I am new to statistical estimation theory, and I have read about the EM algorithm. This algorithm alternates between estimating hidden states using estimated model parameters (the E-step), and using those estimated hidden states to estimate the model parameters (the M-step). To me that is like estimating the hidden states and the parameters together.
The Extended Kalman Filter (EKF) can also estimate states and parameters by augmenting the state vector with model parameters. What is the difference between the EM algorithm and EKF for jointly estimating states and parameters, and why might I choose one over the other?
Forgive my ignorance and thanks in advance.