Initial Estimate Selection Method in Passive TDOA-Based Iterative Position Estimation Algorithms

. 2026 Jul 12;26(14):4431. doi: 10.3390/s26144431

Algorithm 2. Initial Guesses matrix selection algorithm

Input:

s e n s o r . c o o r d = [\begin{matrix} x_{H_{1}} & x_{H_{2}} & \dots & x_{H_{N}} \end{matrix}]

T D O A = [\begin{matrix} T D O A 1 & T D O A 2 & \dots & T D O A m & T D O A 1 \end{matrix}]

r a n g e

Arrange sensors and relevant TDOA clockwise
$if all T D O A \neq 0$ do
$for i = 1 : l e n g t h (T D O A)$ do
$if T D O A (i + 1) > 0$ and $T D O A (i) < 0$ do
Determine the set of Initial Guesses in the selected area
exit loop
end if
end for
if no guesses found do
$for i = 1 : l e n g t h (T D O A)$ do
$if T D O A (i + 1) < 0$ and $T D O A (i) > 0$ do
Determine the set of Initial Guesses in the selected area
exit loop
end if
end for
end if
if no guesses found do
$for i = 1 : l e n g t h (T D O A)$ do
$if T D O A (i + 1) > 0$ and $T D O A (i) > 0$ do
Determine the set of Initial Guesses in the selected area
exit loop
end if
end for
end if
if no guesses found do
$for i = 1 : l e n g t h (T D O A)$ do
$if T D O A (i + 1) < 0$ and $T D O A (i) < 0$ do
Determine the set of Initial Guesses in the selected area
exit loop
end if
end for
end if
$elseif o n e T D O A = 0$ or ( $m u l t i p l e T D O A = 0 a n d a l l c r o s s p o i n t s a r e o u t o f r a n g e$ ) do
Determine the set of Initial Guess’s on TDOA = 0 line(s) starting from cross point
else do
$Determine one Initial point as cross point of T D O A = 0$ lines
end if

Output:

I n i t i a l . G u e s s e s