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paper_example.cpp
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paper_example.cpp
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#include <iostream>
#include <vector>
#include <cmath>
#include <random>
#include "distribution/normal_distribution.h"
#include "distribution/two_dimensional_normal_distribution.h"
#include "distribution/three_dimensional_normal_distribution.h"
#include "distribution/exponential_distribution.h"
#include "distribution/uniform_distribution.h"
#include "filter/paper_example_2d_ukf.h"
#include "filter/paper_example_3d_ukf.h"
int main()
{
// Two Dimensional
{
const double x_lambda = 1.0;
const double lower_theta = -M_PI/3.0;
const double upper_theta = M_PI/6.0;
auto x_dist = ExponentialDistribution(x_lambda);
auto theta_dist = UniformDistribution(lower_theta, upper_theta);
const Eigen::Vector2d mean = {x_dist.calc_mean(), theta_dist.calc_mean()};
const Eigen::Matrix2d cov = (Eigen::Matrix2d() << x_dist.calc_variance(), 0.0, 0.0, theta_dist.calc_variance()).finished();
// E[xy]
{
// Exact Moment
const double exact_moment = x_dist.calc_moment(1) * theta_dist.calc_moment(1);
// Linear(E[x]E[y)])
const double linear_moment = x_dist.calc_moment(1) * theta_dist.calc_moment(1);
// E[x]E[y]
const double non_correlation_exact = x_dist.calc_moment(1) * theta_dist.calc_moment(1);
// Unscented Transform
PaperExample2DUKF ukf(mean, cov);
const double ukf_moment = ukf.predict("xy");
std::cout << "E[xy]" << std::endl;
std::cout << "Exact Moment: " << exact_moment << std::endl;
std::cout << "Linear: " << linear_moment << std::endl;
std::cout << "E[x]E[y]: " << non_correlation_exact << std::endl;
std::cout << "UKF Moment: " << ukf_moment << std::endl;
std::cout << "MonteCarlo: " << -0.2618191494201287 << std::endl;
std::cout << "-----------------------------" << std::endl;
}
// E[xcos(theta)]
{
// Exact Moment
const double exact_moment = x_dist.calc_moment(1) * theta_dist.calc_cos_moment(1);
// Linear(E[x]E[cos(theta)])
const double linear_moment = x_dist.calc_moment(1) * std::cos(theta_dist.calc_moment(1));
// E[x]E[cos(theta)]
const double non_correlation_exact = x_dist.calc_moment(1) * theta_dist.calc_cos_moment(1);
// Unscented Transform
PaperExample2DUKF ukf(mean, cov);
const double ukf_moment = ukf.predict("xcos");
std::cout << "E[xcos(theta)]" << std::endl;
std::cout << "Exact Moment: " << exact_moment << std::endl;
std::cout << "Linear: " << linear_moment << std::endl;
std::cout << "E[x]E[cos(theta)]: " << non_correlation_exact << std::endl;
std::cout << "UKF Moment: " << ukf_moment << std::endl;
std::cout << "MonteCarlo: " << 0.8696105959403237 << std::endl;
std::cout << "----------------------" << std::endl;
}
// E[xcos(theta)sin(theta)]
{
// Exact Moment
const double exact_moment = x_dist.calc_moment(1) * theta_dist.calc_cos_sin_moment(1, 1);
// Linear(E[x]E[cos(theta)]E[sin(theta)])
const double linear_moment = x_dist.calc_moment(0) * std::cos(theta_dist.calc_moment(1)) * std::sin(theta_dist.calc_moment(1));
// E[x]E[cos(theta)sin(theta)]
const double non_correlation_exact = x_dist.calc_moment(1) * theta_dist.calc_cos_sin_moment(1, 1);
// Unscented Transform
PaperExample2DUKF ukf(mean, cov);
const double ukf_moment = ukf.predict("xcossin");
std::cout << "E[xcos(theta)sin(theta)]" << std::endl;
std::cout << "Exact Moment: " << exact_moment << std::endl;
std::cout << "Linear: " << linear_moment << std::endl;
std::cout << "E[x]E[cos(theta)sin(theta)]: " << non_correlation_exact << std::endl;
std::cout << "UKF Moment: " << ukf_moment << std::endl;
std::cout << "MonteCarlo: " << -0.15915291917551003 << std::endl;
}
}
std::cout << "------------------------------" << std::endl;
std::cout << "------------------------------" << std::endl;
std::cout << "------------------------------" << std::endl;
std::cout << "Non-Gaussian Example Finished" << std::endl;
// Two Dimensional
{
const Eigen::Vector2d mean = {10.0, M_PI/3.0};
const Eigen::Matrix2d cov = (Eigen::Matrix2d() << 5.0, 0.1, 0.1, M_PI/6.0).finished();
// E[xy]
{
// Exact Moment
TwoDimensionalNormalDistribution two_dim_normal_dist(mean, cov);
const double exact_moment = two_dim_normal_dist.calc_xy_moment();
// Linear(E[x]E[y)])
NormalDistribution x_dist(mean(0), cov(0, 0));
NormalDistribution theta_dist(mean(1), cov(1, 1));
const double linear_moment = x_dist.calc_moment(1) * theta_dist.calc_moment(1);
// E[x]E[y]
const double non_correlation_exact = x_dist.calc_moment(1) * theta_dist.calc_moment(1);
// Unscented Transform
PaperExample2DUKF ukf(mean, cov);
const double ukf_moment = ukf.predict("xy");
std::cout << "E[xy]" << std::endl;
std::cout << "Exact Moment: " << exact_moment << std::endl;
std::cout << "Linear: " << linear_moment << std::endl;
std::cout << "E[x]E[y]: " << non_correlation_exact << std::endl;
std::cout << "UKF Moment: " << ukf_moment << std::endl;
std::cout << "MonteCarlo: " << 2.1774640733069437 << std::endl;
std::cout << "-----------------------------" << std::endl;
}
// E[xcos(theta)]
{
// Exact Moment
TwoDimensionalNormalDistribution two_dim_normal_dist(mean, cov);
const double exact_moment = two_dim_normal_dist.calc_x_cos_y_moment();
// Linear(E[x]E[cos(theta)])
NormalDistribution x_dist(mean(0), cov(0, 0));
NormalDistribution theta_dist(mean(1), cov(1, 1));
const double linear_moment = x_dist.calc_moment(1) * std::cos(theta_dist.calc_moment(1));
// E[x]E[cos(theta)]
const double non_correlation_exact = x_dist.calc_moment(1) * theta_dist.calc_cos_moment(1);
// Unscented Transform
PaperExample2DUKF ukf(mean, cov);
const double ukf_moment = ukf.predict("xcos");
std::cout << "E[xcos(theta)]" << std::endl;
std::cout << "Exact Moment: " << exact_moment << std::endl;
std::cout << "Linear: " << linear_moment << std::endl;
std::cout << "E[x]E[cos(theta)]: " << non_correlation_exact << std::endl;
std::cout << "UKF Moment: " << ukf_moment << std::endl;
std::cout << "MonteCarlo: " << 2.1774640733069437 << std::endl;
std::cout << "----------------------" << std::endl;
}
// E[xcos(theta)sin(theta)]
{
// Exact Moment
TwoDimensionalNormalDistribution two_dim_normal_dist(mean, cov);
const double exact_moment = two_dim_normal_dist.calc_x_cos_y_sin_y_moment();
// Linear(E[x]E[cos(theta)]E[sin(theta)])
NormalDistribution x_dist(mean(0), cov(0, 0));
NormalDistribution theta_dist(mean(1), cov(1, 1));
const double linear_moment = x_dist.calc_moment(0) * std::cos(theta_dist.calc_moment(1)) * std::sin(theta_dist.calc_moment(1));
// E[x]E[cos(theta)sin(theta)]
const double non_correlation_exact = x_dist.calc_moment(1) * theta_dist.calc_cos_sin_moment(1, 1);
// Unscented Transform
PaperExample2DUKF ukf(mean, cov);
const double ukf_moment = ukf.predict("xcossin");
std::cout << "E[xcos(theta)sin(theta)]" << std::endl;
std::cout << "Exact Moment: " << exact_moment << std::endl;
std::cout << "Linear: " << linear_moment << std::endl;
std::cout << "E[x]E[cos(theta)sin(theta)]: " << non_correlation_exact << std::endl;
std::cout << "UKF Moment: " << ukf_moment << std::endl;
std::cout << "MonteCarlo: " << 2.1774640733069437 << std::endl;
}
}
std::cout << "------------------------------" << std::endl;
std::cout << "------------------------------" << std::endl;
{
const Eigen::Vector2d mean = {10.0, M_PI/3.0};
const Eigen::Matrix2d cov = (Eigen::Matrix2d() << 5.0, 1.5, 1.5, M_PI/6.0).finished();
// E[xy]
{
// Exact Moment
TwoDimensionalNormalDistribution two_dim_normal_dist(mean, cov);
const double exact_moment = two_dim_normal_dist.calc_xy_moment();
// Linear(E[x]E[y)])
NormalDistribution x_dist(mean(0), cov(0, 0));
NormalDistribution theta_dist(mean(1), cov(1, 1));
const double linear_moment = x_dist.calc_moment(1) * theta_dist.calc_moment(1);
// E[x]E[y]
const double non_correlation_exact = x_dist.calc_moment(1) * theta_dist.calc_moment(1);
// Unscented Transform
PaperExample2DUKF ukf(mean, cov);
const double ukf_moment = ukf.predict("xy");
std::cout << "E[xy]" << std::endl;
std::cout << "Exact Moment: " << exact_moment << std::endl;
std::cout << "Linear: " << linear_moment << std::endl;
std::cout << "E[x]E[y]: " << non_correlation_exact << std::endl;
std::cout << "UKF Moment: " << ukf_moment << std::endl;
std::cout << "MonteCarlo: " << 2.1774640733069437 << std::endl;
std::cout << "-----------------------------" << std::endl;
}
// E[xcos(theta)]
{
// Exact Moment
TwoDimensionalNormalDistribution two_dim_normal_dist(mean, cov);
const double exact_moment = two_dim_normal_dist.calc_x_cos_y_moment();
// Linear
NormalDistribution x_dist(mean(0), cov(0, 0));
NormalDistribution theta_dist(mean(1), cov(1, 1));
const double linear_moment = x_dist.calc_moment(1) * std::cos(theta_dist.calc_moment(1));
// E[x]E[cos(theta)]
const double non_correlation_exact = x_dist.calc_moment(1) * theta_dist.calc_cos_moment(1);
// Unscented Transform
PaperExample2DUKF ukf(mean, cov);
const double ukf_moment = ukf.predict("xcos");
std::cout << "E[xcos(theta)]" << std::endl;
std::cout << "Exact Moment: " << exact_moment << std::endl;
std::cout << "Linear: " << linear_moment << std::endl;
std::cout << "E[x]E[cos(theta)]: " << non_correlation_exact << std::endl;
std::cout << "UKF Moment: " << ukf_moment << std::endl;
std::cout << "MonteCarlo: " << 2.8476949077323734 << std::endl;
std::cout << "------------------------------" << std::endl;
}
// E[xcos(theta)sin(theta)]
{
// Exact Moment
TwoDimensionalNormalDistribution two_dim_normal_dist(mean, cov);
const double exact_moment = two_dim_normal_dist.calc_x_cos_y_sin_y_moment();
// Linear(E[x]E[cos(theta)]E[sin(theta)])
NormalDistribution x_dist(mean(0), cov(0, 0));
NormalDistribution theta_dist(mean(1), cov(1, 1));
const double linear_moment = x_dist.calc_moment(0) * std::cos(theta_dist.calc_moment(1)) * std::sin(theta_dist.calc_moment(1));
// E[x]E[cos(theta)sin(theta)]
const double non_correlation_exact = x_dist.calc_moment(1) * theta_dist.calc_cos_sin_moment(1, 1);
// Unscented Transform
PaperExample2DUKF ukf(mean, cov);
const double ukf_moment = ukf.predict("xcossin");
std::cout << "E[xcos(theta)sin(theta)]" << std::endl;
std::cout << "Exact Moment: " << exact_moment << std::endl;
std::cout << "Linear: " << linear_moment << std::endl;
std::cout << "E[x]E[cos(theta)sin(theta)]: " << non_correlation_exact << std::endl;
std::cout << "UKF Moment: " << ukf_moment << std::endl;
std::cout << "MonteCarlo: " << 2.1774640733069437 << std::endl;
}
}
std::cout << "------------------------------" << std::endl;
std::cout << "------------------------------" << std::endl;
{
const Eigen::Vector3d mean = {10.0, 5.0, M_PI/3.0};
const Eigen::Matrix3d cov = (Eigen::Matrix3d() << 3.0, 0.5, 0.5,
0.5, 2.0, 0.3,
0.5, 0.3, M_PI/10.0).finished();
// E[xysin(theta)]
{
// Exact Moment
ThreeDimensionalNormalDistribution two_dim_normal_dist(mean, cov);
const double exact_moment = two_dim_normal_dist.calc_xy_sin_z_moment();
// Linear
NormalDistribution x_dist(mean(0), cov(0, 0));
NormalDistribution y_dist(mean(1), cov(1, 1));
NormalDistribution theta_dist(mean(2), cov(2, 2));
const double linear_moment = x_dist.calc_moment(1) * y_dist.calc_moment(1) * std::sin(theta_dist.calc_moment(1));
// E[x^2]E[y]E[cos(theta)]
const double non_correlation_exact = x_dist.calc_moment(1) * y_dist.calc_moment(1) * theta_dist.calc_sin_moment(1);
// Unscented Transform
PaperExample3DUKF ukf(mean, cov);
const double ukf_moment = ukf.predict("xysin");
std::cout << "E[xysin(theta)]" << std::endl;
std::cout << "Exact Moment: " << exact_moment << std::endl;
std::cout << "Linear: " << linear_moment << std::endl;
std::cout << "E[x]E[y]E[sin(theta)]: " << non_correlation_exact << std::endl;
std::cout << "UKF Moment: " << ukf_moment << std::endl;
std::cout << "MonteCarlo: " << 162.29415844773192 << std::endl;
std::cout << "------------" << std::endl;
}
// E[xxycos(theta)]
{
// Exact Moment
ThreeDimensionalNormalDistribution two_dim_normal_dist(mean, cov);
const double exact_moment = two_dim_normal_dist.calc_xxy_cos_z_moment();
// Linear
NormalDistribution x_dist(mean(0), cov(0, 0));
NormalDistribution y_dist(mean(1), cov(1, 1));
NormalDistribution theta_dist(mean(2), cov(2, 2));
const double separate_moment = x_dist.calc_moment(2) * y_dist.calc_moment(1) * std::cos(theta_dist.calc_moment(1));
// E[x^2]E[y]E[cos(theta)]
const double non_correlation_exact = x_dist.calc_moment(2) * y_dist.calc_moment(1) * theta_dist.calc_cos_moment(1);
// Unscented Transform
PaperExample3DUKF ukf(mean, cov);
const double ukf_moment = ukf.predict("xxycos");
std::cout << "E[xxycos(theta)]" << std::endl;
std::cout << "Exact Moment: " << exact_moment << std::endl;
std::cout << "Linear: " << separate_moment << std::endl;
std::cout << "E[x^2]E[cos(theta)]: " << non_correlation_exact << std::endl;
std::cout << "UKF Moment: " << ukf_moment << std::endl;
std::cout << "MonteCarlo: " << 162.29415844773192 << std::endl;
}
}
return 0;
}