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Update README.md
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mgrouch authored Oct 4, 2024
1 parent a939310 commit 3cf6dc0
Showing 1 changed file with 14 additions and 14 deletions.
28 changes: 14 additions & 14 deletions README.md
Original file line number Diff line number Diff line change
Expand Up @@ -38,31 +38,31 @@ velocity:

$$
\begin{flalign}
& \Large v_k = v_{k-1} + aT - \hat{a}_{k-1}T &
& \large v_k = v_{k-1} + aT - \hat{a}_{k-1}T &
\end{flalign}
$$

displacement:

$$
\begin{flalign}
& \Large y _k = y _{k-1} + v _{k-1}T + {a \over 2}T^2 - {\hat{a} _{k-1} \over 2}T^2 &
& \large y _k = y _{k-1} + v _{k-1}T + {a \over 2}T^2 - {\hat{a} _{k-1} \over 2}T^2 &
\end{flalign}
$$

displacement integral:

$$
\begin{flalign}
& \Large z _k = z _{k-1} + y _{k-1}T + {v _{k-1} \over 2}T^2 + {a \over 6}T^3 - {\hat{a} _{k-1} \over 6}T^3 &
& \large z _k = z _{k-1} + y _{k-1}T + {v _{k-1} \over 2}T^2 + {a \over 6}T^3 - {\hat{a} _{k-1} \over 6}T^3 &
\end{flalign}
$$

accelerometer bias:

$$
\begin{flalign}
& \Large \hat {a} _k = \hat {a} _{k-1} &
& \large \hat {a} _k = \hat {a} _{k-1} &
\end{flalign}
$$

Expand All @@ -71,7 +71,7 @@ State vector:
$$
\begin{flalign}
&
\Large
\large
x =
\begin{bmatrix}
z \\
Expand All @@ -89,7 +89,7 @@ Process model in matrix form:
$$
\begin{flalign}
&
\Large
\large
x _k = Fx _{k-1} + B u _k + w _k
&
\end{flalign}
Expand All @@ -108,7 +108,7 @@ Observation matrix:
$$
\begin{flalign}
&
\Large
\large
H =
\begin{bmatrix}
1 \\
Expand All @@ -124,7 +124,7 @@ Process matrix:

$$
\begin{flalign}
& \Large
& \large
F =
\begin{bmatrix}
1, & T, & {1 \over 2}T^2, & -{1 \over 6}T^3\\
Expand All @@ -140,7 +140,7 @@ Transition matrix:

$$
\begin{flalign}
& \Large
& \large
B =
\begin{bmatrix}
{1 \over 6}T^3\\
Expand All @@ -166,7 +166,7 @@ $y$ - displacement (at any time):

$$
\begin{flalign}
& \Large
& \large
y = - {L \over {2 \pi}} {a \over g}
&
\end{flalign}
Expand All @@ -179,7 +179,7 @@ wave length L:

$$
\begin{flalign}
& \Large
& \large
L = { {period^2} g \over {2 \pi}}
&
\end{flalign}
Expand All @@ -190,7 +190,7 @@ wave period via frequency:

$$
\begin{flalign}
& \Large
& \large
period = {1 \over f}
&
\end{flalign}
Expand All @@ -200,7 +200,7 @@ acceleration:

$$
\begin{flalign}
& \Large
& \large
a = - (2 \pi f)^2 y
&
\end{flalign}
Expand All @@ -210,7 +210,7 @@ let

$$
\begin{flalign}
& \Large
& \large
\hat{k} = - (2 \pi f)^2
&
\end{flalign}
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