$$dS_t=\alpha_tdt+\sigma_1dW^1_t$$
$$d\alpha_tdt=-\xi\alpha_tdt+\sigma_2dW^2_t$$
where \(S_t\) is the observable price; \(\alpha_t\) is the unobservable trend; \(dW^1_t\) and \(dW^2_t\) are two Brownian motions.
I think \(S_t\) can be sampled with regular discrete time, so that this model can be formulated as a state space model and be estimated by MATLAB.
https://www.mathworks.com/help/econ/estimate-a-time-invariant-state-space-model.html
However, MATLAB uses general Kalman filter to do this, which takes lots of computational effort. Is there any more efficient algorithm to estimate this specific model?