Adapting the Kalman filter to use the State Space Model (SSM) in the context of Schwartz-Smith code requires understanding both the Kalman filter algorithm and how it integrates with the SSM framework.
Here's a general approach,
- Express the SSM in terms that fit with the Kalman filter algorithm. You'll need to define the state transition matrix, observation matrix, process noise covariance, observation noise covariance, initial state estimate, and initial error covariance matrix.
- Modify the prediction step of the Kalman filter to incorporate the transition equation of the SSM. This involves predicting the next state and the error covariance matrix based on the dynamics of the system.
- Modify the update step of the Kalman filter to incorporate the observation equation of the SSM. This involves updating the state estimate and error covariance matrix based on the new observation.
- Iterate over each time step, performing prediction and update steps alternately.
- Ensure proper initialization of the state estimate, error covariance matrix, and other parameters before starting the filtering process.
Note: representing the SSM in Kalman Filter terms involves translating the dynamics and uncertainties of the system into matrices and vectors that can be used within the Kalman Filter algorithm for state estimation
Hope this gives an outline to solve your issue!
