Two-track thermal-wind covariance

For a steady density field sampled by two ships at angles $\theta$ and zero, write $\mathbf{y}=C\left(\begin{array}{cc}\sin \theta & -\cos \theta \\ 0& -1\end{array}\right)(u,v{)}^{\mathsf{T}}$. Independent measurement errors of variance ${\sigma }_y^2$ giveNearly parallel tracks poorly constrain $u$ and induce positive component covariance for $0<\theta <\pi /2$. Orthogonal tracks remove this covariance and give equal component precision under the stated independent-noise model.