vulcan::random_walk Namespace Reference

Classes
struct	State
	Random walk process state. More...
struct	Coeffs
	Pre-computed random walk coefficients. More...

Functions
template<typename Scalar>
State< Scalar >	init_state ()
	Initialize random walk state to zero.
Coeffs	compute_coeffs (double K, double dt)
	Compute random walk coefficients.
template<typename Scalar>
Scalar	step (State< Scalar > &state, const Coeffs &coeffs, const Scalar &noise_input)
	Step the random walk process.
template<typename Scalar>
Scalar	step (State< Scalar > &state, double K, double dt, const Scalar &noise_input)
	Step random walk with inline coefficient computation.
double	expected_variance (double K, double t)
	Compute expected variance at given time.
double	expected_stddev (double K, double t)
	Compute expected standard deviation at given time.

Function Documentation

compute_coeffs()

Coeffs vulcan::random_walk::compute_coeffs ( double K, double dt )

inline

Compute random walk coefficients.

Parameters

K	Rate random walk coefficient [units/s/√Hz]
dt	Time step [s]

Returns

Coeffs structure ready for simulation

expected_stddev()

double vulcan::random_walk::expected_stddev ( double K, double t )

inline

Compute expected standard deviation at given time.

Parameters

K	Rate random walk coefficient [units/s/√Hz]
t	Time since start [s]

Returns

Expected standard deviation at time t

expected_variance()

double vulcan::random_walk::expected_variance ( double K, double t )

inline

Compute expected variance at given time.

For a random walk with parameter K, starting from zero: Var(t) = K² * t

Parameters

K	Rate random walk coefficient [units/s/√Hz]
t	Time since start [s]

Returns

Expected variance at time t

init_state()

template<typename Scalar>

State< Scalar > vulcan::random_walk::init_state

(

)

Initialize random walk state to zero.

Template Parameters

Scalar

double or casadi::MX

Returns

State initialized to zero

step() [1/2]

template<typename Scalar>

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

Step the random walk process.

Updates the random walk state by integrating white noise.

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 random walk value after update

step() [2/2]

template<typename Scalar>

Scalar vulcan::random_walk::step	(	State< Scalar > &	state,
		double	K,
		double	dt,
		const Scalar &	noise_input )

Step random walk with inline coefficient computation.

Convenience function for simpler usage when coefficients don't need to be pre-computed.

Template Parameters

Scalar

double or casadi::MX

Parameters

state	Current state (updated in-place)
K	Rate random walk coefficient [units/s/√Hz]
dt	Time step [s]
noise_input	White noise sample with unit variance

Returns

Current random walk value after update