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284 lines
12 KiB
284 lines
12 KiB
#!/usr/bin/env python3
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import numpy as np
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import sympy as sp
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from selfdrive.locationd.kalman.helpers import KalmanError, ObservationKind
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from selfdrive.locationd.kalman.helpers.ekf_sym import EKF_sym, gen_code
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from selfdrive.locationd.kalman.helpers.sympy_helpers import (euler_rotate,
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quat_matrix_r,
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quat_rotate)
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from selfdrive.swaglog import cloudlog
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EARTH_GM = 3.986005e14 # m^3/s^2 (gravitational constant * mass of earth)
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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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# Error-state has different slices because it is an ESKF
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ECEF_POS_ERR = slice(0, 3)
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ECEF_ORIENTATION_ERR = slice(3, 6) # euler angles for orientation error
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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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class LiveKalman():
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name = 'live'
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initial_x = 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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initial_P_diag = np.array([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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(0.05 / 60)**2, (0.05 / 60)**2, (0.05 / 60)**2])
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@staticmethod
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def generate_code():
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name = LiveKalman.name
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dim_state = LiveKalman.initial_x.shape[0]
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dim_state_err = LiveKalman.initial_P_diag.shape[0]
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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.ANGULAR_VELOCITY, :]
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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[States.ODO_SCALE, :][0,:]
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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[States.ECEF_POS, States.ECEF_POS_ERR] = np.eye(States.ECEF_POS.stop - States.ECEF_POS.start)
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H_mod_sym[States.ECEF_ORIENTATION, States.ECEF_ORIENTATION_ERR] = 0.5 * quat_matrix_r(state[3:7])[:, 1:]
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H_mod_sym[States.ECEF_ORIENTATION.stop:, States.ECEF_ORIENTATION_ERR.stop:] = np.eye(dim_state - States.ECEF_ORIENTATION.stop)
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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[States.ECEF_ORIENTATION_ERR, :])
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err_function_sym[States.ECEF_POS, :] = sp.Matrix(nom_x[States.ECEF_POS, :] + delta_x[States.ECEF_POS_ERR, :])
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err_function_sym[States.ECEF_ORIENTATION, 0] = quat_matrix_r(nom_x[States.ECEF_ORIENTATION, 0]) * delta_quat
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err_function_sym[States.ECEF_ORIENTATION.stop:, :] = sp.Matrix(nom_x[States.ECEF_ORIENTATION.stop:, :] + delta_x[States.ECEF_ORIENTATION_ERR.stop:, :])
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inv_err_function_sym = sp.Matrix(np.zeros((dim_state_err, 1)))
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inv_err_function_sym[States.ECEF_POS_ERR, 0] = sp.Matrix(-nom_x[States.ECEF_POS, 0] + true_x[States.ECEF_POS, 0])
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delta_quat = quat_matrix_r(nom_x[States.ECEF_ORIENTATION, 0]).T * true_x[States.ECEF_ORIENTATION, 0]
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inv_err_function_sym[States.ECEF_ORIENTATION_ERR, 0] = sp.Matrix(2 * delta_quat[1:])
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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])
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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, vpitch, vyaw])
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speed = sp.sqrt(vx**2 + vy**2 + vz**2)
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h_speed_sym = sp.Matrix([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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def __init__(self):
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self.dim_state = self.initial_x.shape[0]
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self.dim_state_err = self.initial_P_diag.shape[0]
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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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# init filter
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self.filter = EKF_sym(self.name, self.Q, self.initial_x, np.diag(self.initial_P_diag), 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 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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cloudlog.error("Kalman filter quaternions unstable")
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raise KalmanError
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self.filter.x[States.ECEF_ORIENTATION, 0] = self.filter.x[States.ECEF_ORIENTATION, 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.generate_code()
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