Tracking and prediction of moving objects in less than ideal environments can be an extremely hard problem. A partial, distorted, corrupted view or measurement of the desired object may be all that is available. Indeed, the human eye might not be able to make out the moving object at all. Still, typical real-life problems in the stock market, radar, imaging, etc. require efficient solutions. Particle filtering methods are the answer when the Kalman filter does not apply.
We filter out the distortions and corruption on a given signal object, using mathematical methods capable of not only tracking and prediction, but also smoothing, detection, and estimation. Our particle methods are essentially sophisticated Monte-Carlo simulations that model what could be happening in reality and then use the observations to decide which possible scenarios are more likely. We will discuss the functionality of a Hybrid Weighted-Interacting Particle Filter and its application to industry-motivated problems. In our simulations, we will solve a fish tracking problem, locate vessels, and estimate both a stock price and parameters for option pricing.