public override void func_zeroedyigraphics_and_Pzeroedyigraphics(Vector yi, Vector xv,
MatrixFixed Pxx, MatrixFixed Pxyi, MatrixFixed Pyiyi)
{
((Wide_Camera_Point_Feature_Measurement_Model)wide_model).threed_motion_model.func_xp(xv);
// In this case (where the feature state is the same as the graphics
// state) zeroedyigraphics is the same as zeroedyi
func_zeroedyi_and_dzeroedyi_by_dxp_and_dzeroedyi_by_dyi(yi, ((Wide_Camera_Point_Feature_Measurement_Model)wide_model).threed_motion_model.get_xpRES());
zeroedyigraphicsRES.Update(zeroedyiRES);
MatrixFixed dzeroedyigraphics_by_dxv = dzeroedyi_by_dxpRES * ((Wide_Camera_Point_Feature_Measurement_Model)wide_model).threed_motion_model.get_dxp_by_dxvRES();
PzeroedyigraphicsRES.Update(dzeroedyigraphics_by_dxv * Pxx * dzeroedyigraphics_by_dxv.Transpose() +
dzeroedyi_by_dyiRES * Pxyi.Transpose() * dzeroedyigraphics_by_dxv.Transpose() +
dzeroedyigraphics_by_dxv * Pxyi * dzeroedyi_by_dyiRES.Transpose() +
dzeroedyi_by_dyiRES * Pyiyi * dzeroedyi_by_dyiRES.Transpose());
}
/// <summary>
/// Step the MonoSLAM application on by one frame. This should be called every time
/// a new frame is captured (and care should be taken to avoid skipping frames).
/// Before calling this function, Scene_Single::load_new_image() should be called
/// (e.g. using
/// <code>monoslaminterface.GetRobotNoConst()->load_new_image()</code>), since the
/// first parameter to GoOneStep() is currently ignored.
///
/// GoOneStep() performs the following processing steps:
/// - Kalman filter prediction step (by calling Kalman::predict_filter_fast(),
/// with a zero control vector)
/// - Select a set of features to make measurements from (set by
/// SetNumberOfFeaturesToSelect())
/// - Predict the locations and and make measurements of those features
/// - Kalman filter update step
/// - Delete any bad features (those that have repeatedly failed to be matched)
/// - If we are not currently initialising a enough new features, and the camera is
/// translating, and <code>currently_mapping_flag</code> is set, initialise a new
/// feature somewhere sensible
/// - Update the partially-initialised features
/// </summary>
/// <param name="img">camera image</param>
/// <param name="delta_t">The time between frames in seconds</param>
/// <param name="currently_mapping_flag">Set to be true if new features should be detected and added to the map.</param>
/// <returns></returns>
public bool GoOneStep(float delta_t, bool currently_mapping_flag)
{
if (delta_t > 0)
{
// update the integral image for use in feature detection
//img.updateIntegralImage();
// nullify image selection
robot.nullify_image_selection();
init_feature_search_region_defined_flag = false;
// Control vector of accelerations
Vector u = new Vector(3);
u.Fill(0.0f);
sim_or_rob.set_control(u, delta_t);
// Record the current position so that I can estimate velocity
// (We can guarantee that the state vector has position; we can't
// guarantee that it has velocity.)
Vector xv = scene.get_xv();
scene.get_motion_model().func_xp(xv);
Vector prev_xp_pos = (scene.get_motion_model().get_xpRES()).Extract(3);
// Prediction step
if (currently_mapping_flag)
kalman.predict_filter_fast(scene, u, delta_t);
// if features are not seen the first time try a few more times
int tries = 0;
number_of_visible_features = 0;
while (((tries == 0) || (scene.get_no_selected() < 2)) && (tries < 5))
{
number_of_visible_features = scene.auto_select_n_features(NUMBER_OF_FEATURES_TO_SELECT);
if (scene.get_no_selected() > 0)
{
//scene.predict_measurements(); // commented out in original code
number_of_matched_features = (uint)SceneLib.make_measurements(scene, sim_or_rob, rnd);
if (scene.get_successful_measurement_vector_size() != 0)
{
// this function is the slowest part of the algorithm
kalman.total_update_filter_slow(scene);
scene.normalise_state();
}
}
tries++;
}
if (currently_mapping_flag)
scene.delete_bad_features();
// Let's enforce symmetry of covariance matrix...
// Add to transpose and divide by 2
uint tot_state_size = scene.get_total_state_size();
MatrixFixed Pxx = new MatrixFixed(tot_state_size, tot_state_size);
scene.construct_total_covariance(ref Pxx);
MatrixFixed PxxT = Pxx.Transpose();
Pxx.Update(Pxx * 0.5f + PxxT * 0.5f);
scene.fill_covariances(Pxx);
// Look at camera speed estimate
// Get the current position and estimate the speed from it
xv = scene.get_xv();
scene.get_motion_model().func_xp(xv);
Vector xp_pos = scene.get_motion_model().get_xpRES().Extract(3);
velocity = (xp_pos - prev_xp_pos) / delta_t;
speed = (float)Math.Sqrt(velocity.SquaredMagnitude());
// This section of code is a workaround for a situation where
// the camera suddenly shoots off at high speed, which must be
// a bug perhaps in the state update. If the camera suddenly accelerates
// at a high rate then this just sets the state back to the previous one.
if (prev_speed == 0)
prev_speed = speed;
else
{
float speed_change = speed / prev_speed;
if ((speed > 1) && (speed_change > 1.2) && (prev_xv != null))
{
xv.Update(prev_xv);
}
}
prev_speed = speed;
if (prev_xv != null) // TODO: minor bug here with vector != operator
prev_xv.Update(xv);
else
prev_xv = new Vector(xv);
if (currently_mapping_flag)
{
if (speed > 0.2)
{
if ((number_of_visible_features < NUMBER_OF_FEATURES_TO_KEEP_VISIBLE) &&
(scene.get_feature_init_info_vector().Count < (uint)(MAX_FEATURES_TO_INIT_AT_ONCE)))
{
// if the number of features is low make more attempts
// to initialise new ones
tries = 1;
if (number_of_visible_features < 8) tries = 2;
if (number_of_visible_features < 5) tries = 3;
for (int i = 0; i < tries; i++) AutoInitialiseFeature(u, delta_t);
}
}
}
MatchPartiallyInitialisedFeatures();
recordCameraHistory();
}
return true;
}
//*************************Some important operations***************************
public void zero_axes()
{
uint size = get_total_state_size();
Vector x = new Vector(size);
x.Fill(0.0f);
MatrixFixed dxnew_by_dxold = new MatrixFixed(size, size);
dxnew_by_dxold.Fill(0.0f);
// We form the new state and Jacobian of the new state w.r.t. the old state
uint state_position = 0;
// Robot part
motion_model.func_zeroedxv_and_dzeroedxv_by_dxv(xv);
x.Update(motion_model.get_zeroedxvRES(), 0);
dxnew_by_dxold.Update(motion_model.get_dzeroedxv_by_dxvRES(), 0, 0);
state_position += motion_model.STATE_SIZE;
// Each feature in turn
uint feature_no = 0;
// Copy these to be on the safe side
motion_model.func_xp(xv);
Vector local_xp = new Vector(motion_model.get_xpRES());
//Vector local_xp = motion_model.get_xpRES();
motion_model.func_dxp_by_dxv(xv);
//MatrixFixed local_dxp_by_dxv = motion_model.get_dxp_by_dxvRES();
MatrixFixed local_dxp_by_dxv = new MatrixFixed(motion_model.get_dxp_by_dxvRES());
Feature it;
MatrixFixed Temp_FS1;
for (int i=0; i < feature_list.Count; i++)
{
it = (Feature)feature_list[i];
it.get_feature_measurement_model().func_zeroedyi_and_dzeroedyi_by_dxp_and_dzeroedyi_by_dyi(it.get_y(), local_xp);
x.Update(it.get_feature_measurement_model().get_zeroedyiRES(), (int)state_position);
// Calculate dzeroedyi_by_dxv in Temp_FS1
Temp_FS1 = it.get_feature_measurement_model().get_dzeroedyi_by_dxpRES() * local_dxp_by_dxv;
dxnew_by_dxold.Update(Temp_FS1, (int)state_position, 0);
dxnew_by_dxold.Update(it.get_feature_measurement_model().get_dzeroedyi_by_dyiRES(),
(int)state_position, (int)state_position);
// We also want to redefine xp_orig for this feature: the robot
// position at which is was initialised into the map (used by
// functions for checking visibility)
motion_model.func_xpredef_and_dxpredef_by_dxp_and_dxpredef_by_dxpdef(
it.get_xp_orig(), local_xp);
it.set_xp_orig(it.get_feature_measurement_model().get_motion_model().get_xpredefRES());
feature_no++;
state_position += it.get_feature_measurement_model().FEATURE_STATE_SIZE;
}
// Check we've counted properly
//assert (feature_no == feature_list.size() &&
// state_position == total_state_size);
// Do a Jacobian transform to get the new covariance
MatrixFixed P = new MatrixFixed(size, size);
construct_total_covariance(ref P);
P = dxnew_by_dxold * P * dxnew_by_dxold.Transpose();
// Finally load the scene data structures with the new state and covariance
fill_states(x);
fill_covariances(P);
}
/// <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);
}
/// <summary>
/// Fill noise covariance matrix Pnn: this is the covariance of
/// the noise vector (V)
/// (Omega)
/// that gets added to the state.
/// Form of this could change later, but for now assume that
/// V and Omega are independent, and that each of their components is
/// independent...
/// </summary>
/// <param name="xv"></param>
/// <param name="v"></param>
/// <param name="delta_t"></param>
public override void func_Q(Vector xv, Vector v, float delta_t)
{
float linear_velocity_noise_variance =
SD_A_component_filter * SD_A_component_filter * delta_t * delta_t;
float angular_velocity_noise_variance =
SD_alpha_component_filter * SD_alpha_component_filter * delta_t * delta_t;
// Independence means that the matrix is diagonal
MatrixFixed Pnn = new MatrixFixed(6,6);
Pnn.Fill(0.0f);
Pnn.Put(0, 0, linear_velocity_noise_variance);
Pnn.Put(1, 1, linear_velocity_noise_variance);
Pnn.Put(2, 2, linear_velocity_noise_variance);
Pnn.Put(3, 3, angular_velocity_noise_variance);
Pnn.Put(4, 4, angular_velocity_noise_variance);
Pnn.Put(5, 5, angular_velocity_noise_variance);
// Form Jacobian dxnew_by_dn
// Is like this:
// I * delta_t 0
// 0 dqnew_by_dOmega
// I 0
// 0 I
// Start by zeroing
MatrixFixed dxnew_by_dn = new MatrixFixed(13,6);
dxnew_by_dn.Fill(0.0f);
// Fill in easy bits first
MatrixFixed Temp33A = new MatrixFixed(3,3);
Temp33A.SetIdentity();
dxnew_by_dn.Update(Temp33A, 7, 0);
dxnew_by_dn.Update(Temp33A, 10, 3);
Temp33A *= delta_t;
dxnew_by_dn.Update(Temp33A, 0, 0);
// Tricky bit is dqnew_by_dOmega
// Is actually the same calculation as in func_fv...
// Since omega and Omega are additive...?
Vector3D rold = new Vector3D(0, 0, 0);
Vector3D vold = new Vector3D(0, 0, 0);
Vector3D omegaold = new Vector3D(0, 0, 0);
Quaternion qold=new Quaternion();
extract_r_q_v_omega(xv, rold, qold, vold, omegaold); // overkill but easy
// Fill in dqnew_by_domega = d(q x qwt)_by_dqwt . dqwt_by_domega
// Temp44A is d(q x qwt) by dqwt
MatrixFixed Temp44A = MatrixFixed.dq3_by_dq1(qold);
// Use function below for dqwt_by_domega
MatrixFixed Temp43A = new MatrixFixed(4,3);
dqomegadt_by_domega(omegaold, delta_t, Temp43A);
// Multiply them together
MatrixFixed Temp43B = Temp44A * Temp43A;
// And then plug into Jacobian
dxnew_by_dn.Update(Temp43B, 3, 3);
// Finally do Q = dxnew_by_dn . Pnn . dxnew_by_dnT
QxRES.Update( dxnew_by_dn * Pnn * dxnew_by_dn.Transpose() );
// cout << "QxRES" << QxRES;
}
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);
}
/// <summary>
/// Calculate the innovation covariance. This is the overall measurement
/// uncertainty in the feature, a combination of the uncertainty in the robot
/// state, the feature state, and the measurement uncertainty. This calculation is
/// generic to all feature measurement models, but could be over-ridden if necessary
/// (e.g. for an efficient implementation). The innovation covariance is given by
/// \f[S_i = \frac{\partial h_i}{\partial x_v} P_{xx}
/// \frac{\partial h_i}{\partial x_v}^T
/// + \frac{\partial h_i}{\partial x_v} P_{xy_i}
/// \frac{\partial h_i}{\partial y_i}^T
/// + \frac{\partial h_i}{\partial y_i} P_{y_i x}
/// \frac{\partial h_i}{\partial x_v}^T
/// + \frac{\partial h_i}{\partial y_i} P_{y_i y_i}
/// \frac{\partial h_i}{\partial y_i}^T
/// + R_i ]
/// where R_i is the noise covariance of measurements (usually assumed to
/// be diagonal with magnitude determined by the image resolution).
/// </summary>
/// <param name="Pxx">The covariance P_{xy_i} between the robot state x_v and the feature state y_i .</param>
/// <param name="Pxyi">The covariance of the feature, P_{y_iy_i} </param>
/// <param name="Pyiyi">The Jacobian \frac{\partial h_i}{\partial x_v} between the feature measurement h_i and the robot state x_v </param>
/// <param name="dhi_by_dxv">The Jacobian \frac{\partial h_i}{\partial y_i} between the feature measurement h_i and the feature state y_i </param>
/// <param name="dhi_by_dyi">The innovation covariance R_i</param>
/// <param name="Ri"></param>
public void func_Si(MatrixFixed Pxx,
MatrixFixed Pxyi,
MatrixFixed Pyiyi,
MatrixFixed dhi_by_dxv,
MatrixFixed dhi_by_dyi,
MatrixFixed Ri)
{
// Zero SiRES and add bits on
SiRES.Fill(0.0f);
SiRES += dhi_by_dxv * Pxx * dhi_by_dxv.Transpose();
MatrixFixed Temp_MM1 = dhi_by_dxv * Pxyi * dhi_by_dyi.Transpose();
SiRES += Temp_MM1;
SiRES += Temp_MM1.Transpose();
SiRES += dhi_by_dyi * Pyiyi * dhi_by_dyi.Transpose();
SiRES += Ri;
}
public void func_Sv(MatrixFixed Pxx,
MatrixFixed dhv_by_dxv,
MatrixFixed Rv)
{
// Zero SiRES and add bits on
SvRES.Fill(0.0f);
SvRES += dhv_by_dxv * Pxx * dhv_by_dxv.Transpose();
SvRES += Rv;
}
/// <summary>
/// Form the covariance matrix Q of the process noise associated with x_v .
/// </summary>
/// <param name="xv"></param>
/// <param name="v"></param>
/// <param name="delta_t"></param>
public override void func_Q(Vector xv, Vector v, float delta_t)
{
// Fill noise covariance matrix Pnn: this is the covariance of
// the noise vector (V)
// (Omega)
// that gets added to the state.
// Form of this could change later, but for now assume that
// V and Omega are independent, and that each of their components is
// independent...
float linear_velocity_noise_variance =
SD_A_component_filter * SD_A_component_filter * delta_t * delta_t;
float angular_velocity_noise_variance =
SD_alpha_component_filter * SD_alpha_component_filter * delta_t * delta_t;
// Independence means that the matrix is diagonal
MatrixFixed Pnn = new MatrixFixed(6, 6);
Pnn.Fill(0.0f);
Pnn.Put(0, 0, linear_velocity_noise_variance);
Pnn.Put(1, 1, linear_velocity_noise_variance);
Pnn.Put(2, 2, linear_velocity_noise_variance);
Pnn.Put(3, 3, angular_velocity_noise_variance);
Pnn.Put(4, 4, angular_velocity_noise_variance);
Pnn.Put(5, 5, angular_velocity_noise_variance);
// Form Jacobian dxnew_by_dn
// Is like this:
// I * delta_t 0
// 0 dqnew_by_dOmega
// Start by zeroing
MatrixFixed dxnew_by_dn = new MatrixFixed(7, 6);
dxnew_by_dn.Fill(0.0f);
// The translation part is just I \Delta t
MatrixFixed Temp33A = new MatrixFixed(3, 3);
Temp33A.SetIdentity();
Temp33A *= delta_t;
dxnew_by_dn.Update(Temp33A, 0, 0);
// qnew = q x \Omega \Deltat
// dqnew_by_d\Omega = dqnew_by_d\Omega\Delta t . d\Omega\Delta t_by_d\Omega
// Get the first part
Vector qRXYZ = xv.Extract(4, 3);
Quaternion qold = new Quaternion();
qold.SetRXYZ(qRXYZ);
MatrixFixed Temp44A = MatrixFixed.dq3_by_dq1(qold);
// Use function below for dqwt_by_dOmega
Vector Omega = new Vector(3);
Omega.Fill(SD_alpha_component_filter);
MatrixFixed Temp43A = new MatrixFixed(4, 3);
dqomegadt_by_domega(new Vector3D(Omega), delta_t, Temp43A);
// Multiply them together
MatrixFixed Temp43B = Temp44A * Temp43A;
// And then plug into Jacobian
dxnew_by_dn.Update(Temp43B, 3, 3);
// Finally do Q = dxnew_by_dn . Pnn . dxnew_by_dnT
QxRES.Update(dxnew_by_dn * Pnn * dxnew_by_dn.Transpose());
}