The Kalman Filter Equations

  1. Prediction:

    x t = Dt x tΔt + Σt = ΣDt + Dt ΣtΔt + Dt T
  2. Correction:

    Kt = Σt Mt T ( Mt Σt Mt T + ΣMt )1 x t + = x t + Kt ( yt Mt x t ) Σt + =(I Kt Mt ) Σt

Note

  • D t = D t ( Δ t )

  • Typically, D t = D ( Δ t ) and M t = M .

  • We do not need “full” measurements; just manipulate M accordingly.