# The Situation Assessment of UAVs Based on an Improved Whale Optimization Bayesian Network Parameter-Learning Algorithm

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## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

#### 2.1. BN Parameter Learning

#### 2.2. Parameter Constraints

- Axiomatic constraint.

- 2.
- Range constraint.

- 3.
- Approximate equality constraint.

- 4.
- Inequality constraint.

- Intra-distribution constraint:

- Cross-distribution constraint:

- Inter-distribution constraint:

- 5.
- Synergy constraint.

- Additive synergy constraint:

- Product synergy constraint:

#### 2.3. Whale Optimization Algorithm

- 1.
- Encircling prey:

- 2.
- Bubble-net attacking (exploitation phase)

- 3.
- Search for prey (exploration phase)

## 3. Structure Establishment of Situation Assessment BN

## 4. IWOA-PPI for Parameter Learning

#### 4.1. Parameter Prior Interval

- By performing MC sampling on the parameter space delimited by the parameter constraints, the parameters without samples are obtained using Equation (26):$${\theta}_{ijk}^{MC}=P\left({X}_{i}=k,pa\left({X}_{i}\right)=j|\Omega \right)=\frac{{\displaystyle \sum _{l=1}^{S}{P}_{l}\left({X}_{i}=k,pa\left({X}_{i}\right)=j|\Omega \right)}}{S}$$${\theta}_{ijk}^{MC}$ is the parameter obtained via MC sampling without considering the samples. Its numerical value is close to the true parameter to some extent, and the degree of closeness is positively related to the number of constraints.
- Using the interval transform formulas, the uncorrected PPIs are obtained. ${\theta}_{ijk}^{MC}$ ($k=1,2,\dots ,{r}_{i}$) are denoted from small to large, as shown in Equation (27):$${\theta}_{ij{k}_{1}}^{MC}\le {\theta}_{ij{k}_{2}}^{MC}\le \dots \le {\theta}_{ij{k}_{m}}^{MC}\le \dots \le {\theta}_{ij{k}_{{r}_{i}}}^{MC}$$${d}_{{k}_{m}}^{low}$ is defined as the lower bound interval of ${\theta}_{ij{k}_{m}}^{MC}$, ${d}_{{k}_{m}}^{up}$ is defined as the upper bound interval of ${\theta}_{ij{k}_{m}}^{MC}$, and $[{\theta}_{ij{k}_{m}}^{MC}-{d}_{{k}_{m}}^{low},{\theta}_{ij{k}_{m}}^{MC}+{d}_{{k}_{m}}^{up}]$ is the uncorrected PPI of ${\theta}_{ij{k}_{m}}^{MC}$. The determination of ${d}_{{k}_{m}}^{low}$ and ${d}_{{k}_{m}}^{up}$ needs to be categorized into two cases:

- When ${\theta}_{ij{k}_{1}}^{MC}<{\theta}_{ij{k}_{2}}^{MC}<\dots <{\theta}_{ij{k}_{m}}^{MC}<\dots <{\theta}_{ij{k}_{{r}_{i}}}^{MC}$, the interval transform formulas of ${\theta}_{ij{k}_{m}}^{MC}$ are implemented as Equations (28) and (29):$${d}_{{k}_{m}}^{low}=\frac{{\theta}_{ij{k}_{m}}^{MC}-{\theta}_{ij{k}_{m-1}}^{MC}}{{\theta}_{ij{k}_{m}}^{MC}/{\theta}_{ij{k}_{m-1}}^{MC}}$$$${d}_{{k}_{m}}^{up}=\frac{{\theta}_{ij{k}_{m+1}}^{MC}-{\theta}_{ij{k}_{m}}^{MC}}{{\theta}_{ij{k}_{m+1}}^{MC}/{\theta}_{ij{k}_{m}}^{MC}}$$For ${\theta}_{ij{k}_{1}}^{MC}$, ${d}_{{k}_{1}}^{up}$ is calculated first, and then ${d}_{{k}_{1}}^{low}={d}_{{k}_{1}}^{up}$. For ${\theta}_{ij{k}_{{r}_{i}}}^{MC}$, ${d}_{{k}_{{r}_{i}}}^{low}$ is calculated first, and then ${d}_{{k}_{{r}_{i}}}^{up}={d}_{{k}_{{r}_{i}}}^{low}$.
- When ${\theta}_{ij{k}_{p}}^{MC}={\theta}_{ij{k}_{p+1}}^{MC}=\dots ={\theta}_{ij{k}_{p+q}}^{MC}$, the interval transform formulas of ${\theta}_{ij{k}_{m}}^{MC}$ are implemented as Equation (30):$${d}_{{k}_{m}}^{low}={d}_{{k}_{m}}^{up}=\frac{\omega \cdot \left({\theta}_{ij{k}_{p}}^{MC}+{\theta}_{ij{k}_{p+1}}^{MC}+\dots +{\theta}_{ij{k}_{p+q}}^{MC}\right)}{q}$$

- 3.
- Combining the parameter constraints, the PPIs are obtained. The uncorrected PPIs may violate some parameter constraints, so the intersection of the parameter constraints and the uncorrected PPIs is sought to obtain the PPIs. For example, in order to satisfy the axiomatic constraint, the lower bound interval, ${d}_{{k}_{1}}^{low}$, of ${\theta}_{ij{k}_{1}}^{MC}$ is $\mathrm{max}(0,{\theta}_{ij{k}_{1}}^{MC}-{d}_{{k}_{1}}^{low})$ and the upper bound interval, ${d}_{{k}_{1}}^{up}$, of ${\theta}_{ij{k}_{1}}^{MC}$ is $\mathrm{min}({\theta}_{ij{k}_{{r}_{i}}}^{MC}+{d}_{{k}_{i}}^{up},1)$.

#### 4.2. Variable Encircling Factor

#### 4.3. Nonlinear Convergence Factor

#### 4.4. Simulated Annealing Strategy Incorporating Levy Flight

Algorithms 1 Pseudo-code of the IWOA-PPI |

$01:\mathrm{Initialize}\mathrm{the}\mathrm{whales}\mathrm{population}{X}_{l}(l=1,2,\dots ,m)\mathrm{in}\mathrm{the}\mathrm{parameter}\mathrm{prior}\mathrm{internals}$ |

$02:\mathrm{Calculate}\mathrm{the}\mathrm{fitness}\mathrm{of}\mathrm{each}\mathrm{search}\mathrm{agent}$ |

$03:T={T}_{0},{X}^{*}=\mathrm{the}\mathrm{best}\mathrm{search}\mathrm{agent}$ |

$04:\mathbf{While}(t\mathrm{maximum}\mathrm{number}\mathrm{of}\mathrm{iterations})$ |

$05:\begin{array}{c}\end{array}\begin{array}{c}\end{array}\mathbf{for}\mathrm{each}\mathrm{search}\mathrm{agent}$ |

$06:\begin{array}{c}\end{array}\begin{array}{c}\end{array}\mathrm{Update}{a}_{nl},{A}_{nl},{C}^{V},l,\mathrm{and}p$ |

$07:\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\mathbf{if1}(p0.5)$ |

$08:\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\mathbf{if2}(\left|A\right|1)$ |

$09:\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\mathrm{Update}\mathrm{the}\mathrm{position}{X}_{l}\mathrm{of}\mathrm{the}\mathrm{current}\mathrm{search}\mathrm{agent}\mathrm{by}\mathrm{the}\mathrm{Equation}(18)$ |

$10:\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\mathbf{else\; if2}(\left|A\right|\ge 1)$ |

$11:\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\mathrm{Select}\mathrm{a}\mathrm{random}\mathrm{search}\mathrm{agent}({X}_{rand})$ |

$12:\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\mathrm{Update}\mathrm{the}\mathrm{position}{X}_{l}\mathrm{of}\mathrm{the}\mathrm{current}\mathrm{search}\mathrm{agent}\mathrm{by}\mathrm{the}\mathrm{Equation}(25)$ |

$13:\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\mathbf{else\; if2}$ |

$14:\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\mathbf{else\; if1}(p\ge 0.5)$ |

$15:\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\mathrm{Update}\mathrm{the}\mathrm{position}{X}_{l}\mathrm{of}\mathrm{the}\mathrm{current}\mathrm{search}\mathrm{agent}\mathrm{by}\mathrm{the}\mathrm{Equation}(22)$ |

$16:\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\mathbf{else\; if1}$ |

$17:\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\mathrm{Update}\mathrm{the}\mathrm{position}{X}_{l}^{Levy}\mathrm{of}\mathrm{the}\mathrm{current}\mathrm{search}\mathrm{agent}\mathrm{by}\mathrm{the}\mathrm{Equation}\left(35\right)$ |

$18:\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\mathrm{Check}\mathrm{if}{X}_{l}\mathrm{or}{X}_{l}^{Levy}\mathrm{goes}\mathrm{beyond}\mathrm{the}\mathrm{search}\mathrm{space}\mathrm{and}\mathrm{amend}\mathrm{it}$ |

$19:\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\mathrm{Calculate}\mathrm{the}\mathrm{fitness}\mathrm{of}{X}_{l}\mathrm{and}{X}_{l}^{Levy}$ |

$20:\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\Delta f=f({X}_{l}^{Levy})-f({X}_{l})$ |

$21:\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\mathbf{if3}(\Delta f0)\mathrm{or}\mathrm{random}(0,1)\le p(\Delta f,T)$ |

$22:\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}{X}_{l}\leftarrow {X}_{l}^{Levy}$ |

$23:\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\begin{array}{c}\end{array}\mathbf{end\; if3}$ |

$24:\begin{array}{c}\end{array}\begin{array}{c}\end{array}\mathbf{end\; for}$ |

$25:\begin{array}{c}\end{array}\begin{array}{c}\end{array}\mathrm{Update}X*\mathrm{if}\mathrm{there}\mathrm{is}\mathrm{a}\mathrm{better}\mathrm{solution}$ |

$26:\begin{array}{c}\end{array}\begin{array}{c}\end{array}\mathrm{Update}T$ |

$27:\begin{array}{c}\end{array}\begin{array}{c}\end{array}t=t+1$ |

$28:\mathbf{end\; while}$ |

$29:\mathrm{return}{X}^{*}$ |

## 5. Experiment and Discussion

#### 5.1. Experiment for the Standard BNs

- Range constraint. For example, $0.8\le P(\mathrm{tub}=0|\mathrm{asia}=0)\le 0.1$;
- Approximate equality constraint. For example,$P(\mathrm{either}=0|\mathrm{tub}=0,\mathrm{lung}=0)\approx P(\mathrm{either}=1|\mathrm{tub}=0,\mathrm{lung}=1)$;
- Inequality constraint. For example, $P(\mathrm{bronc}=0|\mathrm{smoke}=0)>P(\mathrm{bronc}=1|\mathrm{smoke}=1)$.

- The accuracy ranking of the five algorithms is IWOA-PPI > QMAP > WOA > MAP > MLE. There are roughly three levels of accuracy, the lowest level for MLE, the medium level for the WOA and MAP, and the highest level for the IWOA-PPI and QMAP.
- For all networks and sample sizes, the IWOA-PPI proposed in this article has the smallest KL divergence among the five parameter-learning algorithms, which means that the learning results are the most accurate. The highest accuracy of the IWOA-PPI indicates that, in contrast to the QMAP and WOA, the IWOA-PPI absorbs the advantages of the Bayesian estimation and constrained optimization methods, and fully extracts information from both parameter constraints and sample data.
- Comparing the WOA and the IWOA-PPI, the KL divergence of the former is about three times that of the latter. This indicates that the improvements in Section 4 significantly enhance the optimization ability of the WOA.

#### 5.2. Experiment for the Situation Assessment BN

- Use the IWOA-PPI to learn the parameters of the situation assessment BN in Figure 4;
- For the assumed mission scenario, substitute the learned parameters into the situation assessment BN, and use this BN to evaluate the operational intentions of the opposing targets, i.e., the opposing situation.

#### 5.2.1. Parameter Learning of the Situation Assessment BN

- Range constraint.${\theta}_{233}=P(\begin{array}{c}\begin{array}{c}\mathrm{target}\end{array}\end{array}\begin{array}{c}\mathrm{type}\end{array}=3|\mathrm{intention}=3)$, $0.6\le {\theta}_{233}\le 1$.When the intention is jamming and the target type is EJA, the range of the conditional probability, $P(\begin{array}{c}\begin{array}{c}\mathrm{target}\end{array}\end{array}\begin{array}{c}\mathrm{type}\end{array}|\mathrm{intention})$, is [0.6, 1]. This indicates that if the target is performing the jamming mission, it has at least a 60% chance of being the EJA. Since the probability cannot be greater than one, the range is [0.6, 1].
- Approximate equality constraint.${\theta}_{411}=P(\mathrm{relative}\mathrm{motion}=1|\mathrm{intention}=1)$, ${\theta}_{412}=P(\mathrm{relative}\mathrm{motion}=2|\mathrm{intention}=1)$,${\theta}_{411}\approx {\theta}_{412}$.The conditional probability when the intention is patrol and the relative motion is approach is approximately equal to the one when the intention is patrol and the relative motion is leave. When performing the patrol mission, in order to ensure comprehensive air surveillance of the defense focus, the AEW sets the defense focus as the center of the circle and flies around it according to a certain patrol radius and patrol speed. Since the target makes a circular flight in a fixed area, the approach and leave of the target have no influence on our UAVs. Therefore, when the intention is patrol, the probabilities of approach and leave are approximately equal.
- Inequality constraint.${\theta}_{721}=P(\mathrm{height}=1|\begin{array}{c}\begin{array}{c}\mathrm{target}\end{array}\end{array}\begin{array}{c}\mathrm{type}\end{array}=2)$, ${\theta}_{722}=P(\mathrm{height}=2|\begin{array}{c}\begin{array}{c}\mathrm{target}\end{array}\end{array}\begin{array}{c}\mathrm{type}\end{array}=2)$,${\theta}_{723}=P(\mathrm{height}=3|\begin{array}{c}\begin{array}{c}\mathrm{target}\end{array}\end{array}\begin{array}{c}\mathrm{type}\end{array}=2)$, ${\theta}_{721}<{\theta}_{723}$, ${\theta}_{722}<{\theta}_{723}$.The conditional probability when the target type is RP and the height is low altitude is smaller than the one when the target type is RP and the height is high altitude. So is the one when the target type is RP and the height is medium altitude. Because the RP is often at high altitude when conducting reconnaissance, the conditional probability, $P(\mathrm{height}=3|\begin{array}{c}\begin{array}{c}\mathrm{target}\end{array}\end{array}\begin{array}{c}\mathrm{type}\end{array}=2)$, is the highest.

#### 5.2.2. Result of Situation Assessment

- 1.
- The description of the assumed mission scenario.The existing entities in the environment are several UAVs perceiving the situation and a ground radar belonging to us. An AEW, an RP, an EJA, and a fighter belong to the other side.The assumed missions of the opposing targets are: in the beginning, the AEW is patrolling with a fighter, the RP is conducting reconnaissance and the EJA has no clear mission. After a while, the ground radar is discovered by the RP. Then, the EJA starts to fly towards the radar and implement electronic jamming, and the fighter stops escorting the AEW and assaults the radar after the electronic jamming takes effect.
- 2.
- The acquisition of the observed evidence.The observed evidences are necessary for situation assessment and are transferred from the attributes and states of the targets. Since the attributes and states are continuous variables, and the evidences in the form of probabilities are discrete variables. Then, fuzzy discretization is used to acquire the evidences. Taking the height node as an example, the process to acquire the observed evidence is as below.

- The construction of the membership function.The fuzzy membership function of the height node is defined as Equation (38) and shown in Figure 11.$${\mu}_{H,1}=\left\{\begin{array}{cc}1& 0\le H<5000\\ -H/2000+7/2& 5000\le H<7000\\ 0& \mathrm{other}\end{array}\right.\phantom{\rule{0ex}{0ex}}\hspace{1em}{\mu}_{H,2}=\left\{\begin{array}{cc}H/3000-5/3& 5000\le H8000\\ 1& 8000\le H9000\\ -H/3000+4& 9000\le H\mathrm{12,000}\\ 0& \mathrm{other}\end{array}\right.\phantom{\rule{0ex}{0ex}}\hspace{1em}\hspace{1em}\hspace{1em}{\mu}_{H,3}=\left\{\begin{array}{cc}H/4000-5/2& \mathrm{10,000}\le H\mathrm{14,000}\\ 1& H\ge \mathrm{14,000}\\ 0& \mathrm{other}\end{array}\right.$$The unit of height is meters. The green area is ${\mu}_{H,1}$, the red area is ${\mu}_{H,2}$, and the blue area is ${\mu}_{H,3}$. The brown area is the overlap between ${\mu}_{H,1}$ and ${\mu}_{H,2}$, and the grey area is the overlap between ${\mu}_{H,2}$ and ${\mu}_{H,3}$.
- The transform from the fuzzy membership to the probability.The probability–possibility transformation formula [36] is defined in Equation (39):$${p}_{i}\left(u\right)=\frac{{\mu}_{i}{\left(u\right)}^{1/\alpha}}{{\displaystyle {\sum}_{i=1}^{n}{\mu}_{i}{\left(u\right)}^{1/\alpha}}},0<\alpha <1$$

- 3.
- The application of the situation assessment BN.

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AEW | Air-Borne Early Warning |

AHP | Analytic Hierarchy Process |

BN | Bayesian Network |

CPT | Conditional Probability Table |

EJA | Electronic Jamming Aircraft |

IWOA-PPI | Improved Whale Optimization Algorithm based on PPIs |

MAP | Maximum A Posteriori |

MC | Monte Carlo |

MLE | Maximum Likelihood Estimation |

PPI | Parameter Prior Interval |

QMAP | Qualitative Maximum A Posteriori |

RCS | Radar Cross-Section |

RFV | Radar Frequency Band Variability |

RP | Reconnaissance Plane |

TOPSIS | Technique for Order Preference by Similarity to Ideal Solution |

UAV | Unmanned Aerial Vehicle |

WOA | Whale Optimization Algorithm |

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**Figure 5.**Curves of two convergence factors. The blue curve refers to $a$ and the black curve refers to ${a}_{nl}$.

**Figure 8.**(

**a**) KL divergences of 5 algorithms for the Alarm BN. (

**b**–

**d**) KL divergences with error bars.

**Figure 9.**(

**a**) KL divergences of 5 algorithms for the Win95pts BN. (

**b**–

**d**) KL divergences with error bars.

**Figure 10.**(

**a**) KL divergences of 5 algorithms for the Andes BN. (

**b**–

**d**) KL divergences with error bars.

**Figure 12.**(

**a**) Situation assessment results of the AEW. (

**b**) Situation assessment results of the RP. (

**c**) Situation assessment results of the EJA. (

**d**) Situation assessment results of the fighter.

Node | Number | State Set | State Notation |
---|---|---|---|

Intention | 1 | Patrol, Recon, Jamming, Assault | $\{p,r,j,a\}$ |

Type | 2 | AEW ^{1}, RP ^{2}, EJA ^{3}, Fighter | $\{a,r,e,f\}$ |

Relative velocity | 3 | Low, Medium, High | $\{l,m,h\}$ |

Relative height | 4 | Low, Medium, High | $\{l,m,h\}$ |

Relative motion | 5 | Approach, Leave | $\{a,l\}$ |

Velocity | 6 | Low, Medium, High | $\{l,m,h\}$ |

Height | 7 | Low, Medium, High | $\{l,m,h\}$ |

RCS | 8 | Very small, Small, Medium, Large | $\{v,s,m,l\}$ |

RFV | 9 | Agility, Fixed | $\{a,f\}$ |

Relative distance | 10 | Decrease, Unchanged, Increase | $\{d,u,i\}$ |

Relative bearing | 11 | Low, Medium, High | $\{l,m,h\}$ |

^{1}Air-borne early warning.

^{2}Electronic jamming aircraft.

^{3}Reconnaissance plane.

BNs | Scale | Nodes | Arcs | Parameters |
---|---|---|---|---|

Asia | Small | 8 | 8 | 18 |

Alarm | Medium | 37 | 46 | 509 |

Win95pts | Large | 76 | 112 | 574 |

Andes | Very large | 223 | 338 | 1157 |

BNs | Number of Samples | MLE | MAP | QMAP | WOA | IWOA-PPI |
---|---|---|---|---|---|---|

Asia | 40 | 24.27 ± 3.47 | 2.28 ± 0.67 | 0.62 ± 0.04 | 1.29 ± 0.44 | 0.46 ± 0.06 |

80 | 19.75 ± 3.75 | 2.14 ± 0.54 | 0.57 ± 0.07 | 1.06 ± 0.18 | 0.42 ± 0.06 | |

120 | 14.06 ± 3.73 | 1.57 ± 0.42 | 0.51 ± 0.06 | 0.92 ± 0.17 | 0.40 ± 0.08 | |

160 | 11.27 ± 3.41 | 1.28 ± 0.31 | 0.44 ± 0.02 | 0.84 ± 0.23 | 0.35 ± 0.07 | |

200 | 8.90 ± 2.94 | 1.08 ± 0.26 | 0.41 ± 0.04 | 0.75 ± 0.18 | 0.28 ± 0.07 | |

Alarm | 40 | 183.31 ± 19.57 | 116.41 ± 8.56 | 16.15 ± 0.26 | 34.44 ± 3.96 | 11.43 ± 0.54 |

80 | 172.97 ± 15.24 | 105.91 ± 6.87 | 15.01 ± 0.38 | 33.21 ± 2.61 | 10.79 ± 0.46 | |

120 | 152.38 ± 14.35 | 93.32 ± 6.31 | 14.16 ± 0.39 | 31.55 ± 3.10 | 10.44 ± 0.30 | |

160 | 145.58 ± 21.35 | 89.11 ± 5.99 | 13.65 ± 0.17 | 29.38 ± 1.83 | 10.25 ± 0.32 | |

200 | 127.44 ± 12.06 | 81.33 ± 6.90 | 13.21 ± 0.34 | 28.87 ± 2.22 | 9.88 ± 0.27 | |

Win95pts | 40 | 220.84 ± 12.81 | 133.36 ± 3.84 | 40.57 ± 0.23 | 100.51 ± 3.09 | 34.90 ± 0.82 |

80 | 215.76 ± 20.75 | 129.42 ± 4.62 | 38.71 ± 0.25 | 98.92 ± 4.57 | 33.21 ± 1.09 | |

120 | 220.27 ± 15.16 | 124.19 ± 5.20 | 37.40 ± 0.29 | 95.72 ± 3.32 | 29.28 ± 0.56 | |

160 | 212.96 ± 15.84 | 119.66 ± 5.93 | 36.38 ± 0.31 | 93.97 ± 2.91 | 26.23 ± 0.55 | |

200 | 211.75 ± 13.20 | 118.32 ± 5.12 | 35.73 ± 0.36 | 89.08 ± 3.29 | 24.22 ± 0.34 | |

Andes | 40 | 702.29 ± 36.94 | 226.33 ± 8.55 | 35.68 ± 0.28 | 113.40 ± 3.54 | 29.73 ± 0.91 |

80 | 590.41 ± 29.50 | 190.57 ± 10.73 | 31.33 ± 0.25 | 109.76 ± 3.05 | 28.24 ± 0.53 | |

120 | 504.44 ± 24.21 | 165.79 ± 10.02 | 28.49 ± 0.31 | 105.43 ± 3.47 | 25.49 ± 0.66 | |

160 | 457.17 ± 16.99 | 149.56 ± 9.31 | 26.57 ± 0.27 | 101.27 ± 2.75 | 22.24 ± 0.59 | |

200 | 423.23 ± 31.17 | 139.03 ± 8.80 | 25.76 ± 0.22 | 98.57 ± 3.16 | 20.68 ± 0.41 |

Node | State | Intention | |||
---|---|---|---|---|---|

Patrol | Recon | Jamming | Assault | ||

Target type | AEW | 0.6 | 0.1 | 0.1 | 0.05 |

RP | 0.2 | 0.65 | 0.1 | 0.1 | |

EJA | 0.1 | 0.15 | 0.7 | 0.1 | |

Fighter | 0.1 | 0.1 | 0.1 | 0.75 | |

Relative velocity | Low | 0.7 | 0.5 | 0.3 | 0.1 |

Medium | 0.2 | 0.4 | 0.6 | 0.5 | |

High | 0.1 | 0.1 | 0.1 | 0.4 | |

Relative height | Low | 0.3 | 0.1 | 0.5 | 0.2 |

Medium | 0.6 | 0.2 | 0.4 | 0.5 | |

High | 0.1 | 0.7 | 0.1 | 0.3 | |

Relative motion | Approach | 0.5 | 0.7 | 0.8 | 0.9 |

Leave | 0.5 | 0.3 | 0.2 | 0.1 | |

Target type | |||||

AEW | RP | EJA | Fighter | ||

Velocity | Low | 0.6 | 0.7 | 0.2 | 0.2 |

Medium | 0.3 | 0.2 | 0.7 | 0.3 | |

High | 0.1 | 0.1 | 0.1 | 0.5 | |

Height | Low | 0.2 | 0.1 | 0.3 | 0.1 |

Medium | 0.7 | 0.1 | 0.6 | 0.5 | |

High | 0.1 | 0.8 | 0.1 | 0.4 | |

RCS | Very small | 0.1 | 0.3 | 0.1 | 0.6 |

Small | 0.1 | 0.5 | 0.1 | 0.2 | |

Medium | 0.2 | 0.1 | 0.7 | 0.1 | |

Large | 0.6 | 0.1 | 0.1 | 0.1 | |

RFV | Agility | 0.8 | 0.3 | 0.9 | 0.2 |

Fixed | 0.2 | 0.7 | 0.1 | 0.8 | |

Relative motion | |||||

Approach | Leave | ||||

Relative distance | Decrease | 0.8 | 0.1 | ||

Unchanged | 0.1 | 0.1 | |||

Increase | 0.1 | 0.8 | |||

Relative bearing | Low | 0.7 | 0.1 | ||

Medium | 0.2 | 0.2 | |||

High | 0.1 | 0.7 |

Node | State | Intention | |||
---|---|---|---|---|---|

Patrol | Recon | Jamming | Assault | ||

Target type | AEW | 0.6323 | 0.1007 | 0.1017 | 0.0678 |

RP | 0.1912 | 0.6291 | 0.0995 | 0.0798 | |

EJA | 0.0886 | 0.1705 | 0.6889 | 0.1040 | |

Fighter | 0.0879 | 0.0997 | 0.1099 | 0.7484 | |

Relative velocity | Low | 0.6722 | 0.5060 | 0.2679 | 0.1135 |

Medium | 0.2360 | 0.3833 | 0.6354 | 0.5083 | |

High | 0.0918 | 0.1107 | 0.0967 | 0.3782 | |

Relative height | Low | 0.2358 | 0.1269 | 0.5133 | 0.2142 |

Medium | 0.6394 | 0.1921 | 0.3613 | 0.5112 | |

High | 0.1248 | 0.6810 | 0.1254 | 0.2746 | |

Relative motion | Approach | 0.5121 | 0.6813 | 0.7946 | 0.8582 |

Leave | 0.4879 | 0.3187 | 0.2054 | 0.1418 | |

Target type | |||||

AEW | RP | EJA | Fighter | ||

Velocity | Low | 0.6385 | 0.6790 | 0.2347 | 0.1398 |

Medium | 0.2667 | 0.2309 | 0.6765 | 0.3525 | |

High | 0.0948 | 0.0901 | 0.0888 | 0.5077 | |

Height | Low | 0.2365 | 0.1002 | 0.2825 | 0.1122 |

Medium | 0.6727 | 0.1258 | 0.6187 | 0.5118 | |

High | 0.0908 | 0.7740 | 0.0988 | 0.3760 | |

RCS | Very small | 0.0901 | 0.2958 | 0.1001 | 0.6428 |

Small | 0.0880 | 0.5143 | 0.1003 | 0.1815 | |

Medium | 0.1873 | 0.0952 | 0.6790 | 0.0877 | |

Large | 0.6346 | 0.0947 | 0.1206 | 0.0880 | |

RFV | Agility | 0.7684 | 0.3120 | 0.9351 | 0.2230 |

Fixed | 0.2316 | 0.6880 | 0.0649 | 0.7770 | |

Relative motion | |||||

Approach | Leave | ||||

Relative distance | Decrease | 0.8184 | 0.0997 | ||

Unchanged | 0.0819 | 0.0976 | |||

Increase | 0.0997 | 0.8027 | |||

Relative bearing | Low | 0.6843 | 0.0934 | ||

Medium | 0.2209 | 0.2084 | |||

High | 0.0948 | 0.6982 |

Velocity | Height | RCS | RFV | Relative Velocity | Relative Height | Relative Distance | Relative Bearing | |
---|---|---|---|---|---|---|---|---|

AEW | 0.9, 0.1, 0.0 | 0.2, 0.8, 0.0 | 0.0, 0.0, 0.3, 0.7 | 1.0, 0.0 | 0.9, 0.1, 0.0 | 0.1, 0.9, 0.0 | 0.0, 0.8, 0.2 | 0.0, 0.2, 0.8 |

RP | 0.9, 0.1, 0.0 | 0.0, 0.1, 0.9 | 0.1, 0.9, 0.0, 0.0 | 0.0, 1.0 | 0.9, 0.1, 0.0 | 0.0, 0.1, 0.9 | 0.9, 0.1, 0.0 | 0.9, 0.1, 0.0 |

EJA | 0.2, 0.8, 0.0 | 0.9, 0.1, 0.0 | 0.0, 0.0, 0.9, 0.1 | 1.0, 0.0 | 0.3, 0.7, 0.0 | 0.8, 0.2, 0.0 | 0.8, 0.2, 0.0 | 0.8, 0.2, 0.0 |

Fighter | 0.0, 0.2, 0.8 | 0.2, 0.8, 0.0 | 0.9, 0.1, 0.0, 0.0 | 0.0, 1.0 | 0.0, 0.2, 0.8 | 0.2, 0.8, 0.0 | 0.8, 0.2, 0.0 | 0.8, 0.2, 0.0 |

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© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Li, W.; Zhang, W.; Liu, B.; Guo, Y.
The Situation Assessment of UAVs Based on an Improved Whale Optimization Bayesian Network Parameter-Learning Algorithm. *Drones* **2023**, *7*, 655.
https://doi.org/10.3390/drones7110655

**AMA Style**

Li W, Zhang W, Liu B, Guo Y.
The Situation Assessment of UAVs Based on an Improved Whale Optimization Bayesian Network Parameter-Learning Algorithm. *Drones*. 2023; 7(11):655.
https://doi.org/10.3390/drones7110655

**Chicago/Turabian Style**

Li, Weinan, Weiguo Zhang, Baoning Liu, and Yicong Guo.
2023. "The Situation Assessment of UAVs Based on an Improved Whale Optimization Bayesian Network Parameter-Learning Algorithm" *Drones* 7, no. 11: 655.
https://doi.org/10.3390/drones7110655