Non-additive Noise Formulation and Equations
The typical formulation of the EKF involves the assumption of additive process and measurement noise. This assumption, however, is not necessary for EKF implementation. Instead, consider a more general system of the form:
Where wk and vk are the process and observation noises which are both assumed to be zero mean multivariate Gaussian noises with covariance Qk and Rk respectively. Then the covariance prediction and innovation equations become
where the matrices and are Jacobian matrices:
The predicted state estimate and measurement residual are evaluated at the mean of the process and measurement noise terms, which is assumed to be zero. Otherwise, the non-additive noise formulation is implemented in the same manner as the additive noise EKF.
Read more about this topic: Extended Kalman Filter
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