a$)$ Explain what the Sagnac effect is and how it is used in strapdown inertial navigation systems $($INS$).$

b$)$ Explain how Global Navigation Satellite Systems $($GNSS$)$ works and how INS can be augmented with GNSS$.$

c$)$ A jet aircraft is fitted with a forward looking infrared $($FLIR$)$ camera as a pilot$-$flying aid. If the FLIR operates in the mid$-$wave infrared band $(3-5$ microns$),$ has a field of view of $17\mathrm{.}517\mathrm{.}5$ and has a $256256$ focal plane array:

i$)$ Find the angular resolution of the sensor in radians.

$($Answer: $0\mathrm{.}0012$ rad $)$

ii$)$ Use Johnson's criteria to find the Detection range and Recognition range for an object with a critical dimension of $3$ metres $($with $50\%$ probability$).($Answer: $833\mathrm{.}3$ m for detection and $358\mathrm{.}3$ m for recognition$)$