vulcan::gaussian Namespace Reference

Functions
template<typename Scalar>
Scalar	apply (const Scalar &noise_input, double sigma)
	Apply Gaussian white noise scaling.
template<typename Scalar>
Scalar	apply_psd (const Scalar &noise_input, double psd_density, double dt)
	Apply white noise with PSD-based scaling.
double	variance_from_psd (double psd_density, double dt)
	Compute discrete variance from continuous PSD.
double	psd_from_variance (double variance, double dt)
	Compute continuous PSD from discrete variance.
double	sigma_from_arw (double N, double dt)
	Compute white noise gain from Allan variance N parameter.

Function Documentation

apply()

template<typename Scalar>

Scalar vulcan::gaussian::apply	(	const Scalar &	noise_input,
		double	sigma )

Apply Gaussian white noise scaling.

Scales a unit-variance white noise sample by the specified standard deviation. For discrete-time simulation with a given PSD, use the appropriate scaling: σ_discrete = σ_continuous / √(Δt)

Template Parameters

Scalar

double or casadi::MX

Parameters

noise_input	White noise sample with unit variance (N(0,1))
sigma	Standard deviation of the output noise

Returns

Scaled noise value with variance σ²

apply_psd()

template<typename Scalar>

Scalar vulcan::gaussian::apply_psd	(	const Scalar &	noise_input,
		double	psd_density,
		double	dt )

Apply white noise with PSD-based scaling.

Converts continuous-time power spectral density to discrete-time variance and applies appropriate scaling. This is the correct way to generate discrete noise samples from a continuous PSD specification.

For one-sided PSD S(f) [units²/Hz]: σ²_discrete = S(f) / Δt

Template Parameters

Scalar

double or casadi::MX

Parameters

noise_input	White noise sample with unit variance
psd_density	One-sided power spectral density [units²/Hz]
dt	Time step [s]

Returns

Scaled noise value

psd_from_variance()

double vulcan::gaussian::psd_from_variance ( double variance, double dt )

inline

Compute continuous PSD from discrete variance.

Inverse of variance_from_psd.

Parameters

variance	Discrete-time variance [units²]
dt	Time step [s]

Returns

One-sided power spectral density [units²/Hz]

sigma_from_arw()

double vulcan::gaussian::sigma_from_arw ( double N, double dt )

inline

Compute white noise gain from Allan variance N parameter.

The angle/velocity random walk parameter N from Allan variance analysis is related to the white noise PSD by: PSD = N²

For discrete-time: σ = N / √(Δt)

Parameters

N	Angle or velocity random walk [rad/s/√Hz] or [m/s²/√Hz]
dt	Time step [s]

Returns

Standard deviation for discrete noise samples

variance_from_psd()

double vulcan::gaussian::variance_from_psd ( double psd_density, double dt )

inline

Compute discrete variance from continuous PSD.

Given a one-sided power spectral density S(f) [units²/Hz] and sample period Δt, computes the variance of discrete-time samples.

Parameters

psd_density	One-sided power spectral density [units²/Hz]
dt	Time step [s]

Returns

Variance of discrete samples [units²]