#!/usr/bin/env python3 import sys import numpy as np import sympy as sp from selfdrive.locationd.models.constants import ObservationKind from rednose.helpers import KalmanError from rednose.helpers.ekf_sym import EKF_sym, gen_code from rednose.helpers.sympy_helpers import euler_rotate, quat_matrix_r, quat_rotate EARTH_GM = 3.986005e14 # m^3/s^2 (gravitational constant * mass of earth) class States(): ECEF_POS = slice(0, 3) # x, y and z in ECEF in meters ECEF_ORIENTATION = slice(3, 7) # quat for pose of phone in ecef ECEF_VELOCITY = slice(7, 10) # ecef velocity in m/s ANGULAR_VELOCITY = slice(10, 13) # roll, pitch and yaw rates in device frame in radians/s GYRO_BIAS = slice(13, 16) # roll, pitch and yaw biases ODO_SCALE = slice(16, 17) # odometer scale ACCELERATION = slice(17, 20) # Acceleration in device frame in m/s**2 IMU_OFFSET = slice(20, 23) # imu offset angles in radians # Error-state has different slices because it is an ESKF ECEF_POS_ERR = slice(0, 3) ECEF_ORIENTATION_ERR = slice(3, 6) # euler angles for orientation error ECEF_VELOCITY_ERR = slice(6, 9) ANGULAR_VELOCITY_ERR = slice(9, 12) GYRO_BIAS_ERR = slice(12, 15) ODO_SCALE_ERR = slice(15, 16) ACCELERATION_ERR = slice(16, 19) IMU_OFFSET_ERR = slice(19, 22) class LiveKalman(): name = 'live' initial_x = np.array([-2.7e6, 4.2e6, 3.8e6, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]) # state covariance initial_P_diag = np.array([10000**2, 10000**2, 10000**2, 10**2, 10**2, 10**2, 10**2, 10**2, 10**2, 1**2, 1**2, 1**2, 0.05**2, 0.05**2, 0.05**2, 0.02**2, 1**2, 1**2, 1**2, (0.01)**2, (0.01)**2, (0.01)**2]) # process noise Q = np.diag([0.03**2, 0.03**2, 0.03**2, 0.0**2, 0.0**2, 0.0**2, 0.0**2, 0.0**2, 0.0**2, 0.1**2, 0.1**2, 0.1**2, (0.005 / 100)**2, (0.005 / 100)**2, (0.005 / 100)**2, (0.02 / 100)**2, 3**2, 3**2, 3**2, (0.05 / 60)**2, (0.05 / 60)**2, (0.05 / 60)**2]) @staticmethod def generate_code(generated_dir): name = LiveKalman.name dim_state = LiveKalman.initial_x.shape[0] dim_state_err = LiveKalman.initial_P_diag.shape[0] state_sym = sp.MatrixSymbol('state', dim_state, 1) state = sp.Matrix(state_sym) x, y, z = state[States.ECEF_POS, :] q = state[States.ECEF_ORIENTATION, :] v = state[States.ECEF_VELOCITY, :] vx, vy, vz = v omega = state[States.ANGULAR_VELOCITY, :] vroll, vpitch, vyaw = omega roll_bias, pitch_bias, yaw_bias = state[States.GYRO_BIAS, :] odo_scale = state[States.ODO_SCALE, :][0,:] acceleration = state[States.ACCELERATION, :] imu_angles = state[States.IMU_OFFSET, :] dt = sp.Symbol('dt') # calibration and attitude rotation matrices quat_rot = quat_rotate(*q) # Got the quat predict equations from here # A New Quaternion-Based Kalman Filter for # Real-Time Attitude Estimation Using the Two-Step # Geometrically-Intuitive Correction Algorithm A = 0.5 * sp.Matrix([[0, -vroll, -vpitch, -vyaw], [vroll, 0, vyaw, -vpitch], [vpitch, -vyaw, 0, vroll], [vyaw, vpitch, -vroll, 0]]) q_dot = A * q # Time derivative of the state as a function of state state_dot = sp.Matrix(np.zeros((dim_state, 1))) state_dot[States.ECEF_POS, :] = v state_dot[States.ECEF_ORIENTATION, :] = q_dot state_dot[States.ECEF_VELOCITY, 0] = quat_rot * acceleration # Basic descretization, 1st order intergrator # Can be pretty bad if dt is big f_sym = state + dt * state_dot state_err_sym = sp.MatrixSymbol('state_err', dim_state_err, 1) state_err = sp.Matrix(state_err_sym) quat_err = state_err[States.ECEF_ORIENTATION_ERR, :] v_err = state_err[States.ECEF_VELOCITY_ERR, :] omega_err = state_err[States.ANGULAR_VELOCITY_ERR, :] acceleration_err = state_err[States.ACCELERATION_ERR, :] # Time derivative of the state error as a function of state error and state quat_err_matrix = euler_rotate(quat_err[0], quat_err[1], quat_err[2]) q_err_dot = quat_err_matrix * quat_rot * (omega + omega_err) state_err_dot = sp.Matrix(np.zeros((dim_state_err, 1))) state_err_dot[States.ECEF_POS_ERR, :] = v_err state_err_dot[States.ECEF_ORIENTATION_ERR, :] = q_err_dot state_err_dot[States.ECEF_VELOCITY_ERR, :] = quat_err_matrix * quat_rot * (acceleration + acceleration_err) f_err_sym = state_err + dt * state_err_dot # Observation matrix modifier H_mod_sym = sp.Matrix(np.zeros((dim_state, dim_state_err))) H_mod_sym[States.ECEF_POS, States.ECEF_POS_ERR] = np.eye(States.ECEF_POS.stop - States.ECEF_POS.start) H_mod_sym[States.ECEF_ORIENTATION, States.ECEF_ORIENTATION_ERR] = 0.5 * quat_matrix_r(state[3:7])[:, 1:] H_mod_sym[States.ECEF_ORIENTATION.stop:, States.ECEF_ORIENTATION_ERR.stop:] = np.eye(dim_state - States.ECEF_ORIENTATION.stop) # these error functions are defined so that say there # is a nominal x and true x: # true x = err_function(nominal x, delta x) # delta x = inv_err_function(nominal x, true x) nom_x = sp.MatrixSymbol('nom_x', dim_state, 1) true_x = sp.MatrixSymbol('true_x', dim_state, 1) delta_x = sp.MatrixSymbol('delta_x', dim_state_err, 1) err_function_sym = sp.Matrix(np.zeros((dim_state, 1))) delta_quat = sp.Matrix(np.ones((4))) delta_quat[1:, :] = sp.Matrix(0.5 * delta_x[States.ECEF_ORIENTATION_ERR, :]) err_function_sym[States.ECEF_POS, :] = sp.Matrix(nom_x[States.ECEF_POS, :] + delta_x[States.ECEF_POS_ERR, :]) err_function_sym[States.ECEF_ORIENTATION, 0] = quat_matrix_r(nom_x[States.ECEF_ORIENTATION, 0]) * delta_quat err_function_sym[States.ECEF_ORIENTATION.stop:, :] = sp.Matrix(nom_x[States.ECEF_ORIENTATION.stop:, :] + delta_x[States.ECEF_ORIENTATION_ERR.stop:, :]) inv_err_function_sym = sp.Matrix(np.zeros((dim_state_err, 1))) inv_err_function_sym[States.ECEF_POS_ERR, 0] = sp.Matrix(-nom_x[States.ECEF_POS, 0] + true_x[States.ECEF_POS, 0]) delta_quat = quat_matrix_r(nom_x[States.ECEF_ORIENTATION, 0]).T * true_x[States.ECEF_ORIENTATION, 0] inv_err_function_sym[States.ECEF_ORIENTATION_ERR, 0] = sp.Matrix(2 * delta_quat[1:]) inv_err_function_sym[States.ECEF_ORIENTATION_ERR.stop:, 0] = sp.Matrix(-nom_x[States.ECEF_ORIENTATION.stop:, 0] + true_x[States.ECEF_ORIENTATION.stop:, 0]) eskf_params = [[err_function_sym, nom_x, delta_x], [inv_err_function_sym, nom_x, true_x], H_mod_sym, f_err_sym, state_err_sym] # # Observation functions # imu_rot = euler_rotate(*imu_angles) h_gyro_sym = imu_rot * sp.Matrix([vroll + roll_bias, vpitch + pitch_bias, vyaw + yaw_bias]) pos = sp.Matrix([x, y, z]) gravity = quat_rot.T * ((EARTH_GM / ((x**2 + y**2 + z**2)**(3.0 / 2.0))) * pos) h_acc_sym = imu_rot * (gravity + acceleration) h_phone_rot_sym = sp.Matrix([vroll, vpitch, vyaw]) speed = sp.sqrt(vx**2 + vy**2 + vz**2) h_speed_sym = sp.Matrix([speed * odo_scale]) h_pos_sym = sp.Matrix([x, y, z]) h_imu_frame_sym = sp.Matrix(imu_angles) h_relative_motion = sp.Matrix(quat_rot.T * v) obs_eqs = [[h_speed_sym, ObservationKind.ODOMETRIC_SPEED, None], [h_gyro_sym, ObservationKind.PHONE_GYRO, None], [h_phone_rot_sym, ObservationKind.NO_ROT, None], [h_acc_sym, ObservationKind.PHONE_ACCEL, None], [h_pos_sym, ObservationKind.ECEF_POS, None], [h_relative_motion, ObservationKind.CAMERA_ODO_TRANSLATION, None], [h_phone_rot_sym, ObservationKind.CAMERA_ODO_ROTATION, None], [h_imu_frame_sym, ObservationKind.IMU_FRAME, None]] gen_code(generated_dir, name, f_sym, dt, state_sym, obs_eqs, dim_state, dim_state_err, eskf_params) def __init__(self, generated_dir): self.dim_state = self.initial_x.shape[0] self.dim_state_err = self.initial_P_diag.shape[0] self.obs_noise = {ObservationKind.ODOMETRIC_SPEED: np.atleast_2d(0.2**2), ObservationKind.PHONE_GYRO: np.diag([0.025**2, 0.025**2, 0.025**2]), ObservationKind.PHONE_ACCEL: np.diag([.5**2, .5**2, .5**2]), ObservationKind.CAMERA_ODO_ROTATION: np.diag([0.05**2, 0.05**2, 0.05**2]), ObservationKind.IMU_FRAME: np.diag([0.05**2, 0.05**2, 0.05**2]), ObservationKind.NO_ROT: np.diag([0.00025**2, 0.00025**2, 0.00025**2]), ObservationKind.ECEF_POS: np.diag([5**2, 5**2, 5**2])} # init filter self.filter = EKF_sym(generated_dir, self.name, self.Q, self.initial_x, np.diag(self.initial_P_diag), self.dim_state, self.dim_state_err) @property def x(self): return self.filter.state() @property def t(self): return self.filter.filter_time @property def P(self): return self.filter.covs() def rts_smooth(self, estimates): return self.filter.rts_smooth(estimates, norm_quats=True) def init_state(self, state, covs_diag=None, covs=None, filter_time=None): if covs_diag is not None: P = np.diag(covs_diag) elif covs is not None: P = covs else: P = self.filter.covs() self.filter.init_state(state, P, filter_time) def predict_and_observe(self, t, kind, data): if len(data) > 0: data = np.atleast_2d(data) if kind == ObservationKind.CAMERA_ODO_TRANSLATION: r = self.predict_and_update_odo_trans(data, t, kind) elif kind == ObservationKind.CAMERA_ODO_ROTATION: r = self.predict_and_update_odo_rot(data, t, kind) elif kind == ObservationKind.ODOMETRIC_SPEED: r = self.predict_and_update_odo_speed(data, t, kind) else: r = self.filter.predict_and_update_batch(t, kind, data, self.get_R(kind, len(data))) # Normalize quats quat_norm = np.linalg.norm(self.filter.x[3:7, 0]) # Should not continue if the quats behave this weirdly if not (0.1 < quat_norm < 10): raise KalmanError("Kalman filter quaternions unstable") self.filter.x[States.ECEF_ORIENTATION, 0] = self.filter.x[States.ECEF_ORIENTATION, 0] / quat_norm return r def get_R(self, kind, n): obs_noise = self.obs_noise[kind] dim = obs_noise.shape[0] R = np.zeros((n, dim, dim)) for i in range(n): R[i, :, :] = obs_noise return R def predict_and_update_odo_speed(self, speed, t, kind): z = np.array(speed) R = np.zeros((len(speed), 1, 1)) for i, _ in enumerate(z): R[i, :, :] = np.diag([0.2**2]) return self.filter.predict_and_update_batch(t, kind, z, R) def predict_and_update_odo_trans(self, trans, t, kind): z = trans[:, :3] R = np.zeros((len(trans), 3, 3)) for i, _ in enumerate(z): R[i, :, :] = np.diag(trans[i, 3:]**2) return self.filter.predict_and_update_batch(t, kind, z, R) def predict_and_update_odo_rot(self, rot, t, kind): z = rot[:, :3] R = np.zeros((len(rot), 3, 3)) for i, _ in enumerate(z): R[i, :, :] = np.diag(rot[i, 3:]**2) return self.filter.predict_and_update_batch(t, kind, z, R) if __name__ == "__main__": generated_dir = sys.argv[2] LiveKalman.generate_code(generated_dir)