Figures (8)  Tables (3)

    • Figure 1. 

      Schematic diagram of the problem scenario.

    • Figure 2. 

      System framework.

    • Figure 3. 

      The tracking performance of different methods.

    • Figure 4. 

      Target tracking process in a test experiment. The target prediction method is MCSI*, and the UAV planning method is the MCTS-based planning method. The blue star represents the position of the target, while the dashed red square denotes the FOV of the UAV. The square blue block indicates the target's starting region, and the green square marks the actual goal region of the target. The red dashed circles represent the sensing fields of the ground sensors. The blue solid line illustrates the trajectory of the target, whereas the red solid line depicts the path taken by the UAV. The green solid line shows the planned global path from the target's starting region to its goal region. The blue dots signify the predicted positions of the target, and the yellow circles indicate the potential predicted goal regions of the target, with larger circles representing a higher likelihood of being the target's goal region.

    • Figure 5. 

      The curve of the estimate of the target behavior parameter throughout the tracking process in Fig. 4.

    • Figure 6. 

      The impacts of the target's global motion behavior on tracking performance.

    • Figure 7. 

      The impacts of the target's evasive behavior on tracking performance.

    • Figure 8. 

      The impacts of the key parameters on tracking performance.

    • Input: Urban road graph $ M=(V,E) $, possible goal regions $ {g}_{i}({g}_{i}\in \mathbf{g}) $, ground sensor set $ C $, target's position $ x_{T}^{t} $, UAV's position $ x_{U}^{t} $, the number of trajectory samples $ N_{T}^{MC} $
      Output: The probability $ P(E({v}_{i},{v}_{j},{t}_{1},{t}_{2})) $
      1: //The target does not reach its goal region
      2: while $ x_{T}^{t} $ not at $ {g}_{T} $ do
      3: 　//Target is in the UAV's FOV or in the sensing field of ground sensors
      4: 　if $ x_{T}^{t}\in {F}_{t} $ or $ x_{T}^{t}\in {S}_{c} $ then
      5: 　　//Update target's intention
      6: 　　$ P({g}_{T}|x_{T}^{0: t})\propto P(v_{T}^{n}|v_{T}^{c},{g}_{T},\Omega )P({g}_{T}|x_{T}^{0: t-1}) $
      7: 　　// Sampled trajectories
      8: 　　$ \Theta \leftarrow \varnothing $
      9: 　　for each $ {g}_{i}\in \mathbf{g} $ do
      10: 　　　// Calculate the number of trajectories
      11: 　　　$ N_{i}^{MC}=N_{T}^{MC}P({g}_{i}|x_{T}^{0: t}) $
      12: 　　　for $ i=1,2,...,N_{i}^{MC} $ do
      13: 　　Draw a sample trajectory ${\mathcal{T}}$ from node $ v_{T}^{l} $ to node $ {g}_{i} $ using (5)
      14: 　　　　$\Theta \leftarrow \Theta \cup {\mathcal{T}}$
      15: 　　　end for
      16: 　　end for
      17: 　　for each ${\mathcal{T}} \in \Theta $ do
      18: 　　　// $ {v}_{j} $ is the next node of $ {v}_{i} $ in the trajectory ${\mathcal{T}}$
      19: 　　　for each $({v_i},{v_j}) \in {\mathcal{T}}$ do
      20: 　　　　Record the times $ {t}_{T}({v}_{i}) $ and $ {t}_{T}({v}_{j}) $
      21: 　　　end for
      22: 　　end for
      23: 　end if
      24: 　Calculate $ P(E({v}_{i},{v}_{j},{t}_{1},{t}_{2})) $ using (9) and (10)
      25: end while

      Table 1. 

      Target trajectory prediction algorithm (MCSI)

    • Input: Urban road graph $ M=(V,E) $, possible goal regions $ {g}_{i}({g}_{i}\in \mathbf{g}) $ and posterior probability $ P({g}_{i}|x_{T}^{0: t}) $, target's position $ x_{T}^{t} $, UAV's position $ x_{U}^{t} $, the maximum number of tree search iterations $ N_{p}^{MCTS} $, simulation horizon $ {H}_{p} $, constant $\lambda $
      Output: The next goal node of the UAV, $ v_{U}^{*}(t+1) $
      1: //Target is not in the UAV's FOV
      2: if $ x_{T}^{t}\notin {F}_{t} $ then
      3: 　Create root node $ {v}_{0} $ with node $ v_{U}^{n}(t) $, whose parent is None
      4: 　for $ i=1,2,... $,$ N_{p}^{MCTS} $ do
      5: 　　$ {v}_{l}\leftarrow $ TREEPOLICY$ ({v}_{0}) $
      6: 　　$ {r}_{l}\leftarrow $ DEFAULTPOLICY$ ({v}_{l}) $
      7: 　　BACKUP$ ({v}_{l},{r}_{l}) $
      8: 　end for
      9: 　$ v_{U}^{*}(t+1)\leftarrow $ BESTCHILD$ ({v}_{0},0) $
      10: end if
      11: function TREEPOLICY(v)
      12: while v is a nonterminating state do
      13: 　　if v is not fully expanded then
      14: 　　　return EXPAND(v)
      15: 　　else
      16: 　　　v←BESTCHILD(v,$ \lambda $)
      17: 　　end if
      18: 　end while
      19: 　return v
      20: end function
      21: function EXPAND(v)
      22: 　Choose one of the unvisited child nodes $ {\overline{v}}_{i} $, $ {\overline{v}}_{i}\in \chi (v) $
      23: 　return $ {\overline{v}}_{i} $
      24: end function
      25: function BESTCHILD(v, $ \lambda $)
      26: 　return $ \underset{{v}_{i}\in \chi (v)}{\arg \max }\dfrac{Q({v}_{i})}{N({v}_{i})}+\lambda \sqrt{\dfrac{\log (N(v))}{N({v}_{i})}} $
      27: end function
      28: function DEFAULTPOLICY($ (v_{U}^{n}(t+k)) $)
      29: 　Randomly sampling a goal region $ {g}_{i} $ according to the probability $ P({g}_{i}|x_{T}^{0: t}) $
      30: 　Draw a sample trajectory $ {\mathcal{T}} $from node $ v_{U}^{n}(t+k) $to node $ {g}_{i} $ using (5) with speed $ V_{\max }^{U} $
      31: 　$ \begin{aligned}r\leftarrow \sum \limits_{i=0}^{{H}_{p}-1}{\gamma }^{i}P(E(v_{U}^{n}(t+i),v_{U}^{n}(t+i+1), {t}_{U}(v_{U}^{n}(t+i)),{t}_{U}(v_{U}^{n}(t+i+1)))) \end{aligned} $
      32: 　return r
      33: end function
      34: function BACKUP(v, r)
      35: 　while v is not None do
      36: 　　$ N(v)\leftarrow N(v)+1 $
      37: 　　$ Q(v)\leftarrow Q(v)+r $
      38: 　　$ v\leftarrow $ parent of $ v $
      39: 　end while
      40: end function

      Table 2. 

      MCTS-based planning method.

    • Statistical
      indicators      		 Mean Standard
      deviation      		 U-statistic One-sided
      p-value
      MCS 0.32 0.15 6,912 0.000002
      MCSRM 0.38 0.17 6,158 0.002340
      DQN 0.39 0.18 5,927 0.011790
      MST 0.40 0.17 5,678 0.048912
      MCSI* 0.44 0.18 5,000 0.500488

      Table 1. 

      Statistical significance results.