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Functions | |
double | MSE_snapshot_of_velocity_integrand (double velocity, double tilde_deltat, double xi) |
This function computes the integrand of equation (21): {1}{T {sinc}^2( { v T}{2 })}. More... | |
double | MSE_snapshot_of_velocity (double velocity, double tilde_deltat) |
This function computes the MSE of a snapshot for a given velocity. This is equation (21) up to a 1 factor: {0}^{} {|u|_{L^1()}} {T {sinc}^2( { v T}{2 })}d. More... | |
double | MSE_flutter_of_velocity_integrand (double *code, int code_length, double velocity, double tilde_deltat, double xi) |
This function computes the integrand of equation (21): {| |^2_{L^2()} |u|_{L^1()}}{| ( v)|^2}d. More... | |
double | MSE_flutter_of_velocity (double *code, int code_length, double velocity, double tilde_deltat) |
This function computes the MSE of flutter shutter for a given velocity. This is equation (22) up to a 1 factor: {0}^{} {| |^2_{L^2()} |u|_{L^1()}}{| ( v)|^2}d. More... | |
double | abs_hat_alpha (double *code, int code_length, double xi, double deltat) |
Given a code compute the modulus of the Fourier transform of the Flutter-Shutter function, see equation (2): ()= t {sinc}({ t}{2}) e^{-{i t}{2}} {k=0}^{L-1} e^{-ik t}. More... | |
double | gain_in_terms_of_RMSE_at_velocity_v (double *code, int code_length, double tilde_deltat, double velocity, double deltat) |
This function implements equation (23): G(v)&={ {{0}^{} {1} {T^* {sinc}^2( { v T^*}{2 })}d} { {0}^{} {| |^2_{L^2()}} {| ( v)|^2}d }}. More... | |
double | probability_density (double velocity, int flag_motion_model, double s) |
Given a velocity velocity, the motion model and its parameters the function computes the probability. More... | |
void | average_gain_in_terms_of_RMSE (double *code, int code_length, double tilde_deltat_star, int flag_motion_model, double motion_model_parameter, double deltat, int num_plot_points, double *G_of_v, double *average_gain_mu) |
This function implements equation (24): := G(v) (v) dv. More... | |
void | std_dev_gain_in_terms_of_RMSE (int flag_motion_model, double motion_model_parameter, int num_plot_points, double *G_of_v, double *average_gain_mu, double *std_dev_gain_sigma) |
This function implements equation (25): :={ |G(v)- G(u) (u) du|^2 (v) dv}. More... | |
double abs_hat_alpha | ( | double * | code, |
int | code_length, | ||
double | xi, | ||
double | deltat | ||
) |
Given a code compute the modulus of the Fourier transform of the Flutter-Shutter function, see equation (2): ()= t {sinc}({ t}{2}) e^{-{i t}{2}} {k=0}^{L-1} e^{-ik t}.
double* | code : array of doubles where code[k] contains the ; |
int | code_length : length of the code; |
double | xi : frequency; |
double | deltat : the temporal sampling of the flutter shutter function; |
Gives back the modulus of the Fourier transform, see equation (2)
Definition at line 234 of file gain_evaluation.cpp.
void average_gain_in_terms_of_RMSE | ( | double * | code, |
int | code_length, | ||
double | tilde_deltat_star, | ||
int | flag_motion_model, | ||
double | motion_model_parameter, | ||
double | deltat, | ||
int | num_plot_points, | ||
double * | G_of_v, | ||
double * | average_gain_mu | ||
) |
This function implements equation (24): := G(v) (v) dv.
double* | code : array of doubles where code[k] contains the |
int | code_length : length of the code L; |
double | tilde_deltat_star : the optimal exposure time for the snapshot |
int | flag_motion_model : motion model selection -0 for truncated Gaussian of std-dev s; -1 For uniform of range s; |
double | motion_model_parameter : motion model parameter; |
double | deltat : the of the numerical flutter shutter; |
int | num_plot_point : the lengt of output array for plot; |
double | *G_of_v : will contain G(v), see equation (23); |
double | *_average_gain_mu : will contain equation (24); |
Initialization.
Computation of equation (24).
Definition at line 353 of file gain_evaluation.cpp.
double gain_in_terms_of_RMSE_at_velocity_v | ( | double * | code, |
int | code_length, | ||
double | tilde_deltat, | ||
double | velocity, | ||
double | deltat | ||
) |
This function implements equation (23): G(v)&={ {{0}^{} {1} {T^* {sinc}^2( { v T^*}{2 })}d} { {0}^{} {| |^2_{L^2()}} {| ( v)|^2}d }}.
double* | code : array of doubles where code[k] contains the |
int | code_length : length of the code L; |
double | tilde_deltat : the of the snapshot (best snapshot on average); |
double | velocity : velocity; |
double | deltat : the temporal sampling of the flutter shutter function; |
Definition at line 284 of file gain_evaluation.cpp.
double MSE_flutter_of_velocity | ( | double * | code, |
int | code_length, | ||
double | velocity, | ||
double | deltat | ||
) |
This function computes the MSE of flutter shutter for a given velocity. This is equation (22) up to a 1 factor: {0}^{} {| |^2_{L^2()} |u|_{L^1()}}{| ( v)|^2}d.
double MSE_flutter_of_velocity(double* code, int code_length,double velocity, double tilde_deltat)
double* | code : array of doubles where code[k] contains the |
int | code_length : length of the code L; |
double | velocity : the velocity; |
double | deltat : the temporal sampling of the flutter shutter function; |
Initalization.
Definition at line 158 of file gain_evaluation.cpp.
double MSE_flutter_of_velocity_integrand | ( | double * | code, |
int | code_length, | ||
double | velocity, | ||
double | deltat, | ||
double | xi | ||
) |
This function computes the integrand of equation (21): {| |^2_{L^2()} |u|_{L^1()}}{| ( v)|^2}d.
double MSE_flutter_of_velocity_integrand(double* code, int code_length, double velocity, double tilde_deltat, double xi)
double* | code : array of doubles where code[k] contains the |
int | code_length : length of the code L; |
double | velocity : the velocity; |
double | deltat : the temporal sampling of the flutter shutter function; |
doule | xi: the frequency; |
Step1 compute | ( v)|
Step2 : compute ||||_{l2}^2
Definition at line 200 of file gain_evaluation.cpp.
double MSE_snapshot_of_velocity | ( | double | velocity, |
double | tilde_deltat | ||
) |
This function computes the MSE of a snapshot for a given velocity. This is equation (21) up to a 1 factor: {0}^{} {|u|_{L^1()}} {T {sinc}^2( { v T}{2 })}d.
double MSE_snapshot_of_velocity(double velocity,double tilde_deltat)
double | velocity : the velocity; |
double | tilde_deltat: the exposure time of the snapshot; |
Initalization.
Definition at line 80 of file gain_evaluation.cpp.
double MSE_snapshot_of_velocity_integrand | ( | double | velocity, |
double | tilde_deltat, | ||
double | xi | ||
) |
This function computes the integrand of equation (21): {1}{T {sinc}^2( { v T}{2 })}.
double MSE_snapshot_of_velocity_integrand(double velocity, double tilde_deltat, double xi)
double | velocity : the velocity; |
double | tilde_deltat: the exposure time of the snapshot; |
doule | xi: the frequency; |
Definition at line 119 of file gain_evaluation.cpp.
double probability_density | ( | double | velocity, |
int | flag_motion_model, | ||
double | motion_model_parameter | ||
) |
Given a velocity velocity, the motion model and its parameters the function computes the probability.
double probability_density(double velocity, int flag_motion_model, double motion_model_parameter)
double | velocity : the velocity; |
int | flag_motion_model : motion model selection -0 for Gaussian motion model -1 For uniform motion model |
double | motion_model_parameter : motion model parameter; |
Definition at line 310 of file gain_evaluation.cpp.
void std_dev_gain_in_terms_of_RMSE | ( | int | flag_motion_model, |
double | motion_model_parameter, | ||
int | num_plot_points, | ||
double * | G_of_v, | ||
double * | average_gain_mu, | ||
double * | std_dev_gain_sigma | ||
) |
This function implements equation (25): :={ |G(v)- G(u) (u) du|^2 (v) dv}.
double* | code : array of doubles where code[k] contains the |
int | code_length : length of the code L; |
double | tilde_deltat_star : the optimal exposure time for the snapshot |
int | flag_motion_model : motion model selection -0 for truncated Gaussian of std-dev s; -1 For uniform of range s; |
double | motion_model_parameter : motion model parameter; |
double | deltat : the of the numerical flutter shutter; |
int | num_plot_point : the lengt of output array for plot; |
double | *G_of_v : contains G(v), see equation (23); |
double | *_average_gain_mu : contains equation (24); |
double | *std_dev_gain_sigma : will contains equation (25). |
Initialization.
Computation of equation (25), knowing equations (23) and (24)
Definition at line 446 of file gain_evaluation.cpp.