From 74899d05886934974dccbb95c36cb2c36e690ea0 Mon Sep 17 00:00:00 2001 From: "David B. Adrian" Date: Wed, 2 Aug 2017 19:35:32 +0200 Subject: [PATCH] Fix covariance update formular in kalman filter incorrect sign according to slides P. 133 --- StaSigProc.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/StaSigProc.tex b/StaSigProc.tex index 077c5d0..0fc88c3 100644 --- a/StaSigProc.tex +++ b/StaSigProc.tex @@ -778,7 +778,7 @@ \section{Recursive Estimation} \\ \textbf{2. step: Update}\\ Mean: $\hat{\vec x}_{n|n} = \hat{\vec x}_{n|n-1} + \ma K_n \left( \vec y_n - \ma H_{n} \hat{\vec x}_{n|n-1} \right)$\\ - Covariance: $\ma C_{\vec x_{n|n}} = \ma C_{\vec x_{n|n-1}} + \ma K_n \ma H_{n} \ma C_{\vec x_{n|n-1}}$\\ + Covariance: $\ma C_{\vec x_{n|n}} = \ma C_{\vec x_{n|n-1}} - \ma K_n \ma H_{n} \ma C_{\vec x_{n|n-1}}$\\ $\hat{\vec x}_{n|n} = \underbrace{\hat{\vec x}_{n|n-1}}_{\hspace{-3em}{\text{estimation} \E[\X_n|\Y_{n-1} = y_{n-1} ]}} + \overbrace{ \ma K_n \underbrace{ \left( \vec y_n - \ma H_{n} \hat{\vec x}_{n|n-1} \right)}_{\text{innovation:} Δy_n} }^{\text{correction:}\\ \E[\X_n|Δ\Y_n = y_n]}$\\[1em]