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Diffstat (limited to 'src/kalman/kalman.5c')
| -rwxr-xr-x | src/kalman/kalman.5c | 491 |
1 files changed, 491 insertions, 0 deletions
diff --git a/src/kalman/kalman.5c b/src/kalman/kalman.5c new file mode 100755 index 00000000..cfb7abea --- /dev/null +++ b/src/kalman/kalman.5c @@ -0,0 +1,491 @@ +#!/usr/bin/env nickle + +/* + * Copyright © 2011 Keith Packard <keithp@keithp.com> + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation; version 2 of the License. + * + * This program is distributed in the hope that it will be useful, but + * WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + * General Public License for more details. + * + * You should have received a copy of the GNU General Public License along + * with this program; if not, write to the Free Software Foundation, Inc., + * 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. + */ + +autoimport ParseArgs; + +load "load_csv.5c" +import load_csv; + +load "matrix.5c" +import matrix; + +load "kalman_filter.5c" +import kalman; + +/* + * AltOS keeps speed and accel scaled + * by 4 bits to provide additional precision + */ +real height_scale = 1.0; +real accel_scale = 16.0; +real speed_scale = 16.0; + +/* + * State: + * + * x[0] = height + * x[1] = velocity + * x[2] = acceleration + */ + +/* + * Measurement + * + * z[0] = height + * z[1] = acceleration + */ + +real default_σ_m = 5; +real default_σ_h = 20; +real default_σ_a = 2; + +parameters_t param_both(real t, real σ_m, real σ_h, real σ_a) { + if (σ_m == 0) + σ_m = default_σ_m; + if (σ_h == 0) + σ_h = default_σ_h; + if (σ_a == 0) + σ_a = default_σ_a; + + σ_m = imprecise(σ_m) * accel_scale; + σ_h = imprecise(σ_h) * height_scale; + σ_a = imprecise(σ_a) * accel_scale; + + t = imprecise(t); + + return (parameters_t) { +/* + * Equation computing state k from state k-1 + * + * height = height- + velocity- * t + acceleration- * t² / 2 + * velocity = velocity- + acceleration- * t + * acceleration = acceleration- + */ + .a = (real[3,3]) { + { 1, + t * height_scale / speed_scale , t**2/2 * height_scale / accel_scale }, + { 0, 1, t * speed_scale / accel_scale }, + { 0, 0, 1 } + }, +/* + * Model error covariance. The only inaccuracy in the + * model is the assumption that acceleration is constant + */ + .q = (real[3,3]) { + { 0, 0, 0 }, + { 0, 0, 0 }, + {.0, 0, σ_m**2 }, + }, +/* + * Measurement error covariance + * Our sensors are independent, so + * this matrix is zero off-diagonal + */ + .r = (real[2,2]) { + { σ_h ** 2, 0 }, + { 0, σ_a ** 2 }, + }, +/* + * Extract measurements from state, + * this just pulls out the height and acceleration + * values. + */ + .h = (real[2,3]) { + { 1, 0, 0 }, + { 0, 0, 1 }, + }, + }; +} + +parameters_t param_baro(real t, real σ_m, real σ_h) { + if (σ_m == 0) + σ_m = default_σ_m; + if (σ_h == 0) + σ_h = default_σ_h; + + σ_m = imprecise(σ_m) * accel_scale; + σ_h = imprecise(σ_h) * height_scale; + + t = imprecise(t); + return (parameters_t) { +/* + * Equation computing state k from state k-1 + * + * height = height- + velocity- * t + acceleration- * t² / 2 + * velocity = velocity- + acceleration- * t + * acceleration = acceleration- + */ + .a = (real[3,3]) { + { 1, t * height_scale / speed_scale , t**2/2 * height_scale / accel_scale }, + { 0, 1, t * speed_scale / accel_scale }, + { 0, 0, 1 } + }, +/* + * Model error covariance. The only inaccuracy in the + * model is the assumption that acceleration is constant + */ + .q = (real[3,3]) { + { 0, 0, 0 }, + { 0, 0, 0 }, + {.0, 0, σ_m**2 }, + }, +/* + * Measurement error covariance + * Our sensors are independent, so + * this matrix is zero off-diagonal + */ + .r = (real[1,1]) { + { σ_h ** 2 }, + }, +/* + * Extract measurements from state, + * this just pulls out the height + * values. + */ + .h = (real[1,3]) { + { 1, 0, 0 }, + }, + }; +} + +parameters_t param_accel(real t, real σ_m, real σ_a) { + if (σ_m == 0) + σ_m = default_σ_m; + if (σ_a == 0) + σ_a = default_σ_a; + + σ_m = imprecise(σ_m) * accel_scale; + σ_a = imprecise(σ_a) * accel_scale; + + t = imprecise(t); + return (parameters_t) { +/* + * Equation computing state k from state k-1 + * + * height = height- + velocity- * t + acceleration- * t² / 2 + * velocity = velocity- + acceleration- * t + * acceleration = acceleration- + */ + .a = (real[3,3]) { + { 1, t * height_scale / speed_scale , t**2/2 * height_scale / accel_scale }, + { 0, 1, t * speed_scale / accel_scale }, + { 0, 0, 1 } + }, +/* + * Model error covariance. The only inaccuracy in the + * model is the assumption that acceleration is constant + */ + .q = (real[3,3]) { + { 0, 0, 0 }, + { 0, 0, 0 }, + {.0, 0, σ_m**2 }, + }, +/* + * Measurement error covariance + * Our sensors are independent, so + * this matrix is zero off-diagonal + */ + .r = (real[1,1]) { + { σ_a ** 2 }, + }, +/* + * Extract measurements from state, + * this just pulls out the acceleration + * values. + */ + .h = (real[1,3]) { + { 0, 0, 1 }, + }, + }; +} + +parameters_t param_vel(real t) { + static real σ_m = .1; + static real σ_v = imprecise(10); + + return (parameters_t) { +/* + * Equation computing state k from state k-1 + * + * height = height- + velocity- * t + acceleration- * t² / 2 + * velocity = velocity- + acceleration- * t + * acceleration = acceleration- + */ + .a = (real[3,3]) { + { 1, imprecise(t), imprecise((t**2)/2) }, + { 0, 1, imprecise(t) }, + { 0, 0, 1 } + }, +/* + * Model error covariance. The only inaccuracy in the + * model is the assumption that acceleration is constant + */ + .q = (real[3,3]) { + { 0, 0, 0 }, + { 0, 0, 0 }, + {.0, 0, σ_m**2 }, + }, +/* + * Measurement error covariance + * Our sensors are independent, so + * this matrix is zero off-diagonal + */ + .r = (real[1,1]) { + { σ_v ** 2 }, + }, +/* + * Extract measurements from state, + * this just pulls out the velocity + * values. + */ + .h = (real[1,3]) { + { 0, 1, 0 }, + }, + }; +} + +real max_baro_height = 18000; + +bool just_kalman = true; +real accel_input_scale = 1; + +void run_flight(string name, file f, bool summary) { + state_t current_both = { + .x = (real[3]) { 0, 0, 0 }, + .p = (real[3,3]) { { 0 ... } ... }, + }; + state_t current_accel = current_both; + state_t current_baro = current_both; + real t; + real kalman_apogee_time = -1; + real kalman_apogee = 0; + real raw_apogee_time_first; + real raw_apogee_time_last; + real raw_apogee = 0; + real default_descent_rate = 20; + real speed = 0; + real prev_acceleration = 0; + state_t apogee_state; + parameters_fast_t fast_both; + parameters_fast_t fast_baro; + parameters_fast_t fast_accel; + real fast_delta_t = 0; + bool fast = true; + + for (;;) { + record_t record = parse_record(f, accel_input_scale); + if (record.done) + break; + if (is_uninit(&t)) + t = record.time; + real delta_t = record.time - t; + if (delta_t <= 0) + continue; + t = record.time; + if (record.height > raw_apogee) { + raw_apogee_time_first = record.time; + raw_apogee = record.height; + } + if (record.height == raw_apogee) + raw_apogee_time_last = record.time; + + real acceleration = record.acceleration; + real height = record.height; + + speed = (speed + (acceleration + prev_acceleration / 2) * delta_t); + prev_acceleration = acceleration; + + vec_t z_both = (real[2]) { record.height * height_scale, record.acceleration * accel_scale }; + vec_t z_accel = (real[1]) { record.acceleration * accel_scale }; + vec_t z_baro = (real[1]) { record.height * height_scale }; + + + if (fast) { + if (delta_t != fast_delta_t) { + fast_both = convert_to_fast(param_both(delta_t, 0, 0, 0)); + fast_accel = convert_to_fast(param_accel(delta_t, 0, 0)); + fast_baro = convert_to_fast(param_baro(delta_t, 0, 0)); + fast_delta_t = delta_t; + } + + current_both.x = predict_fast(current_both.x, fast_both); + current_accel.x = predict_fast(current_accel.x, fast_accel); + current_baro.x = predict_fast(current_baro.x, fast_baro); + + current_both.x = correct_fast(current_both.x, z_both, fast_both); + current_accel.x = correct_fast(current_accel.x, z_accel, fast_accel); + current_baro.x = correct_fast(current_baro.x, z_baro, fast_baro); + } else { + parameters_t p_both = param_both(delta_t, 0, 0, 0); + parameters_t p_accel = param_accel(delta_t, 0, 0); + parameters_t p_baro = param_baro(delta_t, 0, 0); + + state_t pred_both = predict(current_both, p_both); + state_t pred_accel = predict(current_accel, p_accel); + state_t pred_baro = predict(current_baro, p_baro); + + state_t next_both = correct(pred_both, z_both, p_both); + state_t next_accel = correct(pred_accel, z_accel, p_accel); + state_t next_baro = correct(pred_baro, z_baro, p_baro); + current_both = next_both; + current_accel = next_accel; + current_baro = next_baro; + } + + 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", + record.time, + record.height, speed, record.acceleration, + current_both.x[0] / height_scale, current_both.x[1] / speed_scale, current_both.x[2] / accel_scale, + current_accel.x[0] / height_scale, current_accel.x[1] / speed_scale, current_accel.x[2] / accel_scale, + current_baro.x[0] / height_scale, current_baro.x[1] / speed_scale, current_baro.x[2] / accel_scale); + if (kalman_apogee_time < 0) { + if (current_both.x[1] < -1 && current_accel.x[1] < -1 && current_baro.x[1] < -1) { + kalman_apogee = current_both.x[0]; + kalman_apogee_time = record.time; + break; + } + } + } + real raw_apogee_time = (raw_apogee_time_last + raw_apogee_time_first) / 2; + if (summary && !just_kalman) { + printf("%s: kalman (%8.2f m %6.2f s) raw (%8.2f m %6.2f s) error %6.2f s\n", + name, + kalman_apogee, kalman_apogee_time, + raw_apogee, raw_apogee_time, + kalman_apogee_time - raw_apogee_time); + } +} + +void main() { + bool summary = false; + int user_argind = 1; + real time_step = 0.01; + string compute = "none"; + string prefix = "AO_K"; + real σ_m = 1; + real σ_h = 4; + real σ_a = 1; + + ParseArgs::argdesc argd = { + .args = { + { .var = { .arg_flag = &summary }, + .abbr = 's', + .name = "summary", + .desc = "Print a summary of the flight" }, + { .var = { .arg_real = &max_baro_height }, + .abbr = 'm', + .name = "maxbaro", + .expr_name = "height", + .desc = "Set maximum usable barometer height" }, + { .var = { .arg_real = &accel_input_scale, }, + .abbr = 'a', + .name = "accel", + .expr_name = "<accel-scale>", + .desc = "Set accelerometer scale factor" }, + { .var = { .arg_real = &time_step, }, + .abbr = 't', + .name = "time", + .expr_name = "<time-step>", + .desc = "Set time step for convergence" }, + { .var = { .arg_string = &prefix }, + .abbr = 'p', + .name = "prefix", + .expr_name = "<prefix>", + .desc = "Prefix for compute output" }, + { .var = { .arg_string = &compute }, + .abbr = 'c', + .name = "compute", + .expr_name = "{both,baro,accel}", + .desc = "Compute Kalman factor through convergence" }, + { .var = { .arg_real = &σ_m }, + .abbr = 'M', + .name = "model", + .expr_name = "<model-accel-error>", + .desc = "Model co-variance for acceleration" }, + { .var = { .arg_real = &σ_h }, + .abbr = 'H', + .name = "height", + .expr_name = "<measure-height-error>", + .desc = "Measure co-variance for height" }, + { .var = { .arg_real = &σ_a }, + .abbr = 'A', + .name = "accel", + .expr_name = "<measure-accel-error>", + .desc = "Measure co-variance for acceleration" }, + }, + + .unknown = &user_argind, + }; + + ParseArgs::parseargs(&argd, &argv); + + if (compute != "none") { + parameters_t param; + + printf ("/* Kalman matrix for %s\n", compute); + printf (" * step = %f\n", time_step); + printf (" * σ_m = %f\n", σ_m); + switch (compute) { + case "both": + printf (" * σ_h = %f\n", σ_h); + printf (" * σ_a = %f\n", σ_a); + param = param_both(time_step, σ_m, σ_h, σ_a); + break; + case "accel": + printf (" * σ_a = %f\n", σ_a); + param = param_accel(time_step, σ_m, σ_a); + break; + case "baro": + printf (" * σ_h = %f\n", σ_h); + param = param_baro(time_step, σ_m, σ_h); + break; + } + printf (" */\n\n"); + mat_t k = converge(param); + int[] d = dims(k); + int time_inc = floor(1/time_step + 0.5); + for (int i = 0; i < d[0]; i++) + for (int j = 0; j < d[1]; j++) { + string name; + if (d[1] == 1) + name = sprintf("%s_K%d_%d", prefix, i, time_inc); + else + name = sprintf("%s_K%d%d_%d", prefix, i, j, time_inc); + printf ("#define %s to_fix32(%12.10f)\n", name, k[i,j]); + } + printf ("\n"); + exit(0); + } + string[dim(argv) - user_argind] rest = { [i] = argv[i+user_argind] }; + + # height_scale = accel_scale = speed_scale = 1; + + if (dim(rest) == 0) + run_flight("<stdin>", stdin, summary); + else { + for (int i = 0; i < dim(rest); i++) { + twixt(file f = File::open(rest[i], "r"); File::close(f)) { + run_flight(rest[i], f, summary); + } + } + } +} +main(); +#kalman(stdin); +#dump(stdin); |