Kalman Filter

kalman_filter!(filter, sys)

Compute predicted states $a$ and forecast errors $v$ with corresponding variances $P$ and $F$ and Kalman gain $K$ for a linear Gaussian State Space model with system matrices sys using the Kalman filter, storing the results in filter.

Arguments

• sys::StateSpaceSystem : state space system matrices

Returns

• filter::MultivariateFilter: Kalman filter output

kalman_filter!(filter, sys)

Compute predicted states $a$ and forecast errors $v$ with corresponding variance $P$ and precision $F⁻¹$ and Kalman gain $K$ for a linear Gaussian State Space model with system matrices sys using the Kalman filter based on Woodbury's Identity, storing the results in filter.

Woodbury's Identity allows direct computation of the inverse variance (precision) $F⁻¹$.

Arguments

• sys::StateSpaceSystem : state space system matrices

Returns

• filter::WoodburyFilter: Kalman filter output

kalman_filter!(filter, sys)

Compute predicted states $a$ and forecast errors $v$ with corresponding variances $P$ and $F$ and Kalman gain $K$ for a linear Gaussian State Space model with system matrices sys using the equation-by-equation or univariate version of the Kalman filter, storing the results in filter.

Arguments

• sys::StateSpaceSystem : state space system matrices

Returns

• filter::UnivariateFilter : Kalman filter output