Faculty Advisor

Zhongqiang Zhang


Filtering has been shown successful in prediction from dynamically changing data. In this thesis, we perform case studies and comparison among three filters: Kalman filter, unscented Kalman filter and particle flow filter. We consider Kalman filter in the first chapter where we focus on studying the S&P model in a time-discrete dynamics with time-discrete observations for dividend yield and S&P returns. For this filtering problem, Kalman filter performs well only in the first few time steps. Since the S&P model we consider is nonlinear, we are motivated to apply nonlinear filters and use unscented Kalman filter. The key technique is to approximate non-Gaussian processes (non-linear models) by assigning the so-called sigma points (nonrandom) around the priori mean. We implement it on the S&P model in Chapter 2. We also implement unscented Kalman filter for a two-dimensional tumor growth model. Unscented Kalman filter works reasonably well for both models with capturing the trend and predicting the values. We consider the recently-developed particle flow filter in Chapter 3. Particle flow filter is a method of moving the particles by partial differential equations generated from proper chosen likelihood functions via the Bayes rule. By solving partial differential equations, one can construct an explicit dynamic model on how to move particles.In this chapter, we implement two models as in Chapter 2. One is the S&P model and the other is perturbed tumor growth model. We compare performance of particle flow filter and unscented Kalman filter for these two models.


Worcester Polytechnic Institute

Degree Name



Mathematical Sciences

Project Type


Date Accepted





filters, Kalman filters