a$)$ Explain, how electronic beam$-$steering functions in phased array radars, and why it would yield a more versatile sensor $($for example, for tracking multiple aircraft compared to a mechanically scanning radar$).$

b$)$ Explain, using diagrams if necessary, how an Inertial Navigation System $($INS$)$ works to estimate the position, velocity and attitude of an aircraft.

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 $3030$ and has a $128128$ focal plane array:

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

$($Answer: $0\mathrm{.}0041$ rad $)$

ii$)$ Use Johnson's criteria to find the Detection range and Recognition range for an object with a critical dimension of $4$ metres $($with $50\%$ probability$).$

$($Answer: Detection range is $325\mathrm{.}2$ m $,$ Recognition range is $139\mathrm{.}4m$