Department of Biomedical Engineering and Computational Science

Tracking a random sine signal, 'ekf_sine_demo'

In this demonstration we use the extended Kalman filter to estimate a sine signal, whose amplitude and angular velocity are pertubed by Gaussian noise. The non-linearity of the signal is expressed by the measurement model while the dynamical model remains linear. The main purpose of this example is to demonstrate the usage of EKF in this toolbox, but the signal is also estimated with UKF. See the documentation for the discussion and results.

Files used in this example:

EKF_SINE_F
EKF_SINE_H
EKF_SINE_DH_DX
EKF_SINE_D2H_DX2
EKF_SINE_DEMO
Dynamic model function (needed by the augmented UKF)
Measurement model function
Jacobian of the measurement model
Hessian of the measurement model
Random sine signal demonstration
Figure 1

Figure 1. Filtering results of first order EKF.

Figure 1

Figure 2. Smoothing results of extended RTS-smoother.

Figure 1

Figure 3. Smoothing results of extended Two Filter smoother.