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.
| Labels | QEG | SG |
| $L_{1}~=~0$ | $\lambda_{\mathrm{QEG1}}~\in~\left[0.25,0.625\right)$ | $\lambda_{\mathrm{SG1}}~\in~\left[0.25,0.625\right)$ |
| $L_{1}~=~1$ | $\lambda_{\mathrm{QEG1}}~\in~\left[0.625,1.125\right)$ | $\lambda_{\mathrm{SG1}}~\in~\left[0.625,1.125\right)$ |
| $L_{1}~=~2$ | $\lambda_{\mathrm{QEG1}}~\in~\left[1.125,1.625\right)$ | $\lambda_{\mathrm{SG1}}~\in~\left[1.125,1.625\right)$ |
| $L_{1}~=~3$ | $\lambda_{\mathrm{QEG1}}~\in~\left[1.625,2\right]$ | $\lambda_{\mathrm{SG1}}~\in~\left[1.625,2\right]$ |
| $L_{2}~=~0$ | $\lambda_{\mathrm{QEG2}}~\in~\left[2,2.75\right)$ | $\lambda_{\mathrm{SG2}}~\in~\left[0.5,0.875\right)$ |
| $L_{2}~=~1$ | $\lambda_{\mathrm{QEG2}}~\in~\left[2.75,3.25\right)$ | $\lambda_{\mathrm{SG2}}~\in~\left[0.875,1.125\right)$ |
| $L_{2}~=~2$ | $\lambda_{\mathrm{QEG2}}~\in~\left[3.25,4.25\right)$ | $\lambda_{\mathrm{SG2}}~\in~\left[1.125,1.625\right)$ |
| $L_{2}~=~3$ | $\lambda_{\mathrm{QEG2}}~\in~\left[4.25,5\right]$ | $\lambda_{\mathrm{SG2}}~\in~\left[1.625,2\right]$ |
/* Initialize the preprocessed measurement. |
Get preprocessed measurements $\tilde{z}_k$ using ( |
/* Trajectory estimation. |
Get preprocessed measurements $\tilde{z}_k$ using ( |
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 ( |
Recognize label $L_{3,k}$, using ( |
Recognize label $L_{1,k}$, using ( |
Recognize label $L_{2,k}$, using ( |
Calculate probability of each motion behavior using ( |
Select models to be used in the estimation (get $I^{\mathrm{s}}_{k}$) according to the probabilities of motion behaviors; |
|
Estimate $\hat{x}^{i}_{k|k}$ and $P^{i}_{k|k}$ using ( |
|
Get the final estimate results $\hat{x}_{k|k}$ and $P_{k|k}$ using ( |
| 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 |
| 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$^2$) | $1\times10^{-5}$ |
| 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 |
