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ml-recall

#state-estimation

1 question from Time Series

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Question 1: Short answer

mediumAI-checkedTime Series

A vehicle on a line moves as xt+1=xt+utx_{t+1} = x_t + u_t with known controls utu_t (no process noise), and you observe yt=xt+zty_t = x_t + z_t with independent zt∼N(0,1)z_t \sim \mathcal{N}(0, 1). The initial position has prior N(0,4)\mathcal{N}(0, 4). After three observations y0,y1,y2y_0, y_1, y_2, what is the posterior variance of the current position x2x_2?

a variance, 3 decimals