Skip to content

Commit

Permalink
fix typos in the formulas
Browse files Browse the repository at this point in the history
fix typos in the formula to make them correct and agree with python code
  • Loading branch information
partev authored Jan 26, 2024
1 parent a1cb385 commit 24291d2
Showing 1 changed file with 5 additions and 5 deletions.
10 changes: 5 additions & 5 deletions docs/notebooks/linear_gaussian_ssm/kf_tracking.ipynb
Original file line number Diff line number Diff line change
Expand Up @@ -27,14 +27,14 @@
"\n",
"Let the hidden state represent\n",
"the position and velocity of the object,\n",
"$z_t =\\begin{pmatrix} u_t & \\dot{u}_t & v_t & \\dot{v}_t \\end{pmatrix}$.\n",
"$z_t =\\begin{pmatrix} u_t & v_t & \\dot{u}_t & \\dot{v}_t \\end{pmatrix}$.\n",
"(We use $u$ and $v$ for the two coordinates,\n",
"to avoid confusion with the state and observation variables.)\n",
"The process evolves in continuous time, but if we discretize it with step size $\\Delta$,\n",
"we can write the dynamics as the following linear system:\n",
"\n",
"\\begin{align*}\n",
"\\underbrace{\\begin{pmatrix} u_t\\\\ \\dot{u}_t \\\\ v_t \\\\ \\dot{v}_t \\end{pmatrix}}_{z_t}\n",
"\\underbrace{\\begin{pmatrix} u_t\\\\ v_t \\\\ \\dot{u}_t \\\\ \\dot{v}_t \\end{pmatrix}}_{z_t}\n",
" = \n",
"\\underbrace{\n",
"\\begin{pmatrix}\n",
Expand All @@ -44,7 +44,7 @@
"0 & 0 & 0 & 1\n",
"\\end{pmatrix}\n",
"}_{F}\n",
"\\underbrace{\\begin{pmatrix} u_{t-1} \\\\ \\dot{u}_{t-1} \\\\ v_{t-1} \\\\ \\dot{v}_{t-1} \\end{pmatrix}}_{z_{t-1}}\n",
"\\underbrace{\\begin{pmatrix} u_{t-1} \\\\ v_{t-1} \\\\ \\dot{u}_{t-1} \\\\ \\dot{v}_{t-1} \\end{pmatrix}}_{z_{t-1}}\n",
"+ q_t\n",
"\\end{align*}\n",
"\n",
Expand All @@ -62,11 +62,11 @@
" \\underbrace{\n",
" \\begin{pmatrix}\n",
"1 & 0 & 0 & 0 \\\\\n",
"0 & 0 & 1 & 0\n",
"0 & 1 & 0 & 0\n",
" \\end{pmatrix}\n",
" }_{H}\n",
" \\;\n",
"\\underbrace{\\begin{pmatrix} u_t\\\\ \\dot{u}_t \\\\ v_t \\\\ \\dot{v}_t \\end{pmatrix}}_{z_t} \n",
"\\underbrace{\\begin{pmatrix} u_t\\\\ v_t \\\\ \\dot{u}_t \\\\ \\dot{v}_t \\end{pmatrix}}_{z_t} \n",
" + r_t\n",
"\\end{align*}\n",
"\n",
Expand Down

0 comments on commit 24291d2

Please sign in to comment.