A Gentle Introduction to Predictive Filters
AbstractPredictive filters are essential tools in modern science. They perform state prediction and parameter estimation in fields such as robotics, computer vision, and computer graphics. Sometimes also called Bayesian filters, they apply the Bayesian rule of conditional probability to combine a predicted behavior with some corrupted indirect observation. When we study and solve a problem, we first need its proper mathematical formulation. Finding the essential parameters that best describe the system is hard; modeling their behaviors over time is even more challenging. Usually, we also have an inspection mechanism that provides us with indirect measurements, the observations, of the hidden underlying parameters. We also need to deal with the concept of uncertainty, and use random variables to represent both the state and the observations. Predictive filters are a family of estimation techniques. They combine the uncertain prediction from the system’s dynamics and the corrupted observation. There are many different predictive filters, each dealing with different types of mathematical representations for random variables and system dynamics. Here, the reader will find a dense introduction to predictive filters. After a general introduction, we discuss briefly discussion about mathematical modeling of systems: state representation, dynamics, and observation. Then, we expose some basic issues related to random variables and uncertainty modeling, and discuss four implementations of predictive filters, in order of complexity: the Kalman filter, the extended Kalman filter, the particle filter, and the unscented Kalman filter. Keywords: Predictive Filters, Density Estimators, Kalman Filter, Particle Filter, Unscented Kalman Filter.
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How to Cite
Goldenstein, S. K. (2004). A Gentle Introduction to Predictive Filters. Revista De Informática Teórica E Aplicada, 11(1), 63–92. https://doi.org/10.22456/2175-2745.5962