Fig. illustrates the underlying physical cause of the unresponsiveness to a composition change, using as an example the HKUST-1 sensor immersed in a CH Comparing Co-MOF-74 and HKUST-1 for CH 4 /C 2 H 6 /CO 2 sensing, the sensitive direction v 1 for HKUST-1 has a larger component along x = [0.5, 0.5] (see Fig. ). Therefore, HKUST-1 is a more suitable sensor for estimating the sum of the CO 2 and C 2 H 6 mole fractions and, thus, the mole fraction of CH 4 . In other words, the component of the unresponsive direction for HKUST-1 along x = [0.5, 0.5] is smaller than for Co-MOF-74; so, HKUST-1 is not as blind to changes in the CH 4 mole fraction in the CH 4 /C 2 H 6 /CO 2 mixture than Co-MOF-74. Fig. clarifies: observation of the response m op of the HKUST-1 sensor places tighter bounds on x CH 4 than of the Co-MOF-74 sensor because x CH 4 is approximately constant along its unresponsive direction. This exemplifies how unresponsive directions and loci could be used to juxtapose two noninjective sensors. However, a more rigorous comparison of the two sensors should include sensitivity to measurement noise . v 1 (green vector) is orthogonal to the level set {x : a(x) = m op }, and the unresponsive subspace, a plane spanned by v 2 and v 3 (red vectors), is tangent to it. Note the vectors v 2 and v 3 are not ranked, i.e. one is not more or less unresponsive than the other, and are not unique, in that any two orthonormal vectors that lie in the unresponsive plane can be chosen. The unresponsive subspace is two-dimensional due to the single constraint imposed by the response of the sensor on the three degrees of freedom in the gas composition. Small changes in gas composition on the unresponsive plane are undetectable since the sensor response remains constant. The sensitive direction v 1 is orthogonal to the unresponsive plane.