fix(events): correct covariance uncertainty propagation in groupoid compose() - #24
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hongjin-he merged 1 commit intoAug 25, 2026
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…compose()`
The uncertainty propagation inside `compose()` computes `Sigma_comp_sq` by squaring `Sigma_w` directly (`Sigma_w @ Sigma_w`) rather than forming the covariance via `Sigma_w @ Sigma_w.T`.
#### Maths
Given affine operators with noise terms $\eta_i = \Sigma_i \epsilon_i$ where $\epsilon_i \sim \mathcal{N}(0, I)$, the covariance of the noise is:
$$\operatorname{Cov}(\eta_i) = \Sigma_i \Sigma_i^\top$$
Under composition $T_1 \circ T_2$:
$$T_1(T_2(s)) = A_1 A_2 s + (A_1 b_2 + b_1) + (A_1 \Sigma_2 \epsilon_2 + \Sigma_1 \epsilon_1)$$
Because $\epsilon_1 \perp \epsilon_2$, the covariance of total noise $\eta_{\text{comp}}$ is:
$$\operatorname{Cov}(\eta_{\text{comp}}) = \Sigma_1 \Sigma_1^\top + A_1 (\Sigma_2 \Sigma_2^\top) A_1^\top$$
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The uncertainty propagation inside
compose()computesSigma_comp_sqby squaringSigma_wdirectly (Sigma_w @ Sigma_w) rather than forming the covariance viaSigma_w @ Sigma_w.T.Maths
Given affine operators with noise terms$\eta_i = \Sigma_i \epsilon_i$ where $\epsilon_i \sim \mathcal{N}(0, I)$ , the covariance of the noise is: $$\operatorname{Cov}(\eta_i) = \Sigma_i \Sigma_i^\top$$
Under composition$T_1 \circ T_2$ :
$$T_1(T_2(s)) = A_1 A_2 s + (A_1 b_2 + b_1) + (A_1 \Sigma_2 \epsilon_2 + \Sigma_1 \epsilon_1)$$
Because$\epsilon_1 \perp \epsilon_2$ , the covariance of total noise $\eta_{\text{comp}}$ is: $$\operatorname{Cov}(\eta_{\text{comp}}) = \Sigma_1 \Sigma_1^\top + A_1 (\Sigma_2 \Sigma_2^\top) A_1^\top$$