HINT: there is no need to equate the tau$2,1$ equation to hyperbola equation, Just span P$0$x from $-4$ to $4$ km and solve for P$0$y$.$ And Vice$-$versa. PLEASE PROVIDE MATLAB CODE AND PLOTS. Base stations at locations $P_1$ through $P_4$ and target at unknown location $P_0$ are deployed $-$

$P_1=(-1\mathrm{.}5,-2)$

$P_2=(2,2)$

$P_3=(-2\mathrm{.}5,2\mathrm{.}5)$

$P_4=(2,-1)$ in $km.$

Answer parts a$)$ and b$)$ for each of the given Time Difference of Arrival $($TDOA$)$ measurement

data given below $($i$,$ ii$,$ and iii$).$

a$)$ Plot the TDOA isogram $($Hyperbola$).$ Plots should contain the location of the base stations

along with the hyperbola associated with the TDOA measurement, using an x$-$range from

$4km,4km$

Note: ${}_{2,1}=\frac{r_2-r_1}{c},$

where $r_i=\sqrt[\phantom{2}]{({}_x-P{0}_x{)}^2+({}_Y-P{0}_y{)}^2},$ the range from $P_{i}to{P}_0,$

and $c=299,792\mathrm{.}458\frac{km}{s}$

Example:

${}_{2,1}**c=r_2-r_1=\sqrt[\phantom{2}]{(P_{2_x}-P_{0_x}{)}^2+(P_{2_y}-P_{0_y}{)}^2}-\sqrt[\phantom{2}]{(P_{1_x}-P_{0_x}{)}^2+(P_{1_y}-P_{0_y}{)}^2}$

$*$No use of MATLAB built$-$in functions $($eg$.$ EZPLOT$)$ allowed for this problem.