Harald Schafer
6 years ago
parent
8321cf283a
commit
4212b7f91c
2 changed files with 311 additions and 0 deletions
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#!/usr/bin/env python3 |
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import numpy as np |
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from live_model import gen_model, States |
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from .kalman_helpers import ObservationKind |
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from .ekf_sym import EKF_sym |
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class LiveKalman(): |
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def __init__(self, N=0, max_tracks=3000): |
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x_initial = np.array([-2.7e6, 4.2e6, 3.8e6, |
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1, 0, 0, 0, |
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0, 0, 0, |
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0, 0, 0, |
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0, 0, 0, |
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1, |
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0, 0, 0, |
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0, 0, 0]) |
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# state covariance |
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P_initial = np.diag([10000**2, 10000**2, 10000**2, |
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10**2, 10**2, 10**2, |
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10**2, 10**2, 10**2, |
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1**2, 1**2, 1**2, |
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0.05**2, 0.05**2, 0.05**2, |
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0.02**2, |
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1**2, 1**2, 1**2, |
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(0.01)**2, (0.01)**2, (0.01)**2]) |
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# process noise |
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Q = np.diag([0.03**2, 0.03**2, 0.03**2, |
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0.0**2, 0.0**2, 0.0**2, |
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0.0**2, 0.0**2, 0.0**2, |
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0.1**2, 0.1**2, 0.1**2, |
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(0.005/100)**2, (0.005/100)**2, (0.005/100)**2, |
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(0.02/100)**2, |
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3**2, 3**2, 3**2, |
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0.001**2, |
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(0.05/60)**2, (0.05/60)**2, (0.05/60)**2]) |
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self.obs_noise = {ObservationKind.ODOMETRIC_SPEED: np.atleast_2d(0.2**2), |
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ObservationKind.PHONE_GYRO: np.diag([0.025**2, 0.025**2, 0.025**2]), |
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ObservationKind.PHONE_ACCEL: np.diag([.5**2, .5**2, .5*2]), |
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ObservationKind.CAMERA_ODO_ROTATION: np.diag([0.05**2, 0.05**2, 0.05**2]), |
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ObservationKind.IMU_FRAME: np.diag([0.05**2, 0.05**2, 0.05**2]), |
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ObservationKind.NO_ROT: np.diag([0.00025**2, 0.00025**2, 0.00025**2]), |
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ObservationKind.ECEF_POS: np.diag([5**2, 5**2, 5**2])} |
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name = 'live' % N |
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gen_model(name, self.dim_state, self.dim_state_err) |
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# init filter |
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self.filter = EKF_sym(name, Q, x_initial, P_initial, self.dim_state, self.dim_state_err) |
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@property |
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def x(self): |
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return self.filter.state() |
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@property |
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def t(self): |
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return self.filter.filter_time |
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@property |
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def P(self): |
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return self.filter.covs() |
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def predict(self, t): |
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return self.filter.predict(t) |
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def rts_smooth(self, estimates): |
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return self.filter.rts_smooth(estimates, norm_quats=True) |
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def init_state(self, state, covs_diag=None, covs=None, filter_time=None): |
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if covs_diag is not None: |
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P = np.diag(covs_diag) |
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elif covs is not None: |
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P = covs |
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else: |
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P = self.filter.covs() |
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self.filter.init_state(state, P, filter_time) |
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def predict_and_observe(self, t, kind, data): |
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if len(data) > 0: |
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data = np.atleast_2d(data) |
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if kind == ObservationKind.CAMERA_ODO_TRANSLATION: |
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r = self.predict_and_update_odo_trans(data, t, kind) |
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elif kind == ObservationKind.CAMERA_ODO_ROTATION: |
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r = self.predict_and_update_odo_rot(data, t, kind) |
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elif kind == ObservationKind.ODOMETRIC_SPEED: |
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r = self.predict_and_update_odo_speed(data, t, kind) |
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else: |
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r = self.filter.predict_and_update_batch(t, kind, data, self.get_R(kind, len(data))) |
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# Normalize quats |
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quat_norm = np.linalg.norm(self.filter.x[3:7,0]) |
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# Should not continue if the quats behave this weirdly |
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if not 0.1 < quat_norm < 10: |
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raise RuntimeError("Sir! The filter's gone all wobbly!") |
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self.filter.x[3:7,0] = self.filter.x[3:7,0]/quat_norm |
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return r |
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def get_R(self, kind, n): |
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obs_noise = self.obs_noise[kind] |
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dim = obs_noise.shape[0] |
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R = np.zeros((n, dim, dim)) |
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for i in range(n): |
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R[i,:,:] = obs_noise |
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return R |
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def predict_and_update_odo_speed(self, speed, t, kind): |
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z = np.array(speed) |
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R = np.zeros((len(speed), 1, 1)) |
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for i, _ in enumerate(z): |
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R[i,:,:] = np.diag([0.2**2]) |
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return self.filter.predict_and_update_batch(t, kind, z, R) |
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def predict_and_update_odo_trans(self, trans, t, kind): |
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z = trans[:,:3] |
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R = np.zeros((len(trans), 3, 3)) |
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for i, _ in enumerate(z): |
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R[i,:,:] = np.diag(trans[i,3:]**2) |
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return self.filter.predict_and_update_batch(t, kind, z, R) |
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def predict_and_update_odo_rot(self, rot, t, kind): |
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z = rot[:,:3] |
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R = np.zeros((len(rot), 3, 3)) |
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for i, _ in enumerate(z): |
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R[i,:,:] = np.diag(rot[i,3:]**2) |
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return self.filter.predict_and_update_batch(t, kind, z, R) |
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if __name__ == "__main__": |
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LiveKalman() |
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@ -0,0 +1,177 @@ |
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import numpy as np |
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import sympy as sp |
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import os |
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from laika.constants import EARTH_GM |
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from .kalman_helpers import ObservationKind |
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from .ekf_sym import gen_code |
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from common.sympy_helpers import euler_rotate, quat_rotate, quat_matrix_r |
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class States(): |
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ECEF_POS = slice(0, 3) # x, y and z in ECEF in meters |
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ECEF_ORIENTATION = slice(3, 7) # quat for pose of phone in ecef |
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ECEF_VELOCITY = slice(7, 10) # ecef velocity in m/s |
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ANGULAR_VELOCITY = slice(10, 13) # roll, pitch and yaw rates in device frame in radians/s |
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GYRO_BIAS = slice(13, 16) # roll, pitch and yaw biases |
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ODO_SCALE = slice(16, 17) # odometer scale |
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ACCELERATION = slice(17, 20) # Acceleration in device frame in m/s**2 |
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IMU_OFFSET = slice(20, 23) # imu offset angles in radians |
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ECEF_POS_ERR = slice(0, 3) |
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ECEF_ORIENTATION_ERR = slice(3, 6) |
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ECEF_VELOCITY_ERR = slice(6, 9) |
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ANGULAR_VELOCITY_ERR = slice(9, 12) |
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GYRO_BIAS_ERR = slice(12, 15) |
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ODO_SCALE_ERR = slice(15, 16) |
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ACCELERATION_ERR = slice(16, 19) |
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IMU_OFFSET_ERR = slice(19, 22) |
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def gen_model(name, |
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dim_state, dim_state_err, |
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maha_test_kinds): |
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# check if rebuild is needed |
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try: |
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dir_path = os.path.dirname(__file__) |
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deps = [dir_path + '/' + 'ekf_c.c', |
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dir_path + '/' + 'ekf_sym.py', |
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dir_path + '/' + name + '_model.py', |
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dir_path + '/' + name + '_kf.py'] |
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outs = [dir_path + '/' + name + '.o', |
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dir_path + '/' + name + '.so', |
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dir_path + '/' + name + '.cpp'] |
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out_times = list(map(os.path.getmtime, outs)) |
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dep_times = list(map(os.path.getmtime, deps)) |
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rebuild = os.getenv("REBUILD", False) |
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if min(out_times) > max(dep_times) and not rebuild: |
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return |
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list(map(os.remove, outs)) |
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except OSError: |
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pass |
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# make functions and jacobians with sympy |
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# state variables |
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state_sym = sp.MatrixSymbol('state', dim_state, 1) |
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state = sp.Matrix(state_sym) |
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x,y,z = state[States.ECEF_POS,:] |
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q = state[States.ECEF_ORIENTATION,:] |
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v = state[States.ECEF_VELOCITY,:] |
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vx, vy, vz = v |
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omega = state[States.GYRO_BIAS,:] |
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vroll, vpitch, vyaw = omega |
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roll_bias, pitch_bias, yaw_bias = state[States.GYRO_BIAS,:] |
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odo_scale = state[16,:] |
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acceleration = state[States.ACCELERATION,:] |
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imu_angles= state[States.IMU_OFFSET,:] |
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dt = sp.Symbol('dt') |
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# calibration and attitude rotation matrices |
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quat_rot = quat_rotate(*q) |
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# Got the quat predict equations from here |
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# A New Quaternion-Based Kalman Filter for |
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# Real-Time Attitude Estimation Using the Two-Step |
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# Geometrically-Intuitive Correction Algorithm |
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A = 0.5*sp.Matrix([[0, -vroll, -vpitch, -vyaw], |
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[vroll, 0, vyaw, -vpitch], |
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[vpitch, -vyaw, 0, vroll], |
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[vyaw, vpitch, -vroll, 0]]) |
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q_dot = A * q |
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# Time derivative of the state as a function of state |
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state_dot = sp.Matrix(np.zeros((dim_state, 1))) |
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state_dot[States.ECEF_POS,:] = v |
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state_dot[States.ECEF_ORIENTATION,:] = q_dot |
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state_dot[States.ECEF_VELOCITY,0] = quat_rot * acceleration |
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# Basic descretization, 1st order intergrator |
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# Can be pretty bad if dt is big |
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f_sym = state + dt*state_dot |
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state_err_sym = sp.MatrixSymbol('state_err',dim_state_err,1) |
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state_err = sp.Matrix(state_err_sym) |
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quat_err = state_err[States.ECEF_ORIENTATION_ERR,:] |
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v_err = state_err[States.ECEF_VELOCITY_ERR,:] |
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omega_err = state_err[States.ANGULAR_VELOCITY_ERR,:] |
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acceleration_err = state_err[States.ACCELERATION_ERR,:] |
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# Time derivative of the state error as a function of state error and state |
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quat_err_matrix = euler_rotate(quat_err[0], quat_err[1], quat_err[2]) |
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q_err_dot = quat_err_matrix * quat_rot * (omega + omega_err) |
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state_err_dot = sp.Matrix(np.zeros((dim_state_err, 1))) |
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state_err_dot[States.ECEF_POS_ERR,:] = v_err |
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state_err_dot[States.ECEF_ORIENTATION_ERR,:] = q_err_dot |
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state_err_dot[States.ECEF_VELOCITY_ERR,:] = quat_err_matrix * quat_rot * (acceleration + acceleration_err) |
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f_err_sym = state_err + dt*state_err_dot |
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# Observation matrix modifier |
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H_mod_sym = sp.Matrix(np.zeros((dim_state, dim_state_err))) |
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H_mod_sym[0:3, 0:3] = np.eye(3) |
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H_mod_sym[3:7,3:6] = 0.5*quat_matrix_r(state[3:7])[:,1:] |
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# these error functions are defined so that say there |
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# is a nominal x and true x: |
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# true x = err_function(nominal x, delta x) |
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# delta x = inv_err_function(nominal x, true x) |
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nom_x = sp.MatrixSymbol('nom_x',dim_state,1) |
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true_x = sp.MatrixSymbol('true_x',dim_state,1) |
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delta_x = sp.MatrixSymbol('delta_x',dim_state_err,1) |
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err_function_sym = sp.Matrix(np.zeros((dim_state,1))) |
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delta_quat = sp.Matrix(np.ones((4))) |
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delta_quat[1:,:] = sp.Matrix(0.5*delta_x[3:6,:]) |
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err_function_sym[3:7,0] = quat_matrix_r(nom_x[3:6,0])*delta_quat |
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err_function_sym[0:3,:] = sp.Matrix(nom_x[0:3,:] + delta_x[0:3,:]) |
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inv_err_function_sym = sp.Matrix(np.zeros((dim_state_err,1))) |
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inv_err_function_sym[0:3,0] = sp.Matrix(-nom_x[0:3,0] + true_x[0:3,0]) |
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delta_quat = quat_matrix_r(nom_x[3:7,0]).T*true_x[3:7,0] |
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inv_err_function_sym[3:6,0] = sp.Matrix(2*delta_quat[1:]) |
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eskf_params = [[err_function_sym, nom_x, delta_x], |
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[inv_err_function_sym, nom_x, true_x], |
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H_mod_sym, f_err_sym, state_err_sym] |
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# |
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# Observation functions |
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# |
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imu_rot = euler_rotate(*imu_angles) |
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h_gyro_sym = imu_rot*sp.Matrix([vroll + roll_bias, |
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vpitch + pitch_bias, |
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vyaw + yaw_bias]) |
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pos = sp.Matrix([x, y, z]) |
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gravity = quat_rot.T * ((EARTH_GM/((x**2 + y**2 + z**2)**(3.0/2.0)))*pos) |
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h_acc_sym = imu_rot*(gravity + acceleration) |
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h_phone_rot_sym = sp.Matrix([vroll, |
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vpitch, |
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vyaw]) |
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speed = vx**2 + vy**2 + vz**2 |
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h_speed_sym = sp.Matrix([sp.sqrt(speed)*odo_scale]) |
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h_pos_sym = sp.Matrix([x, y, z]) |
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h_imu_frame_sym = sp.Matrix(imu_angles) |
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h_relative_motion = sp.Matrix(quat_rot.T * v) |
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obs_eqs = [[h_speed_sym, ObservationKind.ODOMETRIC_SPEED, None], |
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[h_gyro_sym, ObservationKind.PHONE_GYRO, None], |
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[h_phone_rot_sym, ObservationKind.NO_ROT, None], |
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[h_acc_sym, ObservationKind.PHONE_ACCEL, None], |
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[h_pos_sym, ObservationKind.ECEF_POS, None], |
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[h_relative_motion, ObservationKind.CAMERA_ODO_TRANSLATION, None], |
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[h_phone_rot_sym, ObservationKind.CAMERA_ODO_ROTATION, None], |
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[h_imu_frame_sym, ObservationKind.IMU_FRAME, None]] |
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gen_code(name, f_sym, dt, state_sym, obs_eqs, dim_state, dim_state_err, eskf_params) |
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