Financial Derivative and Energy Market Valuation: Theory and Implementation in MATLAB

Chapter 9: Nonlinear and Non-Gaussian Kalman Filter

9.1 Introduction

The Kalman filtration involves the recursive estimation of the first two moments of the state vector based on the currently available information. The Kalman filter is the optimal recursive filtering technique when the process noise and measurement noise terms are Gaussian, and the state and measurement transition models are linear. The linear and Gaussian assumptions ensure that the mean and covariance terms contain all available information regarding the probability distribution function (PDF). Thus, the mean and covariance terms give the optimal estimation of the distribution of the data. In other words, no other estimation technique could provide a superior estimation—assuming the linear and Gaussian assumptions hold (Arulampalam et al., 2002).

At the prediction stage, the linear process model is used to forecast the translation and the spread of the distribution. At the update stage, the new measurement information is used to revise the forecast of the mean and covariance of the distribution. Typically, the Kalman ...