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Page 8 of 27 Wang et al. Intell Robot 2023;3(4):538-64 I http://dx.doi.org/10.20517/ir.2023.30

Figure 6. Grid definition of a probability map.

single detection grid cell, i.e., a mission grid cell, if the existence of a target in the mission grid cell with r-th
row and c-th column is denoted as , then the probability of is:

∏
(7)
( ) = 1 − [1 − ( )]

∈

where ∈ denotes that is within the area of in terms of regional division, and the definition of

such notations in the rest of the paper is the same as here. It can be determined that the target is found in

when ( ) is not less than a certain threshold .
ℎ
The transition of the existence probability based on target motion prediction under the influence of the move-
ment of UAVs in any grid cell of the probability map can be represented by the probability diffusion coefficient
of one cell to another. Denote the probability diffusion coefficient for transferring the existence probability of

the target from to at time as Φ ( ), which can be expressed based on target motion prediction

with Equations (4) and (5) as follows:
∫ ∫ ∫ ∫
+ 2 + 2 + 2 + 2
Φ ( ) = {( +1 , +1 )|( , )}d +1 d +1 d d (8)

− − − −
2 2 2 2
where ( , ) and ( , ) are the centers of and . Obviously, the sum of the probability diffusion

coefficient from any grid cell to all cells remains constant at 1. According to the definition of maximum move-
ment distance, it can be further constrained to have a sum of 1 from any grid cell to the adjacent cells and
itself:

+1 +1
∑ ∑ ∑ ∑
Φ ( ) = Φ ( ) = 1 (9)

=1 =1 = −1 = −1