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In this study, a collaborative radar selection and transmit resource allocation strategy is proposed for multitarget tracking applications in multiple distributed phased array radar networks with imperfect detection performance. The closed-form expression for the Bayesian Cramér-Rao Lower Bound (BCRLB) with imperfect detection performance is obtained and adopted as the criterion function to characterize the precision of target state estimates. The key concept of the developed strategy is to collaboratively adjust the radar node selection, transmitted power, and effective bandwidth allocation of multiple distributed phased array radar networks to minimize the total transmit power consumption in an imperfect detection environment. This will be achieved under the constraints of the predetermined tracking accuracy requirements of multiple targets and several illumination resource budgets to improve its radio frequency stealth performance. The results revealed that the formulated problem is a mixed-integer programming, nonlinear, and nonconvex optimization model. By incorporating the barrier function approach and cyclic minimization technique, an efficient four-step-based solution methodology is proposed to solve the resulting optimization problem. The numerical simulation examples demonstrate that the proposed strategy can effectively reduce the total power consumption of multiple distributed phased array radar networks by at least 32.3% and improve its radio frequency stealth performance while meeting the given multitarget tracking accuracy requirements compared with other existing algorithms.

For the resource allocation problem of multitarget tracking in a spectral coexistence environment, this study proposes a joint transmit power and dwell time allocation algorithm for radar networks. First, the predicted Bayesian Cramér-Rao Lower Bound (BCRLB) with the variables of radar node selection, transmit power and dwell time is derived as the performance metric for multi-target tracking accuracy. On this basis, a joint optimization model of transmit power and dwell time allocation for multitarget tracking in radar networks under spectral coexistence is built to collaboratively optimize the radar node selection, transmit power and dwell time of radar networks, This joint optimization model aims to minimize the multitarget tracking BCRLB while satisfying the given transmit resources of radar networks and the predetermined maximum allowable interference energy threshold of the communication base station. Subsequently, for the aforementioned optimization problem, a two-step decomposition method is used to decompose it into multiple subconvex problems, which are solved by combining the Semi-Definite Programming (SDP) and cyclic minimization algorithms. The simulation results showed that, compared with the existing algorithms, the proposed algorithm can effectively improve the multitarget tracking accuracy of radar networks while ensuring that the communication base station works properly.

The joint optimization problem of transmit power and dwell time of radar for asynchronous multi-target tracking in heterogeneous multiple radar networks with imperfect detection is investigated. Firstly, all the asynchronous measurements from different radar node in each fusion sampling interval are fused into composite measurement, thus the Bayesian Cramér-Rao Lower Bound (BCRLB) analytical expression of the asynchronous target tracking error with parameters such as radar node selection, transmit power and dwell time with imperfect detection is derived and used as the asynchronous target tracking accuracy measure. Based on this, a joint optimization model of transmit power and dwell time for asynchronous multi-target tracking in heterogeneous multiple radar networks with imperfect detection is established, with the optimization objective of minimizing the asynchronous multi-target tracking error and the constraints of given system transmit resource limitations, the parameters such as radar node selection, transmit power and dwell time in different radar networks are designed adaptively and optimally so as to improve the asynchronous multi-target tracking accuracy of the heterogeneous multiple radar networks system. Finally, a four-step decomposition algorithm combined with the Sequential Quadratic Programming (SQP) algorithm and cyclic minimization method is used to solve the optimization problem. Simulation results demonstrate that the asynchronous multi-target tracking accuracy of the heterogeneous multiple radar networks outperforms existing algorithms.

This paper investigates the joint optimization problem of transmit resources and trajectory planning for target tracking in airborne radar networks. First, the analytical expression for the Bayesian Cramér-Rao Lower Bound (BCRLB) with the variables of the radar transmit power, dwell time, transmit signal Gaussian pulse length and signal bandwidth, and speed and heading angle of airborne nodes is derived and adopted as the metric function to evaluate the target tracking accuracy. In addition, the analytical expression of intercept probability with the variables of the radar transmit power, dwell time, and speed and heading angle of airborne nodes is also derived and utilized as the metric function to gauge the radio frequency stealth performance of the overall system. On this basis, a joint optimization model of transmit resources and trajectory planning for target tracking in airborne radar networks is established to jointly optimize the radar transmit power, dwell time, transmit signal Gaussian pulse length and signal bandwidth, and speed and heading angle of airborne nodes. This is done to minimize the target estimation error BCRLB under the constraints of given system resources, aircraft maneuvering and intercept probability threshold, thereby improving the target tracking accuracy of airborne radar network. Subsequently, a five-step decomposition iterative algorithm incorporating the particle swarm algorithm is used to solve the underlying optimization problem. The simulation results demonstrate that the target tracking accuracy of the proposed algorithm outperforms other existing approaches.

Small loop transient electromagnetic method (TEM) is a widely used electromagnetic exploration method in mountainous areas, tunnels, underground coal mines and other areas with difficult construction arrangement. The self-inductance and mutual inductance of the coil are prominent because this method increases the number of turns of the loop and then increases the emitted magnetic dipole moment to increase the detection depth and improve the anti-interference ability. However, the self-inductance and mutual inductance between multi-turn loops often cause severe distortion of early signals measured by TEM, resulting in generally low apparent resistivity. The calculation formulas of self-inductance and mutual inductance for rectangular coils and circular coils are analyzed and summarized, and the corresponding self-inductance and mutual inductance values and their relative errors are calculated respectively when the coil side length or radius is 1 m to 5 m, and the applicability of various calculation formulas is analyzed, and an appropriate calculation formula of inductance for small loop is given.