From 308e48bee56e83db6dc87820100b8379afe09f0d Mon Sep 17 00:00:00 2001 From: Tyler Veness Date: Tue, 21 Mar 2023 05:30:01 -0700 Subject: [PATCH] Add missing superscript to Kalman filter equations (#2222) The a posteriori state estimate should be the input to the state prediction step. --- .../advanced-controls/state-space/state-space-observers.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/source/docs/software/advanced-controls/state-space/state-space-observers.rst b/source/docs/software/advanced-controls/state-space/state-space-observers.rst index a84ee0e617b..c498fa35d23 100644 --- a/source/docs/software/advanced-controls/state-space/state-space-observers.rst +++ b/source/docs/software/advanced-controls/state-space/state-space-observers.rst @@ -39,7 +39,7 @@ The following shows the equations of a discrete-time Kalman filter: .. math:: \text{Predict step} \nonumber \\ - \hat{\mathbf{x}}_{k+1}^- &= \mathbf{A}\hat{\mathbf{x}}_k + \mathbf{B} \mathbf{u}_k \\ + \hat{\mathbf{x}}_{k+1}^- &= \mathbf{A}\hat{\mathbf{x}}_k^+ + \mathbf{B} \mathbf{u}_k \\ \mathbf{P}_{k+1}^- &= \mathbf{A} \mathbf{P}_k^- \mathbf{A}^T + \mathbf{\Gamma}\mathbf{Q}\mathbf{\Gamma}^T \\ \text{Update step} \nonumber \\