A Zakai equation derivation of the extended Kalman filter

作者：Elliott Robert J^*; Haykin Simon

来源：Automatica, 2010, 46(3): 620-624.

DOI：10.1016/j.automatica.2010.01.006

• Extended Kalman filter
• Bayes' rule
• Zakai equation
• Discrete time

A discrete time filter is considered where both the observation and signal process have non-linear dynamics with additive Gaussian noise. Using the reference probability framework a convolution type Zakai equation is obtained which updates the unnormalized conditional density. Using first order approximations this equation can be solved recursively and the extended Kalman filter can be derived.

• 出版日期2010-3