Headers only Cubature Kalman Filter (CKF) [1] implementation in C++. The CKF is a variation of the Unscented Kalman Filter (UKF) [2] with a spherical-radial cubature rule at its core.
This library makes use of the Eigen library for lineal algebra routines and matrix operations.
This is a heades only library, for usign them in your project you only need to add them to your file and point at the correct location during compilation
#include "CKF.cpp"To compile the example, simply run the make command on the proper directory
cd <directory where files are>
cmake .
make
./example
The example will display a list of 20 steps where the actual state is compared with the estimated measurement from the CKF.
Difference between actual states and tracked measurements:
0: 0.12136 (1.00000-1.12136)
1: 1.05234 (2.00000-3.05234)
2: 0.70898 (4.00000-4.70898)
3: 0.81015 (7.00000-7.81015)
4: 0.10093 (11.00000-10.89907)
5: 0.20019 (16.00000-16.20019)
6: 0.27947 (22.00000-21.72053)
7: 0.00576 (29.00000-28.99424)
8: 0.03688 (37.00000-37.03688)
9: 0.16920 (46.00000-45.83080)
10: 1.35327 (56.00000-57.35327)
11: 0.33129 (67.00000-67.33129)
12: 0.52171 (79.00000-79.52171)
13: 0.39297 (92.00000-92.39297)
14: 0.18210 (106.00000-105.81790)
15: 0.16014 (121.00000-120.83986)
16: 0.16330 (137.00000-137.16330)
17: 0.77446 (154.00000-154.77446)
18: 0.62436 (172.00000-172.62436)
19: 1.97809 (191.00000-192.97809)
To use it, a class with the state and measurement functions must be declared
class CKF2DPoint : public CKF {
public:
MatrixXd stateFunction (MatrixXd s)
{
MatrixXd state(4,1);
state(0,0) = s(0,0)+s(2,0); // x position in 2D point
state(1,0) = s(1,0)+s(3,0); // y position in 2D point
state(2,0) = s(2,0); // velocity in x
state(3,0) = s(3,0); // velocity in y
return state;
}
MatrixXd measurementFunction (MatrixXd m)
{
MatrixXd measurement(2,1);
measurement(0,0) = m(0,0); // measured x position in 2D point
measurement(1,0) = m(1,0); // measured y position in 2D point
return measurement;
}
};An object can be created and the remaining required values, namely the covariance, noise covariance and measurement covariance matrices need to be stated, as well as the matrices' size in the n and m values.
CKF2DPoint tracked_point;
tracked_point.n = n;
tracked_point.m = m;
tracked_point.P = MatrixXd; // state covriance
tracked_point.Q = MatrixXd; // covariance of process (size must be nxn)
tracked_point.R = MatrixXd; // covariance of measurement (size must be mxm)The calculations are performed with
tracked_point.ckf(x, z); Where x is the state and z is the measurement.
For more details, please refer to the example in main.cpp
Basic Code Structure taken from https://github.com/Efreeto/UKF
Cubature Kalman Filter calculations taken from https://github.com/rlabbe/filterpy/
[1] Arasaratnam, Ienkaran, and Simon Haykin. "Cubature kalman filters." IEEE Transactions on automatic control 54.6 (2009): 1254-1269.
[2] Wan, Eric A., and Rudolph Van Der Merwe. "The unscented Kalman filter for nonlinear estimation." Adaptive Systems for Signal Processing, Communications, and Control Symposium 2000. AS-SPCC. The IEEE 2000. Ieee, 2000.
MIT License
Copyright (c) 2018 Saul Armendariz
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