diagonal
 197  */
 198                 .r = (real[1,1]) {
 199                         { σ_a ** 2 },
 200                 },
 201 /*
 202  * Extract measurements from state,
 203  * this just pulls out the acceleration
 204  * values.
 205  */
 206                 .h = (real[1,3]) {
 207                         { 0, 0, 1 },
 208                 },
 209          };
 210 }
 211
 212 parameters_t param_vel(real t) {
 213         static real σ_m = .1;
 214         static real σ_v = imprecise(10);
 215
 216         return (parameters_t) {
 217 /*
 218  * Equation computing state k from state k-1
 219  *
 220  * height = height- + velocity- * t + acceleration- * t² / 2
 221  * velocity = velocity- + acceleration- * t
 222  * acceleration = acceleration-
 223  */
 224                 .a = (real[3,3]) {
 225                         { 1, imprecise(t), imprecise((t**2)/2) },
 226                         { 0, 1, imprecise(t) },
 227                         { 0, 0, 1 }
 228                 },
 229 /*
 230  * Model error covariance. The only inaccuracy in the
 231  * model is the assumption that acceleration is constant
 232  */
 233                 .q = model_error (t, σ_m**2),
 234 /*
 235  * Measurement error covariance
 236  * Our sensors are independent, so
 237  * this matrix is zero off-diagonal
 238  */
 239                 .r = (real[1,1]) {
 240                         { σ_v ** 2 },
 241                 },
 242 /*
 243  * Extract measurements from state,
 244  * this just pulls out the velocity
 245  * values.
 246  */
 247                 .h = (real[1,3]) {
 248                         { 0, 1, 0 },
 249                 },
 250          };
 251 }
 252
 253 real    max_baro_height = 18000;
 254
 255 bool    just_kalman = true;
 256 real    accel_input_scale = 1;
 257
 258 void run_flight(string name, file f, bool summary) {
 259         state_t current_both = {
 260                 .x = (real[3]) { 0, 0, 0 },
 261                 .p = (real[3,3]) { { 0 ... } ... },
 262         };
 263         state_t current_accel = current_both;
 264         state_t current_baro = current_both;
 265         real    t;
 266         real    kalman_apogee_time = -1;
 267         real    kalman_apogee = 0;
 268         real    raw_apogee_time_first;
 269         real    raw_apogee_time_last;
 270         real    raw_apogee = 0;
 271         real    default_descent_rate = 20;
 272         real    speed = 0;
 273         real    prev_acceleration = 0;
 274         state_t apogee_state;
 275         parameters_fast_t       fast_both;
 276         parameters_fast_t       fast_baro;
 277         parameters_fast_t       fast_accel;
 278         real                    fast_delta_t = 0;
 279         bool                    fast = true;
 280
 281         for (;;) {
 282                 record_t        record = parse_record(f, accel_input_scale);
 283                 if (record.done)
 284                         break;
 285                 if (is_uninit(&t))
 286                         t = record.time;
 287                 real delta_t = record.time - t;
 288                 if (delta_t <= 0)
 289                         continue;
 290                 t = record.time;
 291                 if (record.height > raw_apogee) {
 292                         raw_apogee_time_first = record.time;
 293                         raw_apogee = record.height;
 294                 }
 295                 if (record.height == raw_apogee)
 296                         raw_apogee_time_last = record.time;
 297
 298                 real    acceleration = record.acceleration;
 299                 real    height = record.height;
 300
 301                 speed = (speed + (acceleration + prev_acceleration / 2) * delta_t);
 302                 prev_acceleration = acceleration;
 303
 304                 vec_t z_both = (real[2]) { record.height * height_scale,  record.acceleration * accel_scale };
 305                 vec_t z_accel = (real[1]) { record.acceleration * accel_scale };
 306                 vec_t z_baro = (real[1]) { record.height * height_scale };
 307
 308
 309                 if (fast) {
 310                         if (delta_t != fast_delta_t) {
 311                                 fast_both = convert_to_fast(param_both(delta_t, 0, 0, 0));
 312                                 fast_accel = convert_to_fast(param_accel(delta_t, 0, 0));
 313                                 fast_baro = convert_to_fast(param_baro(delta_t, 0, 0));
 314                                 fast_delta_t = delta_t;
 315                         }
 316
 317                         current_both.x = predict_fast(current_both.x, fast_both);
 318                         current_accel.x = predict_fast(current_accel.x, fast_accel);
 319                         current_baro.x = predict_fast(current_baro.x, fast_baro);
 320
 321                         current_both.x = correct_fast(current_both.x, z_both, fast_both);
 322                         current_accel.x = correct_fast(current_accel.x, z_accel, fast_accel);
 323                         current_baro.x = correct_fast(current_baro.x, z_baro, fast_baro);
 324                 } else {
 325                         parameters_t p_both = param_both(delta_t, 0, 0, 0);
 326                         parameters_t p_accel = param_accel(delta_t, 0, 0);
 327                         parameters_t p_baro = param_baro(delta_t, 0, 0);
 328
 329                         state_t pred_both = predict(current_both, p_both);
 330                         state_t pred_accel = predict(current_accel, p_accel);
 331                         state_t pred_baro = predict(current_baro, p_baro);
 332
 333                         state_t next_both = correct(pred_both, z_both, p_both);
 334                         state_t next_accel = correct(pred_accel, z_accel, p_accel);
 335                         state_t next_baro = correct(pred_baro, z_baro, p_baro);
 336                         current_both = next_both;
 337                         current_accel = next_accel;
 338                         current_baro = next_baro;
 339                 }
 340
 341                 printf ("%16.8f %16.8f %16.8f %16.8f %16.8f %16.8f %16.8f %16.8f %16.8f %16.8f %16.8f %16.8f %16.8f\n",
 342                         record.time,
 343                         record.height, speed, record.acceleration,
 344                         current_both.x[0] / height_scale, current_both.x[1] / speed_scale, current_both.x[2] / accel_scale,
 345                         current_accel.x[0] / height_scale, current_accel.x[1] / speed_scale, current_accel.x[2] / accel_scale,
 346                         current_baro.x[0] / height_scale, current_baro.x[1] / speed_scale, current_baro.x[2] / accel_scale);
 347                 if (kalman_apogee_time < 0) {
 348                         if (current_both.x[1] < -1 && current_accel.x[1] < -1 && current_baro.x[1] < -1) {
 349                                 kalman_apogee = current_both.x[0];
 350                                 kalman_apogee_time = record.time;
 351                                 break;
 352                         }
 353                 }
 354         }
 355         real raw_apogee_time = (raw_apogee_time_last + raw_apogee_time_first) / 2;
 356         if (summary && !just_kalman) {
 357                 printf("%s: kalman (%8.2f m %6.2f s) raw (%8.2f m %6.2f s) error %6.2f s\n",
 358                        name,
 359                        kalman_apogee, kalman_apogee_time,
 360                        raw_apogee, raw_apogee_time,
 361                        kalman_apogee_time - raw_apogee_time);
 362         }
 363 }
 364
 365 void main() {
 366         bool    summary = false;
 367         int     user_argind = 1;
 368         real    time_step = 0.01;
 369         string  compute = "none";
 370         string  prefix = "AO_K";
 371         real    σ_m = 1;
 372         real    σ_h = 4;
 373         real    σ_a = 1;
 374
 375         ParseArgs::argdesc argd = {
 376                 .args = {
 377                         { .var = { .arg_flag = &summary },
 378                           .abbr = 's',
 379                           .name = "summary",
 380                           .desc = "Print a summary of the flight" },
 381                         { .var = { .arg_real = &max_baro_height },
 382                           .abbr = 'm',
 383                           .name = "maxbaro",
 384                           .expr_name = "height",
 385                           .desc = "Set maximum usable barometer height" },
 386                         { .var = { .arg_real = &accel_input_scale, },
 387                           .abbr = 'a',
 388                           .name = "accel",
 389                           .expr_name = "<accel-scale>",
 390                           .desc = "Set accelerometer scale factor" },
 391                         { .var = { .arg_real = &time_step, },
 392                           .abbr = 't',
 393                           .name = "time",
 394                           .expr_name = "<time-step>",
 395                           .desc = "Set time step for convergence" },
 396                         { .var = { .arg_string = &prefix },
 397                           .abbr = 'p',
 398                           .name = "prefix",
 399                           .expr_name = "<prefix>",
 400                           .desc = "Prefix for compute output" },
 401                         { .var = { .arg_string = &compute },
 402                           .abbr = 'c',
 403                           .name = "compute",
 404                           .expr_name = "{both,baro,accel}",
 405                           .desc = "Compute Kalman factor through convergence" },
 406                         { .var = { .arg_real = &σ_m },
 407                           .abbr = 'M',
 408                           .name = "model",
 409                           .expr_name = "<model-accel-error>",
 410                           .desc = "Model co-variance for acceleration" },
 411                         { .var = { .arg_real = &σ_h },
 412                           .abbr = 'H',
 413                           .name = "height",
 414                           .expr_name = "<measure-height-error>",
 415                           .desc = "Measure co-variance for height" },
 416                         { .var = { .arg_real = &σ_a },
 417                           .abbr = 'A',
 418                           .name = "accel",
 419                           .expr_name = "<measure-accel-error>",
 420                           .desc = "Measure co-variance for acceleration" },
 421                 },
 422
 423                 .unknown = &user_argind,
 424         };
 425
 426         ParseArgs::parseargs(&argd, &argv);
 427
 428         if (compute != "none") {
 429                 parameters_t    param;
 430
 431                 printf ("/* Kalman matrix for %s\n", compute);
 432                 printf (" *     step = %f\n", time_step);
 433                 printf (" *     σ_m = %f\n", σ_m);
 434                 switch (compute) {
 435                 case "both":
 436                         printf (" *     σ_h = %f\n", σ_h);
 437                         printf (" *     σ_a = %f\n", σ_a);
 438                         param = param_both(time_step, σ_m, σ_h, σ_a);
 439                         break;
 440                 case "accel":
 441                         printf (" *     σ_a = %f\n", σ_a);
 442                         param = param_accel(time_step, σ_m, σ_a);
 443                         break;
 444                 case "baro":
 445                         printf (" *     σ_h = %f\n", σ_h);
 446                         param = param_baro(time_step, σ_m, σ_h);
 447                         break;
 448                 }
 449                 printf (" */\n\n");
 450                 mat_t k = converge(param);
 451                 int[] d = dims(k);
 452                 int time_inc = floor(1/time_step + 0.5);
 453                 for (int i = 0; i < d[0]; i++)
 454                         for (int j = 0; j < d[1]; j++) {
 455                                 string name;
 456                                 if (d[1] == 1)
 457                                         name = sprintf("%s_K%d_%d", prefix, i, time_inc);
 458                                 else
 459                                         name = sprintf("%s_K%d%d_%d", prefix, i, j, time_inc);
 460                                 printf ("#define %s to_fix32(%12.10f)\n", name, k[i,j]);
 461                         }
 462                 printf ("\n");
 463                 exit(0);
 464         }
 465         string[dim(argv) - user_argind] rest = { [i] = argv[i+user_argind] };
 466
 467         #       height_scale = accel_scale = speed_scale = 1;
 468
 469         if (dim(rest) == 0)
 470                 run_flight("<stdin>", stdin, summary);
 471         else {
 472                 for (int i = 0; i < dim(rest); i++) {
 473                         twixt(file f = File::open(rest[i], "r"); File::close(f)) {
 474                                 run_flight(rest[i], f, summary);
 475                         }
 476                 }
 477         }
 478 }
 479 main();
 480 #kalman(stdin);
 481 #dump(stdin);