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177 lines
6.4 KiB
177 lines
6.4 KiB
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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