State Estimation of Van-der Pol Oscillator from Noisy Sensor measurement

The Van-der Pol oscillator is used to analyze realistic oscillations in a variety of real-world systems. Among the most famous self-oscillating systems is the Van-der Pol oscillator. Its mathematical model resembles many complicated systems in nature. An approach based on Bayesian theory is presented in this paper for estimating unknown parameters from noisy sensor data. The Gaussian filtering strategy is the most popular among Bayesian approaches. The intractable integrals encountered during the estimation process are approximated numerically, which is a major issue with Gaussian filtering. A well-known Gaussian filter, the cubature Kalman filter (CKF), is used in this work to estimate unknown parameters. An intractable integral’s numerical approximation is achieved by employing a spherical radial rule of third-degree. Its estimation accuracy is demonstrated on a nonlinear oscillator by the root mean square error (RMSE).