Function navtk::navutils::discretize_second_order

• Defined in File navigation.hpp

Function Documentation

std::pair<Matrix, Matrix> navtk::navutils::discretize_second_order(const Matrix &f, const Matrix &q, double dt)

Converts from continuous-time dynamic system representation to discrete-time representation using second order algorithm.

See discretize_first_order() for variable definitions.

This function calculates \(\pmb{\Phi}\) using the second order calculation

\(\pmb{\Phi}_2 \approx \textbf{I} + \textbf{F}\Delta t + \frac{1}{2}\textbf{F}^2\Delta t^2\)

and

\(\textbf{Q}_{d_2} \approx \frac{\pmb{\Phi}\textbf{Q}\pmb{\Phi}^T + \textbf{Q}}{2}\Delta t\)

See also

discretize_first_order()

See also

discretize_van_loan()

Parameters

• f – Continuous-time dynamics matrix \(\textbf{F}\)

• q – Continuous-time process noise \(\textbf{Q}\)

• dt – Time (seconds) over which propagation is to take place ( \(\Delta t\))

Returns

(Phi, Qd) The discrete-time matrices as an std::pair. First is Phi \(=\pmb{\Phi}_2\), second is Qd \(=\textbf{Q}_{d_2}\).