RandomWalk.hpp

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// Random Walk Noise Model
// Integrated white noise (rate random walk / drift)
#pragma once
 
#include <cmath>
#include <janus/janus.hpp>
 
namespace vulcan::random_walk {
 
// =============================================================================
// Random Walk State
// =============================================================================

template <typename Scalar> struct State {
    Scalar value; 
};

template <typename Scalar> State<Scalar> init_state() {
    return State<Scalar>{.value = Scalar(0)};
}
 
// =============================================================================
// Discretized Coefficients
// =============================================================================

struct Coeffs {
    double gain; 
};

inline Coeffs compute_coeffs(double K, double dt) {
    return Coeffs{.gain = K * std::sqrt(dt)};
}
 
// =============================================================================
// Simulation Step
// =============================================================================

template <typename Scalar>
Scalar step(State<Scalar> &state, const Coeffs &coeffs,
            const Scalar &noise_input) {
    state.value = state.value + coeffs.gain * noise_input;
    return state.value;
}

template <typename Scalar>
Scalar step(State<Scalar> &state, double K, double dt,
            const Scalar &noise_input) {
    Coeffs coeffs = compute_coeffs(K, dt);
    return step(state, coeffs, noise_input);
}
 
// =============================================================================
// Analysis Utilities
// =============================================================================

inline double expected_variance(double K, double t) { return K * K * t; }

inline double expected_stddev(double K, double t) { return K * std::sqrt(t); }
 
} // namespace vulcan::random_walk