20 double tilde_deltat,
double xi);
25 double velocity,
double tilde_deltat,
double xi);
30 double abs_hat_alpha(
double* code,
int code_length,
double xi,
double deltat);
33 double tilde_deltat,
double velocity,
double deltat);
38 double tilde_deltat_star,
39 int flag_motion_model,
40 double motion_model_parameter,
double deltat,
43 double *average_gain_mu);
46 double motion_model_parameter,
49 double *average_gain_mu,
50 double *std_dev_gain_sigma);
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_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...
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...
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...
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 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}^{} ...
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 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 ...
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}.