IKFoM (Iterated Kalman Filters on Manifolds) is a computationally efficient and convenient toolkit for deploying iterated Kalman filters on various robotic systems, especially systems operating on high-dimension manifold. It implements a manifold-embedding Kalman filter which separates the manifold structures from system descriptions and is able to be used by only defining the system in a canonical form and calling the respective steps accordingly. The current implementation supports the full iterated Kalman filtering for systems on manifold and any of its sub-manifolds, and it is extendable to other types of manifold when necessary.
Developers
Our related video: https://youtu.be/sz_ZlDkl6fA Our related paper: Symbolic Representation and Toolkit Development of Iterated Error-State Extended Kalman Filters on Manifolds, published on IEEE Transcations on Industrial Electronics, Early access: DOI: 10.1109/TIE.2023.3237872
Eigen >= 3.3.4, Follow Eigen Installation.
Boost >= 1.65.
Clone the repository:
git clone https://github.com/hku-mars/IKFoM.git
- include the necessary head file:
#include<esekfom/esekfom.hpp>
- Select and instantiate the primitive manifolds:
typedef MTK::SO3<double> SO3; // scalar type of variable: double
typedef MTK::vect<3, double> vect3; // dimension of the defined Euclidean variable: 3
typedef MTK::S2<double, 98, 10, 1> S2; // length of the S2 variable: 98/10; choose e1 as the original point of rotation: 1
- Build system state, input and measurement as compound manifolds which are composed of the primitive manifolds:
MTK_BUILD_MANIFOLD(state, // name of compound manifold: state
((vect3, pos)) // ((primitive manifold type, name of variable))
((vect3, vel))
((SO3, rot))
((vect3, bg))
((vect3, ba))
((S2, grav))
((SO3, offset_R_L_I))
((vect3, offset_T_L_I))
);
- Implement the vector field
that is defined as , and its differentiation
,
, where w=0 could be left out:
Eigen::Matrix<double, state_length, 1> f(state &s, const input &i) {
Eigen::Matrix<double, state_length, 1> res = Eigen::Matrix<double, state_length, 1>::Zero();
res(0) = s.vel[0];
res(1) = s.vel[1];
res(2) = s.vel[2];
return res;
}
Eigen::Matrix<double, state_length, state_dof> df_dx(state &s, const input &i) //notice S2 has length of 3 and dimension of 2 {
Eigen::Matrix<double, state_length, state_dof> cov = Eigen::Matrix<double, state_length, state_dof>::Zero();
cov.template block<3, 3>(0, 12) = Eigen::Matrix3d::Identity();
return cov;
}
Eigen::Matrix<double, state_length, process_noise_dof> df_dw(state &s, const input &i) {
Eigen::Matrix<double, state_length, process_noise_dof> cov = Eigen::Matrix<double, state_length, process_noise_dof>::Zero();
cov.template block<3, 3>(12, 3) = -s.rot.toRotationMatrix();
return cov;
}
Those functions would be called during the ekf state predict
- Implement the output equation
and its differentiation
,
:
measurement h(state &s, bool &valid) // the iteration stops before convergence whenever the user set valid as false
{
if (condition){ valid = false;
} // other conditions could be used to stop the ekf update iteration before convergence, otherwise the iteration will not stop until the condition of convergence is satisfied.
measurement h_;
h_.position = s.pos;
return h_;
}
Eigen::Matrix<double, measurement_dof, state_dof> dh_dx(state &s, bool &valid) {}
Eigen::Matrix<double, measurement_dof, measurement_noise_dof> dh_dv(state &s, bool &valid) {}
Those functions would be called during the ekf state update
- Instantiate an esekf object kf and initialize it with initial or default state and covariance.
(1) initial state and covariance:
state init_state;
esekfom::esekf<state, process_noise_dof, input, measurement, measurement_noise_dof>::cov init_P;
esekfom::esekf<state, process_noise_dof, input, measurement, measurement_noise_dof> kf(init_state,init_P);
(2) default state and covariance:
esekfom::esekf<state, process_noise_dof, input, measurement, measurement_noise_dof> kf;
where process_noise_dof is the dimension of process noise, with the type of std int, and so for measurement_noise_dof.
- Deliver the defined models, std int maximum iteration numbers Maximum_iter, and the std array for testing convergence epsi into the esekf object:
double epsi[state_dof] = {0.001};
fill(epsi, epsi+state_dof, 0.001); // if the absolute of innovation of ekf update is smaller than epso, the update iteration is converged
kf.init(f, df_dx, df_dw, h, dh_dx, dh_dv, Maximum_iter, epsi);
- In the running time, once an input in or a measurement z is received dt after the last propagation or update, a propagation is executed:
kf.predict(dt, Q, in); // process noise covariance: Q, an Eigen matrix
- Once a measurement z is received, an iterated update is executed:
kf.update_iterated(z, R); // measurement noise covariance: R, an Eigen matrix
Remarks(1):
- We also combine the output equation and its differentiation into an union function, whose usage is the same as the above steps 1-4, and steps 5-9 are shown as follows.
- Implement the output equation
measurement h_share(state &s, esekfom::share_datastruct<state, measurement, measurement_noise_dof> &share_data)
{
if(share_data.converge) {} // this value is true means iteration is converged
if(condition) share_data.valid = false; // the iteration stops before convergence when this value is false if other conditions are satified
share_data.h_x = H_x; // H_x is the result matrix of the first differentiation
share_data.h_v = H_v; // H_v is the result matrix of the second differentiation
share_data.R = R; // R is the measurement noise covariance
share_data.z = z; // z is the obtained measurement
measurement h_;
h_.position = s.pos;
return h_;
}
This function would be called during ekf state update, and the output function and its derivatives, the measurement and the measurement noise would be obtained from this one union function
- Instantiate an esekf object kf and initialize it with initial or default state and covariance.
(1) initial state and covariance:
state init_state;
esekfom::esekf<state, process_noise_dof, input, measurement, measurement_noise_dof>::cov init_P;
esekfom::esekf<state, process_noise_dof, input, measurement, measurement_noise_dof> kf(init_state,init_P);
(2) default state and covariance:
esekfom::esekf<state, process_noise_dof, input, measurement, measurement_noise_dof> kf;
- Deliver the defined models, std int maximum iteration numbers Maximum_iter, and the std array for testing convergence epsi into the esekf object:
double epsi[state_dof] = {0.001};
fill(epsi, epsi+state_dof, 0.001); // if the absolute of innovation of ekf update is smaller than epso, the update iteration is converged
kf.init_share(f, df_dx, df_dw, h_share, Maximum_iter, epsi);
- In the running time, once an input in or a measurement z is received dt after the last propagation or update, a propagation is executed:
kf.predict(dt, Q, in); // process noise covariance: Q
- Once a measurement z is received, an iterated update is executed:
kf.update_iterated_share();
Remarks(2):
- The value of the state x and the covariance P are able to be changed by functions change_x() and change_P():
state set_x;
kf.change_x(set_x);
esekfom::esekf<state, process_noise_dof, input, measurement, measurement_noise_dof>::cov set_P;
kf.change_P(set_P);
Clone the repository:
git clone https://github.com/hku-mars/IKFoM.git
- include the necessary head file:
#include<esekfom/esekfom.hpp>
- Select and instantiate the primitive manifolds:
typedef MTK::SO3<double> SO3; // scalar type of variable: double
typedef MTK::vect<3, double> vect3; // dimension of the defined Euclidean variable: 3
typedef MTK::S2<double, 98, 10, 1> S2; // length of the S2 variable: 98/10; choose e1 as the original point of rotation: 1
- Build system state and input as compound manifolds which are composed of the primitive manifolds:
MTK_BUILD_MANIFOLD(state, // name of compound manifold: state
((vect3, pos)) // ((primitive manifold type, name of variable))
((vect3, vel))
((SO3, rot))
((vect3, bg))
((vect3, ba))
((S2, grav))
((SO3, offset_R_L_I))
((vect3, offset_T_L_I))
);
- Implement the vector field
Eigen::Matrix<double, state_length, 1> f(state &s, const input &i) {
Eigen::Matrix<double, state_length, 1> res = Eigen::Matrix<double, state_length, 1>::Zero();
res(0) = s.vel[0];
res(1) = s.vel[1];
res(2) = s.vel[2];
return res;
}
Eigen::Matrix<double, state_length, state_dof> df_dx(state &s, const input &i) //notice S2 has length of 3 and dimension of 2 {
Eigen::Matrix<double, state_length, state_dof> cov = Eigen::Matrix<double, state_length, state_dof>::Zero();
cov.template block<3, 3>(0, 12) = Eigen::Matrix3d::Identity();
return cov;
}
Eigen::Matrix<double, state_length, process_noise_dof> df_dw(state &s, const input &i) {
Eigen::Matrix<double, state_length, process_noise_dof> cov = Eigen::Matrix<double, state_length, process_noise_dof>::Zero();
cov.template block<3, 3>(12, 3) = -s.rot.toRotationMatrix();
return cov;
}
Those functions would be called during ekf state predict
- Implement the output equation
Eigen::Matrix<double, Eigen::Dynamic, 1> h(state &s, bool &valid) //the iteration stops before convergence when valid is false {
if (condition){ valid = false;
} // other conditions could be used to stop the ekf update iteration before convergence, otherwise the iteration will not stop until the condition of convergence is satisfied.
Eigen::Matrix<double, Eigen::Dynamic, 1> h_;
h_(0) = s.pos[0];
return h_;
}
Eigen::Matrix<double, Eigen::Dynamic, state_dof> dh_dx(state &s, bool &valid) {}
Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> dh_dv(state &s, bool &valid) {}
Those functions would be called during ekf state update
- Instantiate an esekf object kf and initialize it with initial or default state and covariance.
(1) initial state and covariance:
state init_state;
esekfom::esekf<state, process_noise_dof, input>::cov init_P;
esekfom::esekf<state, process_noise_dof, input> kf(init_state,init_P);
(2) default state and covariance:
esekfom::esekf<state, process_noise_dof, input> kf;
where process_noise_dof is the dimension of process noise, with the type of std int, and so for measurement_noise_dof
- Deliver the defined models, std int maximum iteration numbers Maximum_iter, and the std array for testing convergence epsi into the esekf object:
double epsi[state_dof] = {0.001};
fill(epsi, epsi+state_dof, 0.001); // if the absolute of innovation of ekf update is smaller than epso, the update iteration is converged
kf.init_dyn(f, df_dx, df_dw, h, dh_dx, dh_dv, Maximum_iter, epsi);
- In the running time, once an input in or an measurement z is received dt after the last propagation or update, a propagation is executed:
kf.predict(dt, Q, in); // process noise covariance: Q, an Eigen matrix
- Once a measurement z is received, an iterated update is executed:
kf.update_iterated_dyn(z, R); // measurement noise covariance: R, an Eigen matrix
Remarks(1):
- We also combine the output equation and its differentiation into an union function, whose usage is the same as the above steps 1-4, and steps 5-9 are shown as follows.
- Implement the output equation
Eigen::Matrix<double, Eigen::Dynamic, 1> h_dyn_share(state &s, esekfom::dyn_share_datastruct<double> &dyn_share_data)
{
if(dyn_share_data.converge) {} // this value is true means iteration is converged
if(condition) share_data.valid = false; // the iteration stops before convergence when this value is false if other conditions are satified
dyn_share_data.h_x = H_x; // H_x is the result matrix of the first differentiation
dyn_share_data.h_v = H_v; // H_v is the result matrix of the second differentiation
dyn_share_data.R = R; // R is the measurement noise covariance
dyn_share_data.z = z; // z is the obtained measurement
Eigen::Matrix<double, Eigen::Dynamic, 1> h_;
h_(0) = s.pos[0];
return h_;
}
This function would be called during ekf state update, and the output function and its derivatives, the measurement and the measurement noise would be obtained from this one union function
- Instantiate an esekf object kf and initialize it with initial or default state and covariance. (1) initial state and covariance:
state init_state;
esekfom::esekf<state, process_noise_dof, input>::cov init_P;
esekfom::esekf<state, process_noise_dof, input> kf(init_state,init_P);
(2) default state and covariance:
esekfom::esekf<state, process_noise_dof, input> kf;
- Deliver the defined models, std int maximum iteration numbers Maximum_iter, and the std array for testing convergence epsi into the esekf object:
double epsi[state_dof] = {0.001};
fill(epsi, epsi+state_dof, 0.001); // if the absolute of innovation of ekf update is smaller than epso, the update iteration is converged
kf.init_dyn_share(f, df_dx, df_dw, h_dyn_share, Maximum_iter, epsi);
- In the running time, once an input in or a measurement z is received dt after the last propagation or update, a propagation is executed:
kf.predict(dt, Q, in); // process noise covariance: Q, an Eigen matrix
- Once a measurement z is received, an iterated update is executed:
kf.update_iterated_dyn_share();
Remarks(2):
- The value of the state x and the covariance P are able to be changed by functions change_x() and change_P():
state set_x;
kf.change_x(set_x);
esekfom::esekf<state, process_noise_dof, input>::cov set_P;
kf.change_P(set_P);
Clone the repository:
git clone https://github.com/hku-mars/IKFoM.git
- include the necessary head file:
#include<esekfom/esekfom.hpp>
- Select and instantiate the primitive manifolds:
typedef MTK::SO3<double> SO3; // scalar type of variable: double
typedef MTK::vect<3, double> vect3; // dimension of the defined Euclidean variable: 3
typedef MTK::S2<double, 98, 10, 1> S2; // length of the S2 variable: 98/10; choose e1 as the original point of rotation: 1
- Build system state and input as compound manifolds which are composed of the primitive manifolds:
MTK_BUILD_MANIFOLD(state, // name of compound manifold: state
((vect3, pos)) // ((primitive manifold type, name of variable))
((vect3, vel))
((SO3, rot))
((vect3, bg))
((vect3, ba))
((S2, grav))
((SO3, offset_R_L_I))
((vect3, offset_T_L_I))
);
- Implement the vector field
Eigen::Matrix<double, state_length, 1> f(state &s, const input &i) {
Eigen::Matrix<double, state_length, 1> res = Eigen::Matrix<double, state_length, 1>::Zero();
res(0) = s.vel[0];
res(1) = s.vel[1];
res(2) = s.vel[2];
return res;
}
Eigen::Matrix<double, state_length, state_dof> df_dx(state &s, const input &i) //notice S2 has length of 3 and dimension of 2 {
Eigen::Matrix<double, state_length, state_dof> cov = Eigen::Matrix<double, state_length, state_dof>::Zero();
cov.template block<3, 3>(0, 12) = Eigen::Matrix3d::Identity();
return cov;
}
Eigen::Matrix<double, state_length, process_noise_dof> df_dw(state &s, const input &i) {
Eigen::Matrix<double, state_length, process_noise_dof> cov = Eigen::Matrix<double, state_length, process_noise_dof>::Zero();
cov.template block<3, 3>(12, 3) = -s.rot.toRotationMatrix();
return cov;
}
Those functions would be called during ekf state predict
- Implement the differentiation of the output equation
Eigen::Matrix<double, Eigen::Dynamic, state_dof> dh_dx(state &s, bool &valid) {} //the iteration stops before convergence when valid is false
Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> dh_dv(state &s, bool &valid) {}
Those functions would be called during ekf state update
- Instantiate an esekf object kf and initialize it with initial or default state and covariance.
(1) initial state and covariance:
state init_state;
esekfom::esekf<state, process_noise_dof, input>::cov init_P;
esekfom::esekf<state, process_noise_dof, input> kf(init_state,init_P);
(2)
esekfom::esekf<state, process_noise_dof, input> kf;
Where process_noise_dof is the dimension of process noise, of type of std int
- Deliver the defined models, std int maximum iteration numbers Maximum_iter, and the std array for testing convergence epsi into the esekf object:
double epsi[state_dof] = {0.001};
fill(epsi, epsi+state_dof, 0.001); // if the absolute of innovation of ekf update is smaller than epso, the update iteration is converged
kf.init_dyn_runtime(f, df_dx, df_dw, dh_dx, dh_dv, Maximum_iter, epsi);
- In the running time, once an input in or a measurement z is received dt after the last propagation or update, a propagation is executed:
kf.predict(dt, Q, in); // process noise covariance: Q
- Once a measurement z is received, build system measurement as compound manifolds following step 3 and implement the output equation
measurement h(state &s, bool &valid) //the iteration stops before convergence when valid is false
{
if (condition) valid = false; // the update iteration could be stopped when the condition other than convergence is satisfied
measurement h_;
h_.pos = s.pos;
return h_;
}
then an iterated update is executed:
kf.update_iterated_dyn_runtime(z, R, h); // measurement noise covariance: R, an Eigen matrix
Remarks(1):
- We also combine the output equation and its differentiation into an union function, whose usage is the same as the above steps 1-4, and steps 5-9 are shown as follows.
- Instantiate an esekf object kf and initialize it with initial or default state and covariance.
(1) initial state and covariance:
state init_state;
esekfom::esekf<state, process_noise_dof, input>::cov init_P;
esekfom::esekf<state, process_noise_dof, input> kf(init_state,init_P);
(2) default state and covariance:
esekfom::esekf<state, process_noise_dof, input> kf;
- Deliver the defined models, std int maximum iteration numbers Maximum_iter, and the std array for testing convergence epsi into the esekf object:
double epsi[state_dof] = {0.001};
fill(epsi, epsi+state_dof, 0.001); // if the absolute of innovation of ekf update is smaller than epso, the update iteration is converged
kf.init_dyn_runtime_share(f, df_dx, df_dw, Maximum_iter, epsi);
- In the running time, once an input in or a measurement z is received dt after the last propagation or update, a propagation is executed:
kf.predict(dt, Q, in); // process noise covariance: Q. an Eigen matrix
- Once a measurement z is received, build system measurement as compound manifolds following step 3 and implement the output equation
measurement h_dyn_runtime_share(state &s, esekfom::dyn_runtime_share_datastruct<double> &dyn_runtime_share_data)
{
if(dyn_runtime_share_data.converge) {} // this value is true means iteration is converged
if(condition) dyn_runtime_share_data.valid = false; // the iteration stops before convergence when this value is false, if conditions other than convergence is satisfied
dyn_runtime_share_data.h_x = H_x; // H_x is the result matrix of the first differentiation
dyn_runtime_share_data.h_v = H_v; // H_v is the result matrix of the second differentiation
dyn_runtime_share_data.R = R; // R is the measurement noise covariance
measurement h_;
h_.pos = s.pos;
return h_;
}
This function would be called during ekf state update, and the output function and its derivatives, the measurement and the measurement noise would be obtained from this one union function
then an iterated update is executed:
kf.update_iterated_dyn_runtime_share(z, h_dyn_runtime_share);
Remarks(2):
- The value of the state x and the covariance P are able to be changed by functions change_x() and change_P():
state set_x;
kf.change_x(set_x);
esekfom::esekf<state, process_noise_dof, input>::cov set_P;
kf.change_P(set_P);
Clone the repository:
git clone https://github.com/hku-mars/IKFoM.git
Sample 1. In the Sample_1 file folder, there is the scource code that applys the IKFoM on the original source code from FAST LIO. Please follow the README.md shown in that repository excepting the step 2. Build, which is modified as:
cd ~/catkin_ws/src
cp -r ~/IKFoM/Samples/FAST_LIO FAST_LIO
cd ..
catkin_make
source devel/setup.bash
Livox Avia rosbag: Can be downloaded from here
For the indoor bag, run:
roslaunch fast_lio mapping_avia.launch
rosbag play YOUR_DOWNLOADED.bag
For the outdoor bag, run:
roslaunch fast_lio mapping_avia_outdoor.launch
rosbag play YOUR_DOWNLOADED.bag
Sample 2. In the Sample_2 file folder, there is the scource code that applys the IKFoM on the original source code from LINS. Please follow the README.md shown in that repository excepting the step Compile, which is modified as:
cd ~/catkin_ws/src
cp -r ~/IKFoM/Samples/LINS---LiDAR-inertial-SLAM LINS---LiDAR-inertial-SLAM
cd ..
catkin_make -j1
source devel/setup.bash
LIO-SAM Dataset: Can be found here, in which, Campus_dataset(large) and Campus_dataset(small) are tested in our paper.
Run
roslaunch lins run_port_exp.launch
rosbag play YOUR_DOWNLOADED.bag --clock
Thanks for C. Hertzberg, R. Wagner, U. Frese, and L. Schroder. Integratinggeneric sensor fusion algorithms with sound state representationsthrough encapsulation of manifolds.