User:Lipkenzaal2/sandbox

Adopting the convention $$\ell^{(-1)} = 0$$, this can be done via the recursive update rule
 * $$\ell^{(k)} = \ell^{(k-1)} - \frac{1}{2} \left(\tilde{\mathbf{y}}_k^T \mathbf{S}^{-1}_k \tilde{\mathbf{y}}_k + \log \left|\mathbf{S}_k\right| + d_{y}\log 2\pi \right)$$,

where $$d_y$$ is the dimension of the measurement vector. Lütkepohl, Helmut. Introduction to Multiple Time Series Analsysis. Springer-Verlag Berlin, Heidelberg, 1991, p. 435.