Nonlinear Estimation with State-Dependent Gaussian Observation Noise

We consider the problem of estimating the state of a system when measurement noise is a function of the system's state. We propose generalizations of the iterated extended Kalman filter and of the extended Kalman filter that can be utilized when the state estimate distribution is approximately Gaussian. The state estimate is computed by an iterative root-searching method that maximize a maximum likelihood function. For sensor network applications, we also address distributed implementations involving multiple sensors.