vulcan::bias_instability Namespace Reference

Classes
struct	State
	Bias instability state. More...
struct	Coeffs
	Discretized bias instability coefficients. More...

Functions
template<typename Scalar>
State< Scalar >	init_state ()
	Initialize state to zero bias.
template<typename Scalar>
State< Scalar >	init_state (const Scalar &initial_bias)
	Initialize state with given initial bias.
Coeffs	compute_coeffs (double sigma_b, double tau, double dt)
	Compute bias instability coefficients.
template<typename Scalar>
Scalar	step (State< Scalar > &state, const Coeffs &coeffs, const Scalar &noise_input)
	Step the bias instability process.
template<typename Scalar>
Scalar	step (State< Scalar > &state, double sigma_b, double tau, double dt, const Scalar &noise_input)
	Step with inline coefficient computation.
double	steady_state_variance (double sigma_b)
	Steady-state variance of bias instability.
double	time_to_fraction (double tau, double fraction)
	Time to reach fraction of steady-state variance.

Function Documentation

compute_coeffs()

Coeffs vulcan::bias_instability::compute_coeffs ( double sigma_b, double tau, double dt )

inline

Compute bias instability coefficients.

Parameters

sigma_b	Bias instability magnitude (1σ) [units]
tau	Correlation time [s] (typically 100-3600s)
dt	Time step [s]

Returns

Discretized coefficients

init_state() [1/2]

template<typename Scalar>

State< Scalar > vulcan::bias_instability::init_state

(

)

Initialize state to zero bias.

Template Parameters

Scalar

double or casadi::MX

Returns

State initialized to zero

init_state() [2/2]

template<typename Scalar>

State< Scalar > vulcan::bias_instability::init_state

(

const Scalar &

initial_bias

)

Initialize state with given initial bias.

Template Parameters

Scalar

double or casadi::MX

Parameters

initial_bias

Initial bias value

Returns

State initialized to given bias

steady_state_variance()

double vulcan::bias_instability::steady_state_variance ( double sigma_b )

inline

Steady-state variance of bias instability.

At steady state: Var(bias) = σ_b²

Parameters

sigma_b

Bias instability magnitude

Returns

Steady-state variance

step() [1/2]

template<typename Scalar>

Scalar vulcan::bias_instability::step	(	State< Scalar > &	state,
		const Coeffs &	coeffs,
		const Scalar &	noise_input )

Step the bias instability process.

Updates bias: bias[k+1] = a·bias[k] + b·w[k]

Template Parameters

Scalar

double or casadi::MX

Parameters

state	Current state (updated in-place)
coeffs	Pre-computed coefficients
noise_input	White noise sample with unit variance

Returns

Current bias value after update

step() [2/2]

template<typename Scalar>

Scalar vulcan::bias_instability::step	(	State< Scalar > &	state,
		double	sigma_b,
		double	tau,
		double	dt,
		const Scalar &	noise_input )

Step with inline coefficient computation.

Convenience function for simpler usage.

Template Parameters

Scalar

double or casadi::MX

Parameters

state	Current state (updated in-place)
sigma_b	Bias instability magnitude [units]
tau	Correlation time [s]
dt	Time step [s]
noise_input	White noise sample with unit variance

Returns

Current bias value after update

time_to_fraction()

double vulcan::bias_instability::time_to_fraction ( double tau, double fraction )

inline

Time to reach fraction of steady-state variance.

Time for variance to reach (1 - exp(-2t/τ)) of steady-state: t = -τ/2 · ln(1 - fraction)

Parameters

tau	Correlation time [s]
fraction	Fraction of steady-state (e.g., 0.632 for 1-time constant)

Returns

Time [s]