The χ2 Hessian

∇²χ²(θ) = 2 $\displaystyle \sum_{{i=1}}^{n}$ $\displaystyle {\frac{{1}}{{\sigma_i^2}}}$ $\displaystyle \left(\vphantom{\nabla \mathrm{R}_i(\theta) \cdot \nabla \mathrm{... ...T - (\mathrm{R}_i- \mathrm{R}_i(\theta)) \nabla^2 \mathrm{R}_i(\theta) }\right.$ ∇R_i(θ)⋅∇R_i(θ)^T - (R_i - R_i(θ))∇²R_i(θ) $\displaystyle \left.\vphantom{\nabla \mathrm{R}_i(\theta) \cdot \nabla \mathrm{... ...T - (\mathrm{R}_i- \mathrm{R}_i(\theta)) \nabla^2 \mathrm{R}_i(\theta) }\right)$ .

(15.15)