title: How do you calculate a single variable Kalman Filter?
body: <p><strong>Let's say we use common models</strong></p>
  <p><strong>Use the state evolution model: f(t+1)=a×f(t) + (b×u) + v</strong></p>
  <p><strong>Use the output model: y(k)=c×f(t) + n</strong></p>
  <p><strong>For the sake of simplicity.  Rather than time dependent matrices, we just use these values:
  a=2, b=0.05, c=13, and u=1.5</strong>**</p>
  <p><strong>Process noise “v” follows a Gaussian distribution, mean=0 and variance=0.000001</strong></p>
  <p><strong>Measurement noise “n” follows a Gaussian distribution, mean=0 and variance=1</strong></p>
  <p><strong>I just assume an initial state of x(0)=0.5</strong></p>
  <p>The first five measurements are increasing temperatures:</p>
  <p>y(1)=7.479527812</p>
  <p>y(2)=9.015371756</p>
  <p>y(3)=13.76472827</p>
  <p>y(4)=14.10629548</p>
  <p>y(5)=17.28189501</p>
  <p>How do I estimate f(1) through f(5) and the associated variances?</p>