Extended Kalman Filter

An implementation of an EKF in C++ with O(1) runtime complexity.

Based on the excellent tutorial by Simon D. Levy.

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Inteded to use on embedded systems. Uses Blaze for linear algebra.

Example usage may be found in tests/kafi_tests.cc.

No automatic derivation, but also the state and prection scaling are defined as std::function, not as matricies. You can define non-linear transformations by hand.

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If you see this on github, it's only a mirror of our internal municHMotorsport gitlab repository. The repository name may not match in the following build instructions.

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Build

> git clone://gitlab.munichmotorsport.com/fsd-software/Kalman-Filter
> cd Kalman-Filter
> mkdir build && cd build
> cmake .. 
> make -j
> ./tests/kafi_tests

Trigger tests (default ON):

> cmake .. -DENABLE_TESTS_KAFI=OFF

Change debug level (default: 2 ~ everything will be printed to cerr):

> cmake .. -DDEBUG_LEVEL_KAFI=[0,1,2]

Enable optimizations (default OFF):

> cmake .. -DENABLE_OPTIMIZATIONS_KAFI=ON

Installation (cmake only)

Subdirectory

You can easily reference the headers by hand and link to the kafi library in your CMakeLists.txt if you have this repository as a subdirectory of your main repository. Add this to your CMakeLists.txt:

target_link_libraries(${your-awesome-executable} ${your-awesome-library} kafi )

System level installation

If you want a system-level installation just type make install in your build directory. Then you need to add the following to your own code CMakeLists.txt:

find_package(kafi version 1.0 REQUIRED)
target_link_libraries(${your-awesome-executable} ${your-awesome-library} kafi )

To use the library, include this header and check out the documentation

#include <kafi-1.0/kafi.h>

Basic runthrough of the API

Explanation of the first test in tests/kafi_tests.cc.

We try to estimate the temperature based on two uncorrelated thermometers.

• N - this is the state dimension. We estimate only a single temperature, hence N = 1
• M - this is the sensor dimension. We have two thermometers, hence M = 2

We use multiple typenames to avoid auto in the examples.

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// state transition
kafi::jacobian_function<N,N> f(
    std::move(kafi::util::create_identity_jacobian<N,N>()));

// prediction scaling (state -> observations)
kafi::jacobian_function<N,M> h(
    std::move(kafi::util::create_identity_jacobian<N,M>()));

First we have to create the f function, which is the state transition. This means it takes a vector of N element (the state) and returns the modified state based on the knowledge of the environment. If we would've known any control parameters this might look different.

Therefore we can simply have the identity function as the state transition. This looks slightly convoluted, because we also need the derivative of this function, which is also automatically generated for the identity function based on the size N.

The same goes for the h function, which scales the state (N) to the observation dimension (M). The function broadcasts automatically first value of the state vector to all observation dimensions. In our example:

state = [20] # estimated C°
observations = [21.1, 21.5] # noisy C°

[20, 20] = h(state)

# do stuff with observations and h(state)

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// given by our example, read as "the real world temperature changes are 0.22° (0.22^2 =~ 0.05)"
nxn_matrix process_noise( { { 0.05 } } );
// given by our example, read as "both temperature sensors fluctuate by 0.8° (0.8^2 = 0.64)"
mxm_matrix sensor_noise( { { 0.64, 0    }
                         , { 0,    0.64 } });
// given by our example, read as "first time we measured temperature, we got these values"
std::shared_ptr< mx1_vector > first_observation = std::make_shared< mx1_vector >(
                                                       mx1_vector({ { 18.625 } 
                                                                  , { 20     } }));

We create the process noise and the sensor noise as blaze matricies. The first observation is packed in a std::shared_ptr because the EKF does not own it.

We share it with a shared pointer, the EKF uses it, but the ownership never transitions, because we don't want to allocate unnecessarly. The callee has to manage the allocation space for the observations.

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kafi.set_current_observation(first_observation);
// run the estimation
return_t   result          = kafi.step();
nx1_vector estimated_state = std::get<0>(result);

The step() function applies the prediction step and update step consecutively.

result_t consists of:

const nx1_vector & estimated_state  = std::get<0>(result)
const nxn_matrix & prediction error = std::get<1>(result)
const nxm_matrix & gain             = std::get<2>(result)

To access the elements, use the blaze matrix access reference.

double temperature = estimated_state(0,0)

Documentation

Created with doxygen (with Markdown support)

• PDF
• HTML

Update documentation:

> cd Kalman-Filter
> doxygen doxygen.config
> cd documentation/latex
> make

Dependencies

• fast-cpp-csv-parser
  • header only, used for tests (already included)
• blaze (tested on ubuntu 16.04)

> wget https://bitbucket.org/blaze-lib/blaze/downloads/blaze-3.3.tar.gz
> tar -xvf blaze-3.3.tar.gz
> sudo apt-get install libopenblas-dev
> sudo apt-get install libboost-all-dev
> cmake -DCMAKE_INSTALL_PREFIX=/usr/local/
> sudo make install