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SCIENCE CHINA Information Sciences, Volume 63 , Issue 9 : 192202(2020) https://doi.org/10.1007/s11432-019-1515-2

Active switching multiple model method for tracking a noncooperative gliding flight vehicle

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  • ReceivedJan 2, 2019
  • AcceptedJul 10, 2019
  • PublishedJul 2, 2020

Abstract

The study investigates the trajectory estimation problem of a noncooperative gliding flight vehicle with complex and atypical maneuvers. An active switching multiple model (ASMM) method is proposed. This method employs a motion behavior model set (MBMS), a motion behavior recognition algorithm, and an active switching estimation and fusion algorithm.First, a recognizable MBMS, which can capture all the motion behaviors of a gliding flight vehicle, is established.Then, a motion behavior recognition algorithm based on recurrent neural networks (RNNs) is developed to obtain the current probability of each motion behavior. Then, an active switching estimation and fusion algorithm is proposed, in which the adopted models are actively chosen at each time instant according to a model selection strategy. Last, the proposed ASMM method is applied to a noncooperative gliding flight vehicle. The simulation results show that the proposed method has higher estimation precision and better dynamic performance.


Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 61473099, 61333001). The Titan Xp used for the RNNs training is donated by the NVIDIA Corporation.


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  • Figure 1

    (Color online) Data preprocessing.

  • Figure 2

    (Color online) The architecture of the recurrent neural networks.

  • Figure 3

    Active switching estimation and fusion algorithm.

  • Figure 4

    Training results. (a) $\mathrm{RNN}_{\mathrm{t}}$; (b) $\mathrm{RNN}_{1,\mathrm{QEG}}$; (c) $\mathrm{RNN}_{2,\mathrm{QEG}}$; (d) $\mathrm{RNN}_{1,\mathrm{SG}}$; (e) $\mathrm{RNN}_{2,\mathrm{SG}}$; (f) $\mathrm{RNN}_{3}$.

  • Figure 5

    (Color online) Recognition results. (a) Scenario 1; (b) scenario 2; (c) scenario 3.

  • Figure 6

    (Color online) Estimation results of different model selection strategies. (a) Position estimation of scenario 1; (b) velocity estimation of scenario 1; (c) position estimation of scenario 2; (d) velocity estimation of scenario 2; (e) position estimation of scenario 3; (f) velocity estimation of scenario 3.

  • Figure 7

    (Color online) Model usage of different model selection strategies. (a) Scenario 1; (b) scenario 2; (c) scenario 3.

  • Figure 8

    (Color online) Comparison between ASMM and IMM. (a) Position estimation of scenario 1; (b) velocity estimation of scenario 1; (c) position estimation of scenario 2; (d) velocity estimation of scenario 2; (e) position estimation of scenario 3; (f) velocity estimation of scenario 3.

  • Table 1  

    Table 1 Definitions of $L_{1}$ and $L_{2}$

    Labels QEG SG
    $L_{1}~=~0$ $\lambda_{\mathrm{QEG1}}~\in~\left[0.25,0.625\right)$ $\lambda_{\mathrm{SG1}}~\in~\left[0.25,0.625\right)$
    $L_{1}~=~1$ $\lambda_{\mathrm{QEG1}}~\in~\left[0.625,1.125\right)$ $\lambda_{\mathrm{SG1}}~\in~\left[0.625,1.125\right)$
    $L_{1}~=~2$ $\lambda_{\mathrm{QEG1}}~\in~\left[1.125,1.625\right)$ $\lambda_{\mathrm{SG1}}~\in~\left[1.125,1.625\right)$
    $L_{1}~=~3$ $\lambda_{\mathrm{QEG1}}~\in~\left[1.625,2\right]$ $\lambda_{\mathrm{SG1}}~\in~\left[1.625,2\right]$
    $L_{2}~=~0$ $\lambda_{\mathrm{QEG2}}~\in~\left[2,2.75\right)$ $\lambda_{\mathrm{SG2}}~\in~\left[0.5,0.875\right)$
    $L_{2}~=~1$ $\lambda_{\mathrm{QEG2}}~\in~\left[2.75,3.25\right)$ $\lambda_{\mathrm{SG2}}~\in~\left[0.875,1.125\right)$
    $L_{2}~=~2$ $\lambda_{\mathrm{QEG2}}~\in~\left[3.25,4.25\right)$ $\lambda_{\mathrm{SG2}}~\in~\left[1.125,1.625\right)$
    $L_{2}~=~3$ $\lambda_{\mathrm{QEG2}}~\in~\left[4.25,5\right]$ $\lambda_{\mathrm{SG2}}~\in~\left[1.625,2\right]$
  •   

    Algorithm 1 Active switching multiple model fusion

    /* Initialize the preprocessed measurement.

    for $k~=~1$ to $N-1$

    Get preprocessed measurements $\tilde{z}_k$ using (41)–(45);

    end for

    /* Trajectory estimation.

    for $k=N$ to $k_{\max}$

    Get preprocessed measurements $\tilde{z}_k$ using (41)–(45);

    Sequence of preprocessed measurements $\tilde{z}^{N}_{k}~=~[\tilde{z}_{k-N+1},\tilde{z}_{k-N+2},\ldots,\tilde{z}_{k}]$;

    Recognize label $L_{\mathrm{t},k}$, using (46);

    Recognize label $L_{3,k}$, using (49);

    Recognize label $L_{1,k}$, using (47);

    Recognize label $L_{2,k}$, using (48);

    Calculate probability of each motion behavior using (50)–(equ:p-model-03);

    Select models to be used in the estimation (get $I^{\mathrm{s}}_{k}$) according to the probabilities of motion behaviors;

    for $\mathrm{BHV}^i\in~I^{\mathrm{s}}_{k}$

    Estimate $\hat{x}^{i}_{k|k}$ and $P^{i}_{k|k}$ using (57)–(63);

    end for

    Get the final estimate results $\hat{x}_{k|k}$ and $P_{k|k}$ using (64)–(66);

    end for

  • Table 2  

    Table 2 Recognition accuracy of RNNs

    Accuracy on the training set (%) Accuracy on the test set (%)
    $\mathrm{RNN}_{\mathrm{t}}$ 94.92 95.11
    $\mathrm{RNN}_{1,\mathrm{QEG}}$ 96.78 88.25
    $\mathrm{RNN}_{1,\mathrm{SG}}$ 93.18 83.83
    $\mathrm{RNN}_{2,\mathrm{QEG}}$ 93.10 90.39
    $\mathrm{RNN}_{2,\mathrm{SG}}$ 90.08 79.41
    $\mathrm{RNN}_{3}$ 97.23 92.40
  • Table 3  

    Table 3 Simulation set-up

    Item Value
    Initial height, $h_0$ (m) 60000
    Initial longitude, $\theta_0$ (rad) 0
    Initial latitude, $\phi_0$ (rad) 0
    Initial velocity, $v_0$ (m/s) 7000
    Initial flight-path angle, $\gamma_0$ (rad) $-$1
    Initial heading angle, $\psi_0$ (rad) 90
    End up velocity, $v_{\mathrm{f}}$ (m/s) 2000
    Variance of height, $\mathrm{Var}_h$ (m$^2$) $4.9\times10^4$
    Variance of longitude, $\mathrm{Var}_\theta$ (rad$^2$) $1\times10^{-5}$
    Variance of latitude, $\mathrm{Var}_\phi$ (rad$^2$) $1\times10^{-5}$
  • Table 4  

    Table 4 Average time cost of different model selection strategies

    Scenario All (ms/step) Certainty (ms/step) Top-5 (ms/step) CP (ms/step)
    1 68.794 32.933 34.480 33.765
    2 69.459 32.898 34.603 33.478
    3 69.690 33.897 35.471 34.806

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