A Method for Predicting Trajectories of Concealed Targets via a Hybrid Decomposition and State Prediction Framework
Abstract
:1. Introduction
- (1)
- With the ISVMD, the input feature set of a new predictor is constructed on the data–time axis. The algorithm is used to decompose complex signals efficiently and the best decomposition effect is obtained by statistical analysis. Compared to the existing VMD algorithm, this algorithm improves the decomposition accuracy and efficiency, which avoids the impact of abnormal data.
- (2)
- With the help of the RBMO algorithm, a new predicting structure based on the ELM algorithm is designed for the overall system. The RBMO-ELM algorithm is directly used as a predictor, and the optimized hidden layer function and activation function are used to output the optimal prediction set. Compared with the traditional prediction algorithm, the algorithm improves the prediction accuracy and processing efficiency.
- (3)
- The iterative operation process is grouped according to the data input time, and each data set is decomposed by the improved VMD algorithm and continuously passed to the predictor. In the prediction method, the RBMO algorithm is used to optimize the parameters of ISVMD and ELM algorithms simultaneously, and the prediction method performs self-learning and self-training in each iteration. This makes full use of the advantages of the new prediction method and realizes the characteristics of parallel computing.
2. Preliminaries
2.1. Problem Formulation
2.2. Detection Space
2.3. Noise Interference
3. Methods
3.1. ISVMD
3.2. ELM
3.3. The Optimized Algorithm of RBMO
Algorithm 1 ISVMD-ELM-based RBMO optimization | |
1. | Combining RBMO with ISVMD and ELM |
2. | Initialize ISVMD relate parameters |
3. | Initialize ELM network parameters |
4. | for each episode do |
5. | Initialize an observation queue and observation variables : |
6. | obs_a = queue ([0, 0, …, 0, ]) |
7. | for step t = 0, T−1 do |
8. | ; |
9. | ; |
10. | ; |
11. | ; |
12. | ; |
13. | |
14. | Add to the observation queue: |
15. | obs_a = obs_a.append() |
16. | end for |
17. | end for |
3.4. Algorithm Structure
4. Experiments and Results
4.1. Experiment Setting
4.2. Experiment Parameters and Evaluating Indicator
4.3. Performance Evaluation of Algorithms
4.3.1. Performance Comparison of Decomposition Algorithms
4.3.2. Performance Comparison of Prediction Algorithms
5. Conclusions and Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
References
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Experimental Parameters | Value |
---|---|
Initial frequency | 77 GHz |
Frequency modulation slope | 32 MHz/μs |
Chirped signal period | 40 μs |
Number of chirped signals | 64 |
Frame length | 100 ms |
Experimental Parameters | Value | |
---|---|---|
ISVMD | range | [500,3000] |
range | [0.1,1.0] | |
Time-step of the ascent | 0 | |
Tolerance | 1 × 10−6 | |
Condition of convergence | 4 | |
ELM | Initial input layer | 20 |
Initial hidden layer | 20 | |
Initial output layer | 2 | |
Prediction horizon | 5 | |
Activation functions | {sigmoid, tanh, ReLU} | |
RBMO | Upper limit of equilibrium parameters | 1000 |
Lower limit of equilibrium parameters | 5000 | |
Maximum number of cycles | 200 | |
Population size | 30 | |
Exploration rate | 0.7 | |
Cognitive factor | 2.0 | |
Initialized loudness | 1 |
Setting Distance of Target (m) | Distance Calculation Results (m) | Error (m) |
---|---|---|
1 | 1.0067 | 0.0067 |
2 | 2.0033 | 0.0033 |
3 | 3.0067 | 0.0067 |
4 | 4.02 | 0.02 |
5 | 5.0233 | 0.0233 |
6 | 6.03 | 0.03 |
ELM | PSO-ELM | SSA-ELM | RBMO-ELM | |
---|---|---|---|---|
MAE (m) | 3.645 | 0.380712 | 0.512302 | 0.392579 |
MSE (m2) | 28.288 | 1.36262 | 1.43197 | 1.09496 |
RMSE (m) | 5.31865 | 1.16731 | 1.19665 | 1.04641 |
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Yang, Z.; Yu, J.; Liu, M.; Peng, T.; Wang, H. A Method for Predicting Trajectories of Concealed Targets via a Hybrid Decomposition and State Prediction Framework. Sensors 2025, 25, 3639. https://doi.org/10.3390/s25123639
Yang Z, Yu J, Liu M, Peng T, Wang H. A Method for Predicting Trajectories of Concealed Targets via a Hybrid Decomposition and State Prediction Framework. Sensors. 2025; 25(12):3639. https://doi.org/10.3390/s25123639
Chicago/Turabian StyleYang, Zhengpeng, Jiyan Yu, Miao Liu, Tongxing Peng, and Huaiyan Wang. 2025. "A Method for Predicting Trajectories of Concealed Targets via a Hybrid Decomposition and State Prediction Framework" Sensors 25, no. 12: 3639. https://doi.org/10.3390/s25123639
APA StyleYang, Z., Yu, J., Liu, M., Peng, T., & Wang, H. (2025). A Method for Predicting Trajectories of Concealed Targets via a Hybrid Decomposition and State Prediction Framework. Sensors, 25(12), 3639. https://doi.org/10.3390/s25123639