simple_plane.cpp

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// -------------- plane.cpp - Example of Extended Kalman filter ------------------------//
//
// This file is part of kfilter.
// kfilter is a C++ variable-dimension extended kalman filter library.
//
// Copyright (C) 2004        Vincent Zalzal, Sylvain Marleau
// Copyright (C) 2001, 2004  Richard Gourdeau
// Copyright (C) 2004        GRPR and DGE's Automation sector
//                           cole Polytechnique de Montral
//
// Code adapted from algorithms presented in :
//      Bierman, G. J. "Factorization Methods for Discrete Sequential
//      Estimation", Academic Press, 1977.
//
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
//
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

// --------------------------- Example of Extended Kalman filter ------------------------//
/*
% A plane flights in a 2D space where the x axis is the distance traveled
% by the plane and y axis is its altitude.  This system can be represented
% by the fallowing equations:
% (This is just an example)
%
% xpp = F/m - bx/m * xp^2
% ypp = p/m * xp^2 - g
%
% where m is the plane's weight (1000 kg)
%       bx is the drag coefficient (0.35 N/m/s)
%       p is the lift force (3.92 N/m/s)
%       g is the gravitational acceleration (9.8 m/s)
%       F is the motor's thrust
%
% A station on the ground (at the origin) mesures the angle between the
% plane and the ground (x axis) and the distance between the plane and the station.
% These measures are based and the fallowing equations:
%
% theta = atan2(y,x)
% r = sqrt(x^2+y^2)
%
% The variance error matrix of the mesures is:
%
% R = [0.01^2  0
%      0       50^2]
%
% V = [1 0;
%      0 1];
%
% The variance error matrix of the plane's model is: WQW'
%
% Q = [0.01^2    0;
%      0         0.01^2];
%
% W = [0 0;
%      1 0;
%      0 0;
%      0 1];
%
*/

#include "simple_plane.h"
#include <cmath>
#include <iostream>

using namespace std;

cPlaneEKF_sp::cPlaneEKF_sp() 
{
        setDim(4, 1, 2, 2, 2);
        Period = 0.2;
        Gravity = 9.8;
        Bfriction = 0.35;
        Portance = 3.92;
        Mass = 1000;
}

void cPlaneEKF_sp::makeA()
{
        A(1,1) = 1.0;
        A(1,2) = Period - Period*Period*Bfriction/Mass*x(2);
        A(1,3) = 0.0;
        A(1,4) = 0.0;

        A(2,1) = 0.0;
        A(2,2) = 1 - 2*Period*Bfriction/Mass*x(2);
        A(2,3) = 0.0;
        A(2,4) = 0.0;

        A(3,1) = 0.0;
        A(3,2) = Period*Period*Portance/Mass*x(2);
        A(3,3) = 1.0;
        A(3,4) = Period;

        A(4,1) = 0.0;
        A(4,2) = 2*Period*Portance/Mass*x(2);
        A(4,3) = 0.0;
        A(4,4) = 1.0;
}

void cPlaneEKF_sp::makeW()
{
        W(1,1) = 0.0;
        W(1,2) = 0.0;
        W(2,1) = 1.0;
        W(2,2) = 0.0;
        W(3,1) = 0.0;
        W(3,2) = 0.0;
        W(4,1) = 0.0;
        W(4,2) = 1.0;
}

void cPlaneEKF_sp::makeQ()
{
        Q(1,1) = 0.01*0.01;
        Q(1,2) = 0.01*0.01/10.0;
        Q(2,1) = 0.01*0.01/10.0;
        Q(2,2) = 0.01*0.01;
}

void cPlaneEKF_sp::makeH()
{
        H(1,1) = -x(3)/(x(1)*x(1)+x(3)*x(3));
        H(1,2) = 0.0;
        H(1,3) = x(1)/(x(1)*x(1)+x(3)*x(3));
        H(1,4) = 0.0;

        H(2,1) = x(1)/sqrt(x(1)*x(1)+x(3)*x(3));
        H(2,2) = 0.0;
        H(2,3) = x(3)/sqrt(x(1)*x(1)+x(3)*x(3));
        H(2,4) = 0.0;
}

void cPlaneEKF_sp::makeV()
{
        V(1,1) = 1.0;
        V(1,2) = 0.0;
        V(2,1) = 0.0;
        V(2,2) = 1.0;
}

void cPlaneEKF_sp::makeR()
{
        R(1,1) = 0.01*0.01;
        R(1,2) = 0.0;
        R(2,1) = 0.0;
        R(2,2) = 50*50;
}

void cPlaneEKF_sp::makeProcess()
{
        Vector x_(x.size());
        x_(1) = x(1) + x(2)*Period + (Period*Period)/2*(u(1)/Mass - Bfriction/Mass*x(2)*x(2));
        x_(2) = x(2) + (u(1)/Mass - Bfriction/Mass*x(2)*x(2))*Period;
        x_(3) = x(3) + x(4)*Period + (Period*Period)/2*(Portance/Mass*x(2)*x(2)-Gravity);
        x_(4) = x(4) + (Portance/Mass*x(2)*x(2)-Gravity)*Period;
        x.swap(x_);
}

void cPlaneEKF_sp::makeMeasure()
{
        z(1)=atan2(x(3), x(1));
        z(2)=sqrt(x(1)*x(1)+x(3)*x(3));
}