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Use this tag only for regression models in which the response is a nonlinear function of the parameters. Do not use this tag for nonlinear data transformation; use [data-transformation] for that instead.

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Extended Kalman Filter Non-Linear Regression Implementation R, Correct?

In your model, beta is fixed, so you should set processNoise <- diag(c(0, 0)). By specifying non-zero variances for the state, you'd assume that the state (beta) is stochastic. As your initial guess …
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