Kalman-and-Bayesian-Filters-in-Python/ukf_internal.py

# -*- coding: utf-8 -*-
"""
Created on Tue May 27 21:21:19 2014

@author: rlabbe
"""
import matplotlib.pyplot as plt
from matplotlib.patches import Ellipse,Arrow
import stats
import numpy as np
import math


def arrow(x1,y1,x2,y2):
    return Arrow(x1,y1, x2-x1, y2-y1, lw=2, width=0.1, ec='k', color='k')

def show_2d_transform():
    ax=plt.gca()

    ax.add_artist(Ellipse(xy=(2,5), width=2, height=3,angle=70,linewidth=1,ec='k'))
    ax.add_artist(Ellipse(xy=(7,5), width=2.2, alpha=0.3, height=3.8,angle=150,linewidth=1,ec='k'))

    ax.add_artist(arrow(2, 5, 6, 4.8))
    ax.add_artist(arrow(1.5, 5.5, 7, 3.8))
    ax.add_artist(arrow(2.3, 4.1, 8, 6))

    ax.axes.get_xaxis().set_visible(False)
    ax.axes.get_yaxis().set_visible(False)

    plt.axis('equal')
    plt.xlim(0,10); plt.ylim(0,10)
    plt.show()


def show_3_sigma_points():
    xs = np.arange(-4, 4, 0.1)
    var = 1.5
    ys = [stats.gaussian(x, 0, var) for x in xs]
    samples = [0, 1.2, -1.2]
    for x in samples:
        plt.scatter ([x], [stats.gaussian(x, 0, var)], s=80)

    plt.plot(xs, ys)
    plt.show()

def show_sigma_selections():
    ax=plt.gca()
    ax.add_artist(Ellipse(xy=(2,5), alpha=0.5, width=2, height=3,angle=0,linewidth=1,ec='k'))
    ax.add_artist(Ellipse(xy=(5,5), alpha=0.5, width=2, height=3,angle=0,linewidth=1,ec='k'))
    ax.add_artist(Ellipse(xy=(8,5), alpha=0.5, width=2, height=3,angle=0,linewidth=1,ec='k'))
    ax.axes.get_xaxis().set_visible(False)
    ax.axes.get_yaxis().set_visible(False)

    plt.scatter([1.5,2,2.5],[5,5,5],c='k', s=50)
    plt.scatter([2,2],[4.5, 5.5],c='k', s=50)

    plt.scatter([4.8,5,5.2],[5,5,5],c='k', s=50)
    plt.scatter([5,5],[4.8, 5.2],c='k', s=50)

    plt.scatter([7.2,8,8.8],[5,5,5],c='k', s=50)
    plt.scatter([8,8],[4,6],c='k' ,s=50)

    plt.axis('equal')
    plt.xlim(0,10); plt.ylim(0,10)
    plt.show()



def show_sigmas_for_2_kappas():
    # generate the Gaussian data
    
    xs = np.arange(-4, 4, 0.1)
    mean = 0
    sigma = 1.5
    ys = [stats.gaussian(x, mean, sigma*sigma) for x in xs]
    
    def sigma_points(mean, sigma, kappa):
        sigma1 = mean + math.sqrt((1+kappa)*sigma) 
        sigma2 = mean - math.sqrt((1+kappa)*sigma) 
        return mean, sigma1, sigma2
        
    #generate our samples
    kappa = 2
    x0,x1,x2 = sigma_points(mean, sigma, kappa)
    
    samples = [x0,x1,x2]
    for x in samples:
        p1 = plt.scatter([x], [stats.gaussian(x, mean, sigma*sigma)], s=80, color='k')
    
    kappa = -.5
    x0,x1,x2 = sigma_points(mean, sigma, kappa)
    
    samples = [x0,x1,x2]
    for x in samples:
        p2 = plt.scatter([x], [stats.gaussian(x, mean, sigma*sigma)], s=80, color='b')
    
    plt.legend([p1,p2], ['$kappa$=2', '$kappa$=-0.5'])
    plt.plot(xs, ys)
    plt.show()



if __name__ == '__main__':
    show_sigma_selections()