Joint Adaptive Sampling Interval and Power Allocation for Maneuvering Target Tracking in a Multiple Opportunistic Array Radar System
Abstract
:1. Introduction
1.1. Background and Motivation
1.2. Main Contributions and Innovations
- (1)
- The BFG approximation is employed so as to allocate the radar resource conveniently. Due to the diversities of motion states of maneuvering targets, it is difficult to predict the target state, and the radar resource allocation has no referenced criterion at the next sampling instant. Guaranteeing that the state vectors have the same mean and covariance under different models, the BFG approximation is introduced to replace the multimodal prior target PDF at each time step. The target state can be predicted easily by a single motion equation, and then accomplish the resource pre-allocation.
- (2)
- A joint adaptive sampling interval and power allocation scheme is presented. The prior CRLB-like as a measurement criteria is compared with the upper boundary of the given tracking error threshold to determine the next optimal sampling interval. The tracking BCRLB-like is computed for power allocation among the distributed radars. The diagonal elements of BCRLB-like provide a referenced boundary on the variances of the estimation of the target’s hybrid state.
- (3)
- The CCP is brought in to handle the uncertainty of target information in a resource management model. The target RCS is regarded as a random variable. The CCP balances the radar resource and the tracking performance by adjusting the confidence level. If the target environment is simple or the tracking performance requirement is low, the confidence level could be lowered appropriately to save more resources for other tasks.
2. System Model
2.1. Signal Model
2.2. Target Motion Model
2.2.1. Constant Velocity Motion Model
2.2.2. Constant Acceleration Motion Model
2.2.3. Coordinated Turn Motion Model
2.3. Measurement Model
3. Resource Management Model for Maneuvering Target Tracking
3.1. Best-Fitting Gaussian Approximation
3.2. Prior Information JP(ξk)
3.3. Data Information JD(ξk)
3.4. Predictive Bayesian Cramér-Rao lower bound (BCRLB-like)
3.5. Modeling of Chance-Constraint Programming (CCP)
4. Resource Allocation Processing Procedure
4.1. Basic of the Technique
4.2. Stochastic Simulation
4.3. Hybrid Intelligent Optimization Algorithm
4.4. Target State Estimation
4.4.1. Process of BFG-UKF
- 1)
- Let Tk+1 = Tk+1+ΔT, and through the BFG approximation in Section 3.1, determine the mode probability pk+1(i), and then calculate Φk+1 and Qp,k+1 (the detailed calculation process is given in Section 3.1).
- 2)
- Predict the prior CRLB-like FP(Tk+1) according to Equations (40) and (45).
- 3)
- If FP(Tk+1) > η2,k+1 (the upper bound of the error threshold), let Tk+1,opt = Tk+1 and go to Step 9. Otherwise, go to Step 1).
4.4.2. Process of Interacting Multiple Model Unscented Kalman Filter (IMM-UKF)
5. Simulation Results and Analysis
5.1. Adaptive Sampling Interval
5.2. Optimal Allocation of Power
5.3. Chance-Constraint Programming
5.4. Target State Estimation with BFG-UKF and IMM-UKF
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
Appendix A
Appendix B
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Step 1. Set N′=0; |
Step 2. Calculate Φk and Qp,k according to the BFG approximation; |
Step 3. Select a measurement hj,k (j=1, 2, …, NH) from the measurement set and produce F(Tk,Pk,hj,k); |
Step 4. If F(Tk,Pk,hj,k)≤η1,k, N′= N′+1; |
Step 5. Repeat the third and fourth steps NH times; |
Step 6. Pr{F(Tk,Pk,hk)≤η1,k }= N′/NH. |
(1) Initialize pop_size chromosomes, and check the feasibility of the generated chromosomes by the stochastic simulation in Table 1; |
(2) Update the chromosomes by crossover and mutation operations in which the feasibility of offspring can be checked by the stochastic simulation in Table 1, and, if they do not satisfy the constraint, correct the chromosomes; |
(3) Calculate the objective function values of all the chromosomes; |
(4) Compute the fitness of each chromosome according to the objective function values; |
(5) Select the chromosomes by spinning the roulette wheel; |
(6) Repeat the second to fifth steps for a given number of cycles; |
(7) Report the best chromosome as the optimal solution Pk,opt. |
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Han, Q.; Pan, M.; Long, W.; Liang, Z.; Shan, C. Joint Adaptive Sampling Interval and Power Allocation for Maneuvering Target Tracking in a Multiple Opportunistic Array Radar System. Sensors 2020, 20, 981. https://doi.org/10.3390/s20040981
Han Q, Pan M, Long W, Liang Z, Shan C. Joint Adaptive Sampling Interval and Power Allocation for Maneuvering Target Tracking in a Multiple Opportunistic Array Radar System. Sensors. 2020; 20(4):981. https://doi.org/10.3390/s20040981
Chicago/Turabian StyleHan, Qinghua, Minghai Pan, Weijun Long, Zhiheng Liang, and Chenggang Shan. 2020. "Joint Adaptive Sampling Interval and Power Allocation for Maneuvering Target Tracking in a Multiple Opportunistic Array Radar System" Sensors 20, no. 4: 981. https://doi.org/10.3390/s20040981
APA StyleHan, Q., Pan, M., Long, W., Liang, Z., & Shan, C. (2020). Joint Adaptive Sampling Interval and Power Allocation for Maneuvering Target Tracking in a Multiple Opportunistic Array Radar System. Sensors, 20(4), 981. https://doi.org/10.3390/s20040981