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EKF2 simplify covariance propagation (#22344)

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* ekf2-derivation: optimize before generating cpp code

* update EKF2 change indicator

Slight changes due to simplifications done in the covariance prediction

---------

Co-authored-by: bresch <[brescianimathieu@gmail.com](mailto:brescianimathieu@gmail.com)>
This commit is contained in:
Mathieu Bresciani 2023-11-14 17:22:16 +01:00 committed by GitHub
parent 96e05481b4
commit efa12ad224
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5 changed files with 571 additions and 757 deletions
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13
src/modules/ekf2/EKF/covariance.cpp
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@ -108,27 +108,28 @@ void Ekf::predictCovariance(const imuSample &imu_delayed)
// delta angle noise variance // delta angle noise variance
float gyro_noise = math::constrain(_params.gyro_noise, 0.f, 1.f); float gyro_noise = math::constrain(_params.gyro_noise, 0.f, 1.f);
const float d_ang_var = sq(imu_delayed.delta_ang_dt * gyro_noise); const float gyro_var = sq(gyro_noise);
// delta velocity noise variance // delta velocity noise variance
float accel_noise = math::constrain(_params.accel_noise, 0.f, 1.f); float accel_noise = math::constrain(_params.accel_noise, 0.f, 1.f);
Vector3f d_vel_var; Vector3f accel_var;
for (unsigned i = 0; i < 3; i++) { for (unsigned i = 0; i < 3; i++) {
if (_fault_status.flags.bad_acc_vertical || imu_delayed.delta_vel_clipping[i]) { if (_fault_status.flags.bad_acc_vertical || imu_delayed.delta_vel_clipping[i]) {
// Increase accelerometer process noise if bad accel data is detected // Increase accelerometer process noise if bad accel data is detected
d_vel_var(i) = sq(imu_delayed.delta_vel_dt * BADACC_BIAS_PNOISE); accel_var(i) = sq(BADACC_BIAS_PNOISE);
} else { } else {
d_vel_var(i) = sq(imu_delayed.delta_vel_dt * accel_noise); accel_var(i) = sq(accel_noise);
} }
} }
// predict the covariance // predict the covariance
// calculate variances and upper diagonal covariances for quaternion, velocity, position and gyro bias states // calculate variances and upper diagonal covariances for quaternion, velocity, position and gyro bias states
P = sym::PredictCovariance(_state.vector(), P, P = sym::PredictCovariance(_state.vector(), P,
imu_delayed.delta_vel, imu_delayed.delta_vel_dt, d_vel_var, imu_delayed.delta_vel / math::max(imu_delayed.delta_vel_dt, FLT_EPSILON), accel_var,
imu_delayed.delta_ang, imu_delayed.delta_ang_dt, d_ang_var); imu_delayed.delta_ang / math::max(imu_delayed.delta_ang_dt, FLT_EPSILON), gyro_var,
0.5f * (imu_delayed.delta_vel_dt + imu_delayed.delta_ang_dt));
// Construct the process noise variance diagonal for those states with a stationary process model // Construct the process noise variance diagonal for those states with a stationary process model
// These are kinematic states and their error growth is controlled separately by the IMU noise variances // These are kinematic states and their error growth is controlled separately by the IMU noise variances

51
src/modules/ekf2/EKF/python/ekf_derivation/derivation.py
View File

@ -31,6 +31,10 @@
File: derivation.py File: derivation.py
Description: Description:
Derivation of an error-state EKF based on
Sola, Joan. "Quaternion kinematics for the error-state Kalman filter." arXiv preprint arXiv:1711.02508 (2017).
The derivation is directly done in discrete-time as this allows us to define the desired type of discretization
for each element while defining the equations (easier than a continuous-time derivation followed by a block-wise discretization).
""" """
import argparse import argparse
@ -42,6 +46,8 @@ import symforce.symbolic as sf
from symforce import typing as T from symforce import typing as T
from symforce import ops from symforce import ops
from symforce.values import Values from symforce.values import Values
import sympy as sp
from derivation_utils import * from derivation_utils import *
# Initialize parser # Initialize parser
@ -108,12 +114,11 @@ def vstate_to_state(v: VState):
def predict_covariance( def predict_covariance(
state: VState, state: VState,
P: MTangent, P: MTangent,
d_vel: sf.V3, accel: sf.V3,
d_vel_dt: sf.Scalar, accel_var: sf.V3,
d_vel_var: sf.V3, gyro: sf.V3,
d_ang: sf.V3, gyro_var: sf.Scalar,
d_ang_dt: sf.Scalar, dt: sf.Scalar
d_ang_var: sf.Scalar
) -> MTangent: ) -> MTangent:
state = vstate_to_state(state) state = vstate_to_state(state)
@ -143,37 +148,37 @@ def predict_covariance(
for key in state.keys(): for key in state.keys():
if key == "quat_nominal": if key == "quat_nominal":
# Create true quaternion using small angle approximation of the error rotation # Create true quaternion using small angle approximation of the error rotation
state_t["quat_nominal"] = state["quat_nominal"] * sf.Rot3(sf.Quaternion(xyz=(0.5 * state_error["theta"]), w=1)) state_t["quat_nominal"] = state["quat_nominal"] * sf.Rot3(sf.Quaternion(xyz=(state_error["theta"] / 2), w=1))
else: else:
state_t[key] = state[key] + state_error[key] state_t[key] = state[key] + state_error[key]
noise = Values( noise = Values(
d_vel = sf.V3.symbolic("a_n"), accel = sf.V3.symbolic("a_n"),
d_ang = sf.V3.symbolic("w_n"), gyro = sf.V3.symbolic("w_n"),
) )
input_t = Values( input_t = Values(
d_vel = d_vel - state_t["accel_bias"] * d_vel_dt - noise["d_vel"], accel = accel - state_t["accel_bias"] - noise["accel"],
d_ang = d_ang - state_t["gyro_bias"] * d_ang_dt - noise["d_ang"] gyro = gyro - state_t["gyro_bias"] - noise["gyro"]
) )
R_t = state_t["quat_nominal"] R_t = state_t["quat_nominal"]
state_t_pred = state_t.copy() state_t_pred = state_t.copy()
state_t_pred["quat_nominal"] = state_t["quat_nominal"] * sf.Rot3(sf.Quaternion(xyz=(0.5 * input_t["d_ang"]), w=1)) state_t_pred["quat_nominal"] = state_t["quat_nominal"] * sf.Rot3(sf.Quaternion(xyz=(input_t["gyro"] * dt / 2), w=1))
state_t_pred["vel"] = state_t["vel"] + R_t * input_t["d_vel"] + sf.V3(0, 0, g) * d_vel_dt state_t_pred["vel"] = state_t["vel"] + (R_t * input_t["accel"] + sf.V3(0, 0, g)) * dt
state_t_pred["pos"] = state_t["pos"] + state_t["vel"] * d_vel_dt state_t_pred["pos"] = state_t["pos"] + state_t["vel"] * dt
# Nominal state kinematics # Nominal state kinematics
input = Values( input = Values(
d_vel = d_vel - state["accel_bias"] * d_vel_dt, accel = accel - state["accel_bias"],
d_ang = d_ang - state["gyro_bias"] * d_ang_dt gyro = gyro - state["gyro_bias"]
) )
R = state["quat_nominal"] R = state["quat_nominal"]
state_pred = state.copy() state_pred = state.copy()
state_pred["quat_nominal"] = state["quat_nominal"] * sf.Rot3(sf.Quaternion(xyz=(0.5 * input["d_ang"]), w=1)) state_pred["quat_nominal"] = state["quat_nominal"] * sf.Rot3(sf.Quaternion(xyz=(input["gyro"] * dt / 2), w=1))
state_pred["vel"] = state["vel"] + R * input["d_vel"] + sf.V3(0, 0, g) * d_vel_dt state_pred["vel"] = state["vel"] + (R * input["accel"] + sf.V3(0, 0, g)) * dt
state_pred["pos"] = state["pos"] + state["vel"] * d_vel_dt state_pred["pos"] = state["pos"] + state["vel"] * dt
# Error state kinematics # Error state kinematics
state_error_pred = Values() state_error_pred = Values()
@ -184,6 +189,12 @@ def predict_covariance(
else: else:
state_error_pred[key] = state_t_pred[key] - state_pred[key] state_error_pred[key] = state_t_pred[key] - state_pred[key]
# Simplify angular error state prediction
for i in range(state_error_pred["theta"].storage_dim()):
state_error_pred["theta"][i] = sp.expand(state_error_pred["theta"][i]).subs(dt**2, 0) # do not consider dt**2 effects in the derivation
q_est = sf.Quaternion.from_storage(state["quat_nominal"].to_storage())
state_error_pred["theta"][i] = sp.factor(state_error_pred["theta"][i]).subs(q_est.w**2 + q_est.x**2 + q_est.y**2 + q_est.z**2, 1) # unit norm quaternion
zero_state_error = {state_error[key]: state_error[key].zero() for key in state_error.keys()} zero_state_error = {state_error[key]: state_error[key].zero() for key in state_error.keys()}
zero_noise = {noise[key]: noise[key].zero() for key in noise.keys()} zero_noise = {noise[key]: noise[key].zero() for key in noise.keys()}
@ -192,7 +203,7 @@ def predict_covariance(
G = VTangent(state_error_pred.to_storage()).jacobian(noise).subs(zero_state_error).subs(zero_noise) G = VTangent(state_error_pred.to_storage()).jacobian(noise).subs(zero_state_error).subs(zero_noise)
# Covariance propagation # Covariance propagation
var_u = sf.Matrix.diag([d_vel_var[0], d_vel_var[1], d_vel_var[2], d_ang_var, d_ang_var, d_ang_var]) var_u = sf.Matrix.diag([accel_var[0], accel_var[1], accel_var[2], gyro_var, gyro_var, gyro_var])
P_new = A * P * A.T + G * var_u * G.T P_new = A * P * A.T + G * var_u * G.T
# Generate the equations for the upper triangular matrix and the diagonal only # Generate the equations for the upper triangular matrix and the diagonal only

1028
src/modules/ekf2/EKF/python/ekf_derivation/generated/predict_covariance.h
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File diff suppressed because it is too large Load Diff

214
src/modules/ekf2/test/change_indication/ekf_gsf_reset.csv
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22
src/modules/ekf2/test/change_indication/iris_gps.csv
View File

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