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Extended Kalman Filter Tutorial

Extended Kalman Filter TutorialGabriel A. TerejanuDepartment of Computer Science and EngineeringUniversity at Buffalo, Buffalo, NY Dynamic processConsider the following nonlinear system, described by the difference equation and the observationmodel with additive noise:xk=f(xk 1) +wk 1(1)zk=h(xk) +vk(2)Theinitial state x0is a random vector with known mean 0=E[x0] and covarianceP0=E[(x0 0)(x0 0)T].In the following we assume that the random vectorwkcaptures uncertainties in the model andvkdenotes the measurement noise. Both are temporally uncorrelated (white noise), zero-mean randomsequences with known covariances and both of them are uncorrelated with the initial [wk] = 0E[wkwTk] =QkE[wkwTj] = 0 fork6=jE[wkxT0] = 0 for allk(3)E[vk] = 0E[vkvTk] =RkE[vkvTj] = 0 fork6=jE[vkxT0] = 0 for allk(4)Also the two random vectorswkandvkare uncorrelated:E[wkvTj] = 0 for allkandj(5)Vectorial functionsf( ) andh( ) are assumed to beC1functions (the function and its first derivativeare continuous on the given domain).

Extended Kalman Filter Tutorial Gabriel A. Terejanu Department of Computer Science and Engineering University at Buffalo, Buffalo, NY 14260 terejanu@buffalo.edu 1 Dynamic process Consider the following nonlinear system, described by the difference equation and the observation model with additive noise: x k = f(x k−1) +w k−1 (1) z k = h ...

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