Multi‐UAV active target search based on perceptual adaptation in marine environment

Cognitive Computation and SystemsVolume 4, Issue 3 p. 218-228 ORIGINAL RESEARCHOpen Access Multi-UAV active target search based on perceptual adaptation in marine environment Xiang Li, Xiang Li Yellow River Conservancy Technical Institute, China & Shanghai Maritime University, Kaifeng, ChinaSearch for more papers by this authorHebin Wang, Hebin Wang orcid.org/0000-0003-1199-500X Zhengzhou Xinda Institute of Advanced Technology, Zhengzhou, ChinaSearch for more papers by this authorXingfa Shen, Corresponding Author Xingfa Shen [email protected] orcid.org/0000-0002-6419-9149 School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou, China Correspondence Xingfa Shen, School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou, 310018, China. Email: [email protected]Search for more papers by this author Xiang Li, Xiang Li Yellow River Conservancy Technical Institute, China & Shanghai Maritime University, Kaifeng, ChinaSearch for more papers by this authorHebin Wang, Hebin Wang orcid.org/0000-0003-1199-500X Zhengzhou Xinda Institute of Advanced Technology, Zhengzhou, ChinaSearch for more papers by this authorXingfa Shen, Corresponding Author Xingfa Shen [email protected] orcid.org/0000-0002-6419-9149 School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou, China Correspondence Xingfa Shen, School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou, 310018, China. Email: [email protected]Search for more papers by this author First published: 07 March 2022 https://doi.org/10.1049/ccs2.12050AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract This work considers the problem of target search in marine environment. A perceptual adaptive Gaussian sum cubature Kalman filter is proposed for multi-target search in non-linear and non-Gaussian noise environment. Firstly, the robot collects environmental information, conducts environmental perception, and actively makes decisions. Secondly, the Dynamic Time Warping distance and Frechet distance weighted fusion are used to extract the association knowledge by analysing the trajectories of the underwater and surface targets obtained in the search process. The extracted association knowledge is used in the search process to form an evolving search relationship and increase the search efficiency. Finally, it is applied to realise the search of multiple dynamic targets, including underwater and surface targets, in the non-Gaussian marine environment. 1 INTRODUCTION Ships, submarines and other targets in complex marine environment pose a major threat to marine environment security, which plays an important role in national defence [1]. Target search in marine environment is an important means to realise marine environment monitoring, situation assessment and marine security guarantee [2]. Compared with the terrestrial environment, the marine environment is more diverse and complex, and the frequent changes of underwater and surface environments make it difficult to detect targets in the marine environment. In addition, underwater and surface targets have strong uncertainty, which makes it difficult to find the target, and brings difficulties to the design of the target search algorithm. Therefore, the research on target search in Marine environment has practical significance [3]. With the continuous progress of technology, unmanned aerial vehicles (UAVs) is widely used in rescue [4], environmental monitoring [5], target search [6] and other key tasks. With the continuous development of random multi-UAV swarm technology, multi-UAV cooperative search can effectively improve the search efficiency, especially in the dynamic target search under complicated sea conditions such as uncertainty and strong interference. But target search in marine environment is still challenging. There are often links between targets in marine environments, such as aircraft carriers and submarines. The surface targets in the sea environment are easy to be detected by airborne sensors due to their good acoustic and optical characteristics, while the underwater targets are often difficult to be detected. The general underwater target detection methods are determined according to the magnetic characteristics of underwater targets [7]. Therefore, it is important to consider the correlation between the underwater target and surface target in the process of target search in the Marine environment. In the target search task, the environment models can be mainly divided into the known-environment model and unknown-environment model [8]. Existing work has made a lot of progress in a known environment. The traditional search methods in known environment are mainly based on coverage search, such as echo search, traversal search etc [9, 10]. Such search methods usually search for as many targets as possible by maximising the coverage of the task area. However, it is difficult to get good results when the environment changes. In Ref. [8], the reward function and punishment function are designed according to the search efficiency function, and the multi-UAV cooperative search paths are generated online by using the Reinforcement Learning RL method. However, only a single type of targets are considered in Ref. [8]. In Ref. [11], based on the distributed model in the predictive control theory, the maximum coverage increment within the prediction period is set as the reward function, and the differential evolution algorithm is used to solve the problem, so as to obtain the optimal input for the collaborative region search of the UAV cluster. In Ref. [12], based on RL and the distributed control strategy, a distributed multi-AUV cooperative search system (DMACSS) is established, and an autonomous Collaborative Search Learning Algorithm is integrated into DMACSS. Most of the existing target search algorithms are based on Gaussian noise environment and consider a single type of targets. A few studies have been conducted on multi-target search algorithms based on non-Gaussian environment. Targets in Marine environments are often interrelated. So we need to consider the correlation between underwater and surface targets and apply the correlation to the target search process. In conclusion, aiming at the problem of non-linear and non-Gaussian multi-dynamic targets search in sea environment, we propose a method based on perceptual adaptive Gaussian sum cubature Kalman filter algorithms. The main contributions of this work are as follows: (1) Aiming at the problem of underwater and surface target search in marine environment, the relation of the underwater and surface target is considered. Multi-range fusion model is used to analyse association knowledge of the surface and underwater targets, and the obtained knowledge is used in the search process. (2) A perceptual adaptive objective function ensemble is designed to solve the problem of multi-UAV active target search in sea environment. Considering the estimated error covariance, newly explored area and pheromones, the objective function is calculated to get the best one-step solution of the UAV under the current position. (3) For the target search problem in which both the system noise and observation noise are non-Gaussian in sea environment, a multi-UAV active target search algorithm based on the perceptual adaptive algorithm is proposed in this paper. 2 PROBLEM FORMULATION The search and positioning of dynamic targets using multi-UAV in the marine environment is shown in Figure 1. The objective of the search mission is to search for as many targets as possible in the unknown marine environment. The search task requires UAVs to have independent search ability and to search for immediate targets efficiently and autonomously by adaptive navigation and positioning according to different environmental information and acquired knowledge. FIGURE 1Open in figure viewerPowerPoint Multi-unmanned aerial vehicles (UAV) cooperative target search in marine area As shown in Figure 1, the targets include a surface target and an underwater target. The purpose of multiple UAVs is to search for as many targets as possible. In this paper, the target search problem of multi-UAV is considered from a two-dimensional perspective. For the UAV, the number and location distribution of targets are completely unknown. After entering the environment, the UAV cluster carries communication equipment and sensor equipment to search the sea area, obtains and updates target information in real time, and provides support for the subsequent tasks such as combat situation assessment and target strike. Each UAV plans its own trajectory in real time and carries out cooperative search on the task area. The UAV system communicates with each other in real time, including UAV status, optimal decision, environmental information etc. Therefore, this work mainly studies how to plan the multi-UAV system online to conduct dynamic multi-target search in the unknown environment and find as many targets as possible. Environment model As shown in Figure 2, the environment model is in the form of a raster map and the task area Ω is divided into m ∗ n grids [13]. Each grid πij of the environment model is with a Boolean value 0 or 1, which is used to describe whether the area has been explored or not by the end of the current moment k. π i j k = 0 i , j ∈ Ω n c k 1 i , j ∈ Ω c k ${\pi }_{ij}\left(k\right)=\left\{\begin{array}{l}0\,\,\,\,\left(i,j\right)\in {{\Omega}}_{nc}\left(k\right)\quad \hfill \\ 1\,\,\,\,\,\left(i,j\right)\in {{\Omega}}_{c}\left(k\right)\quad \hfill \end{array}\right.$ (1) FIGURE 2Open in figure viewerPowerPoint Search area division UAV model The motion model of the UAV is expressed as follows [14]: x k = x k − 1 + V k − 1 ⋅ cos θ k − 1 + ω Δ t y k = y k − 1 + V k − 1 ⋅ sin θ k − 1 + ω Δ t θ k = θ k − 1 + ω Δ t $\left\{\begin{array}{c}\hfill {x}_{k}={x}_{k-1}+{V}_{k-1}\cdot \mathrm{cos}\left({\theta }_{k-1}+\omega {\Delta}t\right)\hfill \\ \hfill {y}_{k}={y}_{k-1}+{V}_{k-1}\cdot \mathrm{sin}\left({\theta }_{k-1}+\omega {\Delta}t\right)\hfill \\ \hfill {\theta }_{k}={\theta }_{k-1}+\omega {\Delta}t\hfill \end{array}\right.$ (2)In the above motion model, the real input is as follows: u k − 1 = V k − 1 ω ${\mathbf{u}}_{k-1}=\left[\begin{array}{c}\hfill {V}_{k-1}\hfill \\ \hfill \omega \hfill \end{array}\right]$ (3) Where x and y are the horizontal and vertical coordinates of UAV in the environment, θ is the azimuth Angle, Vk−1 is linear velocity, ω is angular velocity, and Δt is process time. The state equation of the multi-UAV system with n UAVs is given as x i , k r = f ( x i , k − 1 r , u i , k − 1 ) + w k − 1 , i ∈ { 1 , 2 , … n } ${\mathbf{x}}_{i,k}^{r}=\mathbf{f}({\mathbf{x}}_{i,k-1}^{r},{\mathbf{u}}_{i,k-1})+\,{\mathbf{w}}_{k-1},i\in \left\{1,2,\text{{\ldots}}n\right\}$ (4)The state vector of UAV at k-1 moment is x k − 1 r = x k − 1 , y k − 1 , θ k − 1 ${\mathbf{x}}_{k-1}^{r}\,=\,\left({x}_{k-1},{y}_{k-1},{\theta }_{k-1}\right)$ . Where x i , k − 1 r ${\mathbf{x}}_{i,k-1}^{r}$ denotes the state of UAVi on time k − 1, and ui,k−1 ∈ U denotes a sequence of control inputs. The wk is non-Gaussian process noise with the probability density p w k $p\left({\mathbf{w}}_{k}\right)$ . According to the Gaussian sum theorem, the probability density function with arbitrary distribution can be approximated by the accumulation of finite Gaussian terms, that is, the sum of several Gaussian terms with different weights is used to describe non-Gaussian noise [15]. Therefore p w k $p\left({\mathbf{w}}_{k}\right)$ can be described as follows: p w k = ∑ j = 1 J α w , k j N w k ; w k j , Q k j $p\left({\mathbf{w}}_{k}\right)=\sum\limits _{j=1}^{J}{\alpha }_{w,k}^{j}N\left({\mathbf{w}}_{k};{\mathbf{w}}_{k}^{j},{\mathbf{Q}}_{k}^{j}\right)$ (5) Where α w , k j ${\alpha }_{w,k}^{j}$ , w k j ${\mathbf{w}}_{k}^{j}$ , and Q k j ${\mathbf{Q}}_{k}^{j}$ , respectively, represent the weight, mean and variance of the jth process noise Gaussian component and satisfy ∑ j = 1 J a w , k j = 1 $\sum\limits _{j=1}^{J}{a}_{w,k}^{j}=1$ . Target model The targets studied in this paper are divided into two categories: surface targets located on the sea surface and underwater target located under the sea surface, which have a certain correlation. Assuming that the dynamic surface targets and underwater targets move in a uniform and straight line, the state of the surface target yk can be expressed as follows [16]: y k = y k x y . k x y k y y . k y ${\mathbf{y}}_{k}=\left[{y}_{k}^{x}\,\,\,{\stackrel{.}{y}}_{k}^{x}\,\,\,{y}_{k}^{y}\,\,\,{\stackrel{.}{y}}_{k}^{y}\right]$ (6) Where y k x ${y}_{k}^{x}$ , y . k x ${\stackrel{.}{y}}_{k}^{x}$ , y k y ${y}_{k}^{y}$ and y . k y ${\stackrel{.}{y}}_{k}^{y}$ represent the position coordinates and velocity values of the surface target in x-axis direction and y-axis direction, respectively. y k + 1 = 1 T 0 0 0 1 0 0 0 0 1 T 0 0 0 1 y k + T 2 / 2 0 T 0 0 T 2 / 2 0 T o k ${\mathbf{y}}_{k+1}=\left[\begin{array}{cccc}\hfill 1\hfill & \hfill \,\,\,T\hfill & \hfill \,\,\,0\hfill & \hfill \,\,\,0\hfill \\ \hfill 0\hfill & \hfill \,\,\,1\hfill & \hfill \,\,\,0\hfill & \hfill \,\,\,0\hfill \\ \hfill 0\hfill & \hfill \,\,\,0\hfill & \hfill \,\,\,1\hfill & \hfill \,\,\,T\hfill \\ \hfill 0\hfill & \hfill \,\,\,0\hfill & \hfill \,\,\,0\hfill & \hfill \,\,\,1\hfill \end{array}\right]{\mathbf{y}}_{k}+\left[\begin{array}{c}\hfill {T}^{2}/2\,\,\,0\hfill \\ \hfill T\,\,\,\,\,\,\,\,\,0\hfill \\ \hfill 0\,\,\,{T}^{2}/2\hfill \\ \hfill 0\,\,\,\,\,\,\,T\hfill \end{array}\right]{\mathbf{o}}_{\mathbf{k}}$ (7)where T is the sampling time, and ok is Gaussian noise with probability density p o k $p\left({\mathbf{o}}_{\mathbf{k}}\right)$ , which is given by p o k = N o k , 0 , O k $p\left({\mathbf{o}}_{\mathbf{k}}\right)=N\left({\mathbf{o}}_{\mathbf{k}},0,{\mathbf{O}}_{k}\right)$ (8) The underwater target, Mk+1 motion state and the surface state of a linear are correlated and expressed as follows: M k + 1 = c y k + d ${\mathbf{M}}_{k+1}=c{\mathbf{y}}_{k}+d$ (9) Where c and d are constant. The underwater target state vector is M k = m k x m . k x m k y m . k y ${\mathbf{M}}_{k}=\left[{m}_{k}^{x}\,\,\,{\stackrel{.}{m}}_{k}^{x}\,\,\,{m}_{k}^{y}\,\,\,{\stackrel{.}{m}}_{k}^{y}\right]$ . Where m k x ${m}_{k}^{x}$ , m . k x ${\stackrel{.}{m}}_{k}^{x}$ , m k y ${m}_{k}^{y}$ and m . k y ${\stackrel{.}{m}}_{k}^{y}$ represent the position coordinates and velocity values of the underwater target in x-axis direction and y-axis direction, respectively. Sensor model UAVs carry two sensors, one of which is the range-angle sensor used to detect targets on the water surface [17], which can be described as follows: z i , k = h x i , k r , y k + v k , i ∈ 1 , 2 , … , n h x i , k r , y k = y k x − x i , k 2 + y k y − y i , k 2 tan − 1 y k y − y i , k / y k x − x i , k − θ i , k $\begin{array}{l}{\mathbf{z}}_{i,k}=\mathbf{h}\left({\mathbf{x}}_{i,k}^{r},{\mathbf{y}}_{k}\right)+{\mathbf{v}}_{k},i\in \left\{1,2,\text{{\ldots}},n\right\}\hfill \\ \mathbf{h}\left({\mathbf{x}}_{i,k}^{r},{\mathbf{y}}_{k}\right)=\left[\begin{array}{c}\hfill \sqrt{{\left({y}_{k}^{x}-{x}_{i,k}\right)}^{2}+\,{\left({y}_{k}^{y}-{y}_{i,k}\right)}^{2}}\hfill \\ \hfill {\mathrm{tan}}^{-1}\left(\left({y}_{k}^{y}-{y}_{i,k}\right)/\left({y}_{k}^{x}-{x}_{i,k}\right)\right)-{\theta }_{i,k}\hfill \end{array}\right]\hfill \end{array}$ (10) Where zi,k is the observation vector of the ith UAV at time k , h ⋅ $k,\mathbf{h}\left(\cdot \right)$ is the non-linear measurement function, x i , k r = x i , k , y i , k , θ i , k ${\mathbf{x}}_{i,k}^{r}=\left({x}_{i,k},{y}_{i,k},{\theta }_{i,k}\right)$ is the motion state of UAVi at time k, and y k = y k x y . k x y k y y . k y ${\mathbf{y}}_{k}=\left[{y}_{k}^{x}\,\,\,{\stackrel{.}{y}}_{k}^{x}\,\,\,{y}_{k}^{y}\,\,\,{\stackrel{.}{y}}_{k}^{y}\right]$ is the motion state of surface target at time k. The observation noise vk is non-Gaussian noise, with the probability density function p v k $p\left({\mathbf{v}}_{k}\right)$ defined as p v k = ∑ l = 1 L α v , k l N v k ; v k l , R k l $p\left({\mathbf{v}}_{k}\right)=\sum\limits _{l=1}^{L}{\alpha }_{v,k}^{l}N\left({\mathbf{v}}_{k};{\mathbf{v}}_{k}^{l},{\mathbf{R}}_{k}^{l}\right)$ (11) Where α v , k l ${\alpha }_{v,k}^{l}$ , v k l ${\mathbf{v}}_{k}^{l}$ , and R k l ${\mathbf{R}}_{k}^{l}$ , respectively, represent the weight, mean and variance of the jth process noise Gaussian component and satisfy ∑ l = 1 L a v , k l = 1 $\sum\limits _{l=1}^{L}{a}_{v,k}^{l}=1$ . Its maximum detection range is 25m. The UAV has a forward vision − ϕ 2 < α ( x , y ) < ϕ 2 $\left(-\frac{\phi }{2}< \alpha (x,y)< \frac{\phi }{2}\right)$ , ϕ = π/3. The magnetic prospecting instrument is a device used for underwater target search [7]. Its detection probability is affected by working parameters, environment, UAV situation and target magnetic characteristics. In order to simplify the calculation, the Euclidean distance l between the UAV and the underwater target is used in this section to describe whether the UAV has found the underwater target or not. When it meets Equation (12), it is considered that the UAV has found the underwater target. l = x i , k ′ − M k ′ ≤ ξ $l={\Vert}{\mathbf{x}}_{i,k}^{\prime }-{\mathbf{M}}_{k}^{\prime }{\Vert}\le \xi $ (12) Where x i , t ′ = x i , k , y i , k ${\mathbf{x}}_{i,t}^{\prime }=\left({x}_{i,k},{y}_{i,k}\right)$ represents the position of the UAVi in the environment at k time, M k ′ = m k x , m k y ${\mathbf{M}}_{k}^{\prime }=\left({m}_{k}^{x},{m}_{k}^{y}\right)$ represents the position of the underwater target in the environment at k time, and x i , k ′ − M k ′ ${\Vert}{\mathbf{x}}_{i,k}^{\prime }-{\mathbf{M}}_{k}^{\prime }{\Vert}$ represents the Euclidean distance between them. Where ≤ ξ is the exploration scope of simplifying the magnetic exploration model in this paper. In particular, we stipulate that the distance angle sensor is only used to find the water surface target, and the simple magnetic exploration model is only used to find the underwater target. Pheromones Pheromones are left behind by UAVs searching for targets. The pheromone matrix is shared by the UAVs and used as a medium to increase information exchange between UAVs. The pheromone acts as a stimulus, and other UAVs will sense and move to target areas with high pheromone concentrations [18]. When the UAV does not find the target during the search of the current location, the pheromone of this location will be reduced. When a UAV finds a target in that location, it increases the pheromones of that location, which in turn influences the decisions of other UAVs. Increase in the pheromones is based on ψ k = ψ k − 1 + λ f x , y $\psi \left(k\right)=\psi \left(k-1\right)+\lambda f\left(x,y\right)$ (13)Reduction in the pheromones is based on ψ k = ψ k − 1 − h x , y $\psi \left(k\right)=\psi \left(k-1\right)-h\left(x,y\right)$ (14) The ψ k $\psi \left(k\right)$ is the global pheromones matrix. Where f x , y $f\left(x,y\right)$ and h x , y $h\left(x,y\right)$ are f x , y = 1 2 π σ 1 e − x − i ∗ x − i + y − j ∗ y − j 2 σ 1 2 , i = 1 : m , j = 1 : n $f\left(x,y\right)=\frac{1}{\sqrt{2\pi }{\sigma }_{1}}{e}^{\frac{-\left(\left(x-i\right)\ast \left(x-i\right)+\left(y-j\right)\ast \left(y-j\right)\right)}{2{\sigma }_{1}^{2}}},i=1:m,j=1:n$ (15) h x , y = 1 2 π σ 2 e − x − i ∗ x − i + y − j ∗ y − j 2 σ 2 2 , i = 1 : m , j = 1 : n $h\left(x,y\right)=\frac{1}{\sqrt{2\pi }{\sigma }_{2}}{e}^{\frac{-\left(\left(x-i\right)\ast \left(x-i\right)+\left(y-j\right)\ast \left(y-j\right)\right)}{2{\sigma }_{2}^{2}}},i=1:m,j=1:n$ (16) Where x and y, respectively, represent the position of UAV in the environment, m ∗ n is the number of grids divided in the search area, and σ1 and σ2 are the variances. 3 DESIGN OF DISTRIBUTED ESTIMATION AND CONTROL METHOD OF MULTI-UAV Gaussian sum cubature Kalman filter based on perceptual adaptive function Because of the process noise of UAV and observation noise of the range-angle sensor, non-Gaussian noise and the traditional cubature Kalman filter algorithm [19] are difficult to solve. Therefore, this paper proposes a perceptual adaptive Gaussian sum cubature Kalman filter algorithm under non-Gaussian noise combined with the Gaussian sum filter framework. Assume that the statistical characteristics p ( x ˆ i , k − 1 | k − 1 r ) $p({\widehat{\mathbf{x}}}_{i,k-1\vert k-1}^{r})$ of state x ˆ i , k − 1 | k − 1 r ${\widehat{\mathbf{x}}}_{i,k-1\vert k-1}^{r}$ of the UAVi at moment k − 1 are known: p x ˆ i , k − 1 | k − 1 r = ∑ m = 1 M α x , k − 1 m N x ˆ i , k − 1 | k − 1 r , m , P i , k − 1 | k − 1 r r , m $p\left({\widehat{\mathbf{x}}}_{i,k-1\vert k-1}^{r}\right)=\sum\limits _{m=1}^{M}{\alpha }_{x,k-1}^{m}N\left({\widehat{\mathbf{x}}}_{i,k-1\vert k-1}^{r,m},{\mathbf{P}}_{i,k-1\vert k-1}^{rr,m}\right)$ (17) Where α x , k − 1 m , x ˆ i , k − 1 | k − 1 r , m , P i , k − 1 | k − 1 r r , m ${\alpha }_{x,k-1}^{m},{\widehat{\mathbf{x}}}_{i,k-1\vert k-1}^{r,m},{\mathbf{P}}_{i,k-1\vert k-1}^{rr,m}$ , respectively, represent the mth state and covariance component of the UAVi and satisfy ∑ m = 1 M α x , k − 1 m = 1 $\sum\limits _{m=1}^{M}{\alpha }_{x,k-1}^{m}=1$ . By splicing the UAV state with the target state yk−1, we can get the following [20]: x i , k − 1 | k − 1 = ∑ m = 1 M α x , k − 1 m x ˆ i , k − 1 | k − 1 r , m y k − 1 T ${\mathbf{x}}_{i,k-1\vert k-1}=\,\sum\limits _{m=1}^{M}{\alpha }_{x,k-1}^{m}{\left[{\widehat{\mathbf{x}}}_{i,k-1\vert k-1}^{r,m}\,\,\,{\mathbf{y}}_{k-1}\right]}^{T}$ P i , k − 1 | k − 1 = ∑ m = 1 M α x , k − 1 m P i , k − 1 | k − 1 r r , m P i , k − 1 | k − 1 r y P i , k − 1 | k − 1 r y T P i , k − 1 | k − 1 y y ${\mathbf{P}}_{i,k-1\vert k-1}=\sum\limits _{m=1}^{M}{\alpha }_{x,k-1}^{m}\left[\begin{array}{c}\hfill {\mathbf{P}}_{i,k-1\vert k-1}^{rr,m}\,\,\,{\mathbf{P}}_{i,k-1\vert k-1}^{ry}\hfill \\ \hfill {\mathbf{P}}_{i,k-1\vert k-1}^{ry\,\,\,\,T}\,\,\,{\mathbf{P}}_{i,k-1\vert k-1}^{yy}\hfill \end{array}\right]$ (18) Where xi,k−1|k−1, Pi,k−1|k−1, respectively, represent the spliced state vector and covariance. Where P i , k − 1 | k − 1 y y ${\mathbf{P}}_{i,k-1\vert k-1}^{yy}$ is the covariance of the target and P i , k − 1 | k − 1 r y ${\mathbf{P}}_{i,k-1\vert k-1}^{ry}$ is the cross covariance between the target and the UAV. Time Update: x ˆ i , k | k − 1 r , m , j = ∑ e = 1 2 n x β e ξ i , k | k − 1 m , e + w k j ${\widehat{\mathbf{x}}}_{i,k\vert k-1}^{r,m,j}=\sum\limits _{e=1}^{2{n}_{x}}{\beta }^{e}{\xi }_{i,k\vert k-1}^{m,e}+{\mathbf{w}}_{k}^{j}$ (19) P i , k | k − 1 r r , m , j = ∑ e = 1 2 n x β e ξ i , k | k − 1 m , e − x ˆ i , k | k − 1 r , m , j ξ i , k | k − 1 m , e − x ˆ i , k | k − 1 r , m , j T + Q k , k − 1 j $\begin{array}{l}{\mathbf{P}}_{i,k\vert k-1}^{rr,m,j}=\sum\limits _{e=1}^{2{n}_{x}}{\beta }^{e}\left({{\xi }_{i,k\vert k-1}^{m,e}-\widehat{\mathbf{x}}}_{i,k\vert k-1}^{r,m,j}\right)\hfill \\ \quad \quad \quad \quad \quad {\left({{\xi }_{i,k\vert k-1}^{m,e}-\widehat{\mathbf{x}}}_{i,k\vert k-1}^{r,m,j}\right)}^{T}+{\mathbf{Q}}_{k,k-1}^{j}\hfill \end{array}$ (20) Where x ˆ i , k | k − 1 r , m , j ${\widehat{\mathbf{x}}}_{i,k\vert k-1}^{r,m,j}$ and P i , k | k − 1 r r , m , j ${\mathbf{P}}_{i,k\vert k-1}^{rr,m,j}$ , respectively, represent the state and covariance of UAV after time update. Where nx is the dimension of state vector, ξ i , k | k − 1 m , e ${\xi }_{i,k\vert k-1}^{m,e}$ is the weight of volume points after propagation, w k j ${\mathbf{w}}_{k}^{j}$ and Q k , k − 1 j ${\mathbf{Q}}_{k,k-1}^{j}$ , respectively, represent the mean and variance of the jth process noise component. The intermediate variables are as follows: P i , k − 1 | k − 1 r r , m = S i , k − 1 | k − 1 m S i , k − 1 | k − 1 m T ξ i , k | k − 1 m , e = f S i , k − 1 | k − 1 m ⋅ χ e + x ˆ i , k − 1 | k − 1 r , m , u i , k α i , k | k − 1 m , j = α i , k − 1 | k − 1 m α w , k j $\left\{\begin{array}{c}\hfill {\mathbf{P}}_{i,k-1\vert k-1}^{rr,m}={\mathbf{S}}_{i,k-1\vert k-1}^{m}{\left({\mathbf{S}}_{i,k-1\vert k-1}^{m}\right)}^{T}\hfill \\ \hfill {\xi }_{i,k\vert k-1}^{m,e}=\mathbf{f}\left({{\mathbf{S}}_{i,k-1\vert k-1}^{m}\cdot {\chi }^{e}+\widehat{\mathbf{x}}}_{i,k-1\vert k-1}^{r,m},{\mathbf{u}}_{i,k}\right)\hfill \\ \hfill {\alpha }_{i,k\vert k-1}^{m,j}={\alpha }_{i,k-1\vert k-1}^{m}{\alpha }_{w,k}^{j}\hfill \end{array}\right.$ (21) Where χe is the eth volume point determined by the spherical radial rule, and α i , k | k − 1 m , j ${\alpha }_{i,k\vert k-1}^{m,j}$ is the weight of each state component after time update. Where ui,k is the control decisions selected based on the perceptual adaptive objective function of Equation (29). Measurement update: x ˆ i , k | k − 1 m , j = x ˆ i , k | k − 1 r , m , j y k − 1 T ${\widehat{\mathbf{x}}}_{i,k\vert k-1}^{m,j}\,=\,{\left[{\widehat{\mathbf{x}}}_{i,k\vert k-1}^{r,m,j}\,\,\,{\mathbf{y}}_{k-1}\right]}^{T}$ (22) P i , k | k − 1 m , j = P i , k | k − 1 r r , m , j P i , k − 1 | k − 1 r y P i , k − 1 | k − 1 r y T P i , k − 1 | k − 1 y y ${\mathbf{P}}_{i,k\vert k-1}^{m,j}=\left[\begin{array}{c}\hfill {\mathbf{P}}_{i,k\vert k-1}^{rr,m,j}\,\,\,\,\,{\mathbf{P}}_{i,k-1\vert k-1}^{ry}\hfill \\ \hfill {\mathbf{P}}_{i,k-1\vert k-1}^{ry\,\,\,\,\,\,\,T}\,\,\,{\mathbf{P}}_{i,k-1\vert k-1}^{yy}\hfill \end{array}\right]$ (23) x ˆ i , k | k m , j , l = x ˆ i , k | k − 1 m , j + K i , k m , j , l z k − z ˆ i , k | k − 1 m , j , l ${\widehat{\mathbf{x}}}_{i,k\vert k}^{m,j,l}={\widehat{\mathbf{x}}}_{i,k\vert k-1}^{m,j}+{\mathbf{K}}_{i,k}^{m,j,l}\left({{\mathbf{z}}_{k}-\widehat{\mathbf{z}}}_{i,k\vert k-1}^{m,j,l}\right)$ (24) P i , k | k m , j , l = P i , k | k − 1 m , j − K i , k m , j , l P i , z z , k | k − 1 m , j , l K i , k m , j , l T ${\mathbf{P}}_{i,k\vert k}^{m,j,l}={\mathbf{P}}_{i,k\vert k-1}^{m,j}-{\mathbf{K}}_{i,k}^{m,j,l}{\mathbf{P}}_{i,zz,k\vert k-1}^{m,j,l}{\left({\mathbf{K}}_{i,k}^{m,j,l}\right)}^{T}$ (25) Where, xi,k|k−1 and Pi,k|k−1, respectively, represent the state vector and covariance component after time update, x ˆ i , k | k m , j , l ${\widehat{\mathbf{x}}}_{i,k\vert k}^{m,j,l}$ and P i , k | k m , j , l ${\mathbf{P}}_{i,k\vert k}^{m,j,l}$ , respectively, represent the state vector and covariance component after measurement update, zk is the observed value, K i , k m , j , l ${\mathbf{K}}_{i,k}^{m,j,l}$ is the Kalman gain component, z ˆ i , k | k − 1 m , j , l ${\widehat{\mathbf{z}}}_{i,k\vert k-1}^{m,j,l}$ is the predicted component of the measured value, and P i , z z , k | k − 1 m , j , l ${\mathbf{P}}_{i,zz,k\vert k-1}^{m,j,l}$ is the component of the innovation covariance. The intermediate variables are as follows: P i , k | k − 1 m , j = S i , k | k − 1 m , j S i , k | k − 1 m , j T φ i , k | k − 1 m , j , r = S i , k | k − 1 m , j ⋅ χ r + x ˆ i , k | k − 1 m , j ξ i , k | k − 1 m , j , r = h φ i , k | k − 1 m , j , r z ˆ i , k | k − 1 m , j , l = ∑ r = 1 2 n x β r ξ i , k | k − 1 m , j , r + v k l P i , z z , k | k − 1 m , j , l = ∑ r = 1 2 n x β r ξ i , k | k − 1 m , j , r − z ˆ i , k | k − 1 m , j , l ξ i , k | k −