kalman_linear.cpp

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#include "sigpack.h"
 
using namespace std;
using namespace sp;
 
int main()
{
    // Number of samples
    arma::uword Nsamp = 120;
    arma::uword N     = 6; // Nr of states
    arma::uword M     = 2; // Nr of measurements
    arma::uword L     = 1; // Nr of inputs
 
    // Instatiate a Kalman Filter
    KF kalman( N, M, L );
 
    // Initialisation and setup of system
    double P0 = 100;
    double Q0 = 0.00003;
    double R0 = 25;
 
    // Meas interval
    double dT = 0.1;
 
    arma::mat x = { 0, 10, 1, 50, -0.08, -9 };
    kalman.set_state_vec( 0.9 * x.t() );
    // [X,Y,Vx,Vy,Ax,Ay] use position, velocity and acceleration as states
    arma::mat A = { { 1, 0, dT, 0, dT * dT / 2, 0 }, { 0, 1, 0, dT, 0, dT * dT / 2 }, { 0, 0, 1, 0, dT, 0 }, { 0, 0, 0, 1, 0, dT }, { 0, 0, 0, 0, 1, 0 }, { 0, 0, 0, 0, 0, 1 } };
    kalman.set_trans_mat( A );
 
    arma::mat H = { { 1, 0, 0, 0, 0, 0 }, { 0, 1, 0, 0, 0, 0 } };
    kalman.set_meas_mat( H );
 
    arma::mat P = P0 * arma::eye( N, N );
    kalman.set_err_cov( P );
    arma::mat Q       = arma::zeros( N, N );
    Q( N - 2, N - 2 ) = 1;
    Q( N - 1, N - 1 ) = 1;
    Q                 = Q0 * Q;
    kalman.set_proc_noise( Q );
 
    arma::mat R = R0 * arma::eye( M, M );
    kalman.set_meas_noise( R );
 
    // Create simulation data
    arma::mat z( M, Nsamp, arma::fill::zeros );
    arma::mat z0( M, Nsamp, arma::fill::zeros );
 
    arma::mat xx( N, 1, arma::fill::zeros );
    xx = x.t();
    for( arma::uword n = 1; n < Nsamp; n++ )
    {
        xx          = A * xx + 0.1 * Q * arma::randn( N, 1 );
        z0.col( n ) = H * xx; //
    }
 
    z.row( 0 ) = z0.row( 0 ) + 0.001 * R0 * arma::randn( 1, Nsamp );
    z.row( 1 ) = z0.row( 1 ) + 0.8 * R0 * arma::randn( 1, Nsamp );
 
    arma::mat  x_log( N, Nsamp );
    arma::mat  e_log( M, Nsamp );
    arma::cube P_log( N, N, Nsamp );
    arma::mat  xs_log( M, Nsamp );
    arma::cube Ps_log( N, N, Nsamp );
 
    // Kalman filter loop
    for( arma::uword n = 0; n < Nsamp; n++ )
    {
        kalman.predict();
        kalman.update( z.col( n ) );
 
        x_log.col( n )   = kalman.get_state_vec();
        e_log.col( n )   = kalman.get_err();
        P_log.slice( n ) = kalman.get_err_cov();
    }
 
    // RTS smoother
    kalman.rts_smooth( x_log, P_log, xs_log, Ps_log );
 
    // Display result
    gplot gp0;
    gp0.window( "Plot", 10, 10, 500, 500 );
    gp0.set_term( "qt" );
    gp0.plot_add( z0.row( 0 ), z0.row( 1 ), "True Y", "lines dashtype 2 linecolor \"black\"" );
    gp0.plot_add( z.row( 0 ), z.row( 1 ), "Meas Y", "points" );
    gp0.plot_add( x_log.row( 0 ), x_log.row( 1 ), "Kalman" );
    gp0.plot_add( xs_log.row( 0 ), xs_log.row( 1 ), "RTS smooth" );
    gp0.plot_show();
 
    return 0;
}