6  Continuous time Kalman Filter

Reference : Simon (2006).

• It is the Kalman filter that deals with continuous time dynamics and continuous time measurement data. They are mentioned to be used in analog circuits.

• These estimations were mentioned to be performed in the frequency domain instead of time domain.

• This is the 8^th chapter in the book Simon (2006). The authors described the following in this chapter.

  • Relationship between continuous time white-noise and discrete time white-noise.
  • Derivation of Kalman filter for continuous time dynamics and continuous time measurements.
  • Described some creative methods to solve the continuous-time Riccati equation i.e. estimation uncertainty propagation equation \(\mathbf{P}_{k+1}\).
  • Continuous time Kalman filter for the cases with correlated noises.
  • Then finally, the steady-state continuous-time Kalman filter and its relationship with Wiener filter discussed previously and its relationship with linear quadratic optimal control.

The chapter was described in-depth with algorithms and can be referred when needed.

Simon, Dan. 2006. Optimal State Estimation: Kalman, h Infinity, and Nonlinear Approaches. John Wiley & Sons.