/// <summary>
/// Simple overall prediction
/// </summary>
/// <param name="scene"></param>
/// <param name="u"></param>
/// <param name="delta_t"></param>
public void predict_filter_slow(Scene_Single scene, Vector u, float delta_t)
{
Debug.WriteLine("*** SLOW PREDICTION ***");
// What we need to do for the prediction:
// Calculate f and grad_f_x
// Calculate Q
// Form x(k+1|k) and P(k+1|k)
int size = (int)scene.get_total_state_size();
// First form original total state and covariance
Vector x = new Vector(size);
MatrixFixed P = new MatrixFixed(size, size);
scene.construct_total_state_and_covariance(ref x, ref P);
// Make model calculations: store results in RES matrices
Vector xv = scene.get_xv();
//Vector xv = new Vector(scene.get_xv());
scene.get_motion_model().func_fv_and_dfv_by_dxv(xv, u, delta_t);
scene.get_motion_model().func_Q(scene.get_xv(), u, delta_t);
// Find new state f
Vector f = new Vector(size);
// Feature elements of f are the same as x
f.Update(x);
f.Update(scene.get_motion_model().get_fvRES(), 0);
// Find new P
// Since most elements of df_by_dx are zero...
MatrixFixed df_by_dx = new MatrixFixed(size, size);
df_by_dx.Fill(0.0f);
// Fill the rest of the elements of df_by_dx: 1 on diagonal for features
for (int i = (int)scene.get_motion_model().STATE_SIZE; i < df_by_dx.Rows; i++)
{
df_by_dx[i, i] = 1.0f;
}
df_by_dx.Update(scene.get_motion_model().get_dfv_by_dxvRES(), 0, 0);
// Calculate the process noise
MatrixFixed Q = new MatrixFixed(size, size);
Q.Fill(0.0f);
Q.Update(scene.get_motion_model().get_QxRES(), 0, 0);
P.Update(df_by_dx * P * df_by_dx.Transpose());
P += Q;
scene.fill_state_and_covariance(f, P);
}
public void update_filter_internal_measurement_slow(Scene_Single scene, uint i)
{
// Size of measurement vector
uint size = ((Internal_Measurement)(scene.internal_measurement_vector[(int)i])).get_internal_measurement_model().MEASUREMENT_SIZE;
uint size2 = scene.get_total_state_size(); // Size of state vector
Vector x = new Vector(size2);
MatrixFixed P = new MatrixFixed(size2, size2);
scene.construct_total_state_and_covariance(ref x, ref P);
// cout << "x:" << x;
// cout << "P:" << P;
// 1. Form nu and dh_by_dx
Vector nu_tot = new Vector(size);
MatrixFixed dh_by_dx_tot = new MatrixFixed(size, size2);
MatrixFixed R_tot = new MatrixFixed(size, size);
scene.construct_total_internal_measurement_stuff(nu_tot, dh_by_dx_tot, R_tot, i);
// 2. Calculate S(k+1)
MatrixFixed S = new MatrixFixed(size, size);
//MatrixFixed Tempss2 = new MatrixFixed(size, size2);
//MatrixFixed Temps2s = new MatrixFixed(size2, size);
MatrixFixed dh_by_dx_totT = dh_by_dx_tot.Transpose();
S.Update(dh_by_dx_tot * P * dh_by_dx_totT);
S += R_tot;
// cout << "R_tot:" << R_tot;
// cout << "S:" << S;
// cout << "dh_by_dx_tot:" << dh_by_dx_tot;
// cout << "dh_by_dx_totT:" << dh_by_dx_totT;
// 3. Calculate W(k+1)
Cholesky S_cholesky = new Cholesky(S);
MatrixFixed W = P * dh_by_dx_totT * S_cholesky.Inverse();
// cout << "W:" << W;
// 4. Calculate x(k+1|k+1)
x += W * nu_tot;
// 5. Calculate P(k+1|k+1)
P -= W * S * W.Transpose();
scene.fill_state_and_covariance(x, P);
// cout << "x after update:" << x;
// cout << "P after update:" << P;
}
/// <summary>
/// Update the filter in a simple overall way
/// </summary>
/// <param name="scene"></param>
public void total_update_filter_slow(Scene_Single scene)
{
// Steps to update the total filter:
// 1. Form h and dh_by_dx and R(k+1) and z
// 2. Calculate S(k+1)
// 3. Calculate W(k+1)
// 4. Calculate x(k+1|k+1)
// 5. Calculate P(k+1|k+1)
uint size = scene.get_successful_measurement_vector_size(); // Size of measurement vector
uint size2 = scene.get_total_state_size(); // Size of state vector
Vector x = new Vector(size2);
MatrixFixed P = new MatrixFixed(size2, size2);
scene.construct_total_state_and_covariance(ref x, ref P);
// 1. Form nu and dh_by_dx
Vector nu_tot = new Vector(size);
MatrixFixed dh_by_dx_tot = new MatrixFixed(size, size2);
MatrixFixed R_tot = new MatrixFixed(size, size);
scene.construct_total_measurement_stuff(nu_tot, dh_by_dx_tot, R_tot);
// 2. Calculate S(k+1)
MatrixFixed temp_matrix = P * dh_by_dx_tot.Transpose(); //pre-calculate to speed up subsequent stuff
MatrixFixed S = dh_by_dx_tot * temp_matrix;
S += R_tot;
// 3. Calculate W(k+1)
Cholesky S_cholesky = new Cholesky(S);
MatrixFixed W = temp_matrix * S_cholesky.Inverse();
// 4. Calculate x(k+1|k+1)
x += W * nu_tot;
// 5. Calculate P(k+1|k+1)
P -= W * S * W.Transpose();
scene.fill_state_and_covariance(x, P);
}