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Page 12 of 27 Wang et al. Intell Robot 2023;3(4):538-64 I http://dx.doi.org/10.20517/ir.2023.30

tiveness with time, will decrease with the search step. Therefore, the definition of is as follows:

2
−
= (21)

4.2.2. Index of uncertainty
The index of uncertainty reflects the focus on the grid cells with a high existence probability of the target
and not being visited for a long time, which is defined as:

 


1 ∑ ∑  ∏ ∏ [ ( )] 

−
( ) = · 1 − − ( + | )· 1 − ( + | ) (22)

 

=1 =1  ∈Ω ( + | ) ∈ 
 
where ( + | ) is the estimation of certainty before the detection occurs at time + during virtual search
−

processes, and it is equivalent to the certainty of the previous step with the updating method, as shown in
Equations (14) and (15).
4.2.3. Index of detection response
The index of detection response reflects the focus on the grid cells with previously discovered targets, which
is defined as:
 
 
1 ∑ ∑  ∏ [ ] 

−
( ) = · 1 − ( + | )· (23)
 

=1 =1  = ∈Ω ( + | ) 
 
where − ( + | ) is the estimation of response value before the detection occurs at time + during virtual

search processes, and it is equivalent to the response value of the previous step with the updating method, as
defined by Equations (17) and (18).
4.2.4. Index of motion cost
The index of motion cost reflects the penalty for UAV motion cost, which is defined as:

] 

1 ∑  1 −1 [ +1 ( ) 
∑


( ) = · C ( ( −1 ), ( | )) + · C ( + −1 | ), ( + | ) (24)
 
=1  =1 
where C = { } is the motion cost matrix, in which represents the UAV motion cost with the previous
flight direction and the next flight direction .
Based on the indices above, the objective function in Equation (19) is defined as follows:

J( ( ), U( | )) = ( ) + ( ) + ( ) + ( ) (25)

where , , , and are the weighting coefficients of each index.