IKFoM

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 menifold 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

Dongjiao He

Our related video: https://youtu.be/sz_ZlDkl6fA

Our related paper: https://arxiv.org/pdf/2102.03804.pdf

1. Prerequisites

1.1. Eigen && Boost

Eigen >= 3.3.4, Follow Eigen Installation.

Boost >= 1.65.

2. Usage when the measurement is of constant dimension and type.

Clone the repository:

    git clone https://github.com/hku-mars/IKFoM.git

1. include the necessary head file:

#include<esekfom/esekfom.hpp>

2. 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

3. 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)) 
);

4. Implement the vector field and its differentiation , :

Eigen::Matrix<double, state_length, 1> f(state &s, input &i) {}
Eigen::Matrix<double, state_length, state_dof> df_dx(state &s, input &i) {} //notice S2 has length of 3 and dimension of 2
Eigen::Matrix<double, state_length, process_noise_dof> df_dw(state &s, input &i) {}

5. Implement the output equation and its differentiation , :

measurement h(state &s, bool &valid) {} //the iteration stops before convergence when valid is false
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) {}

6. Instantiate an esekf object kf and initialize it with 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);

7. Deliver the defined models, maximum iteration numbers Maximum_iter, and the std array for testing convergence limit into the esekf object:

kf.init(f, df_dx, df_dw, h, dh_dx, dh_dv, Maximum_iter, limit);

8. In the running time, once an input in is received with time interval dt, a propagation is executed:

kf.predict(dt, Q, input); // process noise covariance: Q

9. Once a measurement z is received, an iterated update is executed:

kf.update_iterated(z, R); // measurement noise covariance: R

Remarks:

• 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.

5. Implement the output equation and its differentiation , :

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 
	share_data.valid = false; // the iteration stops before convergence when this value is false
	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 
}

6. Instantiate an esekf object kf and initialize it with 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);

7. Deliver the defined models, maximum iteration numbers Maximum_iter, and the std array for testing convergence limit into the esekf object:

kf.init_share(f, df_dx, df_dw, h_share, Maximum_iter, limit);

8. In the running time, once an input in is received with time interval dt, a propagation is executed:

kf.predict(dt, Q, input); // process noise covariance: Q

9. Once a measurement z is received, an iterated update is executed:

kf.update_iterated_share();

3. Usage when the measurement is an Eigen vector of changing dimension.

Clone the repository:

    git clone https://github.com/hku-mars/IKFoM.git

1. include the necessary head file:

#include<esekfom/esekfom.hpp>

2. 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

3. 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)) 
);

4. Implement the vector field and its differentiation , :

Eigen::Matrix<double, state_length, 1> f(state &s, input &i) {}
Eigen::Matrix<double, state_length, state_dof> df_dx(state &s, input &i) {} //notice S2 has length of 3 and dimension of 2
Eigen::Matrix<double, state_length, process_noise_dof> df_dw(state &s, input &i) {}

5. Implement the output equation and its differentiation , :

Eigen::Matrix<double, Eigen::Dynamic, 1> h(state &s, bool &valid) {} //the iteration stops before convergence when valid is false
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) {}

6. Instantiate an esekf object kf and initialize it with 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);

7. Deliver the defined models, maximum iteration numbers Maximum_iter, and the std array for testing convergence limit into the esekf object:

kf.init_dyn(f, df_dx, df_dw, h, dh_dx, dh_dv, Maximum_iter, limit);

8. In the running time, once an input in is received with time interval dt, a propagation is executed:

kf.predict(dt, Q, input); // process noise covariance: Q

9. Once a measurement z is received, an iterated update is executed:

kf.update_iterated_dyn(z, R); // measurement noise covariance: R

Remarks:

• 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.

5. Implement the output equation and its differentiation , :

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 
	dyn_share_data.valid = false; // the iteration stops before convergence when this value is false
	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 
}

6. Instantiate an esekf object kf and initialize it with 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);

7. Deliver the defined models, maximum iteration numbers Maximum_iter, and the std array for testing convergence limit into the esekf object:

kf.init_dyn_share(f, df_dx, df_dw, h_dyn_share, Maximum_iter, limit);

8. In the running time, once an input in is received with time interval dt, a propagation is executed:

kf.predict(dt, Q, input); // process noise covariance: Q

9. Once a measurement z is received, an iterated update is executed:

kf.update_iterated_dyn_share();

4. Usage when the measurement is a changing manifold during the run time.

Clone the repository:

    git clone https://github.com/hku-mars/IKFoM.git

1. include the necessary head file:

#include<esekfom/esekfom.hpp>

2. 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

3. 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)) 
);

4. Implement the vector field and its differentiation , :

Eigen::Matrix<double, state_length, 1> f(state &s, input &i) {}
Eigen::Matrix<double, state_length, state_dof> df_dx(state &s, input &i) {} //notice S2 has length of 3 and dimension of 2
Eigen::Matrix<double, state_length, process_noise_dof> df_dw(state &s, input &i) {}

5. 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) {}

6. Instantiate an esekf object kf and initialize it with 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);

7. Deliver the defined models, maximum iteration numbers Maximum_iter, and the std array for testing convergence limit into the esekf object:

kf.init_dyn_runtime(f, df_dx, df_dw, dh_dx, dh_dv, Maximum_iter, limit);

8. In the running time, once an input in is received with time interval dt, a propagation is executed:

kf.predict(dt, Q, input); // process noise covariance: Q

9. 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

then an iterated update is executed:

kf.update_iterated_dyn_runtime(z, R, h); // measurement noise covariance: R

Remarks:

• 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.

5. Instantiate an esekf object kf and initialize it with 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);

6. Deliver the defined models, maximum iteration numbers Maximum_iter, and the std array for testing convergence limit into the esekf object:

kf.init_dyn_runtime_share(f, df_dx, df_dw, Maximum_iter, limit);

7. In the running time, once an input in is received with time interval dt, a propagation is executed:

kf.predict(dt, Q, input); // process noise covariance: Q

8. Once a measurement z is received, build system measurement as compound manifolds following step 3 and implement the output equation and its differentiation , :

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 
	dyn_runtime_share_data.valid = false; // the iteration stops before convergence when this value is false
	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
}

then an iterated update is executed:

kf.update_iterated_dyn_runtime_share(z, h_dyn_runtime_share);

5. Run the sample

Clone the repository:

    git clone https://github.com/hku-mars/IKFoM.git

In the Samples 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-stable FAST_LIO-stable
cd ..
catkin_make
source devel/setup.bash

6.Acknowledgments

Thanks for C. Hertzberg, R. Wagner, U. Frese, and L. Schroder. Integratinggeneric sensor fusion algorithms with sound state representationsthrough encapsulation of manifolds.