BiasInstability.hpp

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// Bias Instability Noise Model
// Long-correlation-time Markov process for sensor bias drift
#pragma once
 
#include <cmath>
#include <janus/janus.hpp>
#include <vulcan/sensors/MarkovProcess.hpp>
 
namespace vulcan::bias_instability {
 
// =============================================================================
// Bias Instability State
// =============================================================================

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

template <typename Scalar> State<Scalar> init_state() {
    return State<Scalar>{.bias = Scalar(0)};
}

template <typename Scalar>
State<Scalar> init_state(const Scalar &initial_bias) {
    return State<Scalar>{.bias = initial_bias};
}
 
// =============================================================================
// Discretized Coefficients
// =============================================================================

struct Coeffs {
    double a; 
    double b; 
};

inline Coeffs compute_coeffs(double sigma_b, double tau, double dt) {
    double a = std::exp(-dt / tau);
    double b = sigma_b * std::sqrt(1.0 - a * a);
    return Coeffs{.a = a, .b = b};
}
 
// =============================================================================
// Simulation Step
// =============================================================================

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

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

inline double steady_state_variance(double sigma_b) {
    return sigma_b * sigma_b;
}

inline double time_to_fraction(double tau, double fraction) {
    return -tau / 2.0 * std::log(1.0 - fraction);
}
 
} // namespace vulcan::bias_instability