Multi-sensor target allocation model based on NC-PSO

Traditional multi-sensor target allocation often has problems such as slow algorithm iteration and low solution quality. In response to this problem, this paper proposes the NC-PSO algorithm, so that the particles can jump out of the local optimum and increase the convergence speed. At the same time, on the basis of the improved algorithm, the constraint of the target threat degree is added, the interval analytic hierarchy process is used to estimate the target threat, and the allocation principle is optimized, so that the use of sensor resources is better and the allocation is more reasonable. The simulation results prove that NC-PSO can allocate targets to multiple sensors faster and better.


Introduction
In ground air defense operations, various detection sensors are deployed in a distributed manner in accordance with certain principles. They can be space-based satellites, space-based early warning aircraft, ground-based or sea-based radars, and so on. However, with the continuous development of high technology, the target gradually has the characteristics of high speed, stealth, high maneuverability, low altitude and beyond visual range strike. It is difficult for a single sensor to complete the tasks of early warning, detection, and guidance of weapon strikes. This requires the formation of detection alliances by relying on multi-sensors of land-based, sea-based, air-based, and space-based platforms, in order to improve the collaborative detection capabilities and achieve highprecision detection and tracking of targets.
In recent years, the continuous improvement of intelligent algorithms has continuously improved the performance of intelligent algorithms. Intelligent algorithms can better solve the problem of resource allocation. For example, according to the performance of the sensor, the priority of the task, and the distance between the sensor and the task execution location, T Itshak [1] et al. used the improved distributed bee algorithm (MDBA) to assign static heterogeneous sensors to the upcoming unknown task to minimize the task. Successfully minimize the number and time of task inspections. VR Sri [2] et al. used the evolutionary characteristics of genetic algorithms to continuously adjust system parameters, and at the same time introduced adaptive window sizes to limit the time delay time and ensure the latest solutions based on node movement patterns and equipment processing functions. Experiments show that the dynamic task allocation performance of the sensor network is improved. Z Sun [3] et al. used a multi-objective binary particle swarm algorithm to perform sensor-object allocation, and used nonlinear weights and elite, archiving strategies to overcome local optima and improve convergence speed. Experiments show that the algorithm can improve the efficiency of distribution. B Qi [4] et al. used fused ant colony algorithm and particle swarm algorithm to effectively solve the problem of task allocation in sensor networks. LI Tian-Long [5] et al. used the cross-mutation characteristics of genetic algorithm to optimize the update rules of particle swarm algorithm and effectively solved the problem of air-to-ground fire distribution. WZ Guo [6] et al. designed a binary matrix coded discrete particle swarm algorithm, which effectively solved the sensor scheduling problem. X Zhu [7] used the idea of nearest neighbor to initialize the particle task node in the particle swarm algorithm, which greatly reduced the energy consumption in the task distribution of the sensor network.
Although the methods in the literature can find the solution of the problem, the elements of the objective function are somewhat imperfect, which leads to the lack of persuasiveness of the model, and the convergence speed and the quality of the solution in the solution process need to be further improved.
In response to the above problems, this paper adds the link of target threat estimation by studying the modeling principles and conditions in the case of multi-sensor and multi-target, and improves the performance of particle swarm algorithm, and proposes a multi-sensor target allocation model based on NC-PSO. First, this paper builds a multi-sensor alliance detection model, and then introduce negative enhancement factors and collision factors to improve the traditional particle swarm algorithm to increase its optimization speed and the ability to jump out of local optimum, so as to improve the solution speed and accuracy of the multi-sensor detection alliance scheme.

Alliance model establishment
The multi-sensor detection alliance is a joint detection network composed of multiple types and numbers of sensors based on target detection functions, which can improve the utilization efficiency of sensor resources on the premise of ensuring the completion of detection tasks.
Assuming the the number of sensors is m and the number of targets is n , the sensor sequence for target j is  

Alliance accuracy model
The accuracy of the sensor A can be expressed as the ratio of the effective detection time of the sensor i s to the target j and the target movement time, expressed as: In the formula,

Sensor energy consumption model
When the sensor detects the target, it needs to consume energy. The energy consumption of the sensor to detect the target is expressed as: In the formula,   i r s represents the farthest detection distance of the sensor i s , and 1  and 1  are constants, respectively taking 0.01 and 0.1.

Target threat model
Target types are divided into large aircraft (strong area attack capability), small aircraft (strong fixed-point attack capability), and helicopters. The threat index is set at 0.8, 0.5, and 0.3 respectively.
The distance threat index of target j to our defensive area can be expressed as: In the formula, 5 2 4 10 km , j d represents the distance between the target and our defensive area.
(3) Target height threat index( j H ) The height threat index of target j to our defensive area can be expressed as: In the formula, j h is the height of target j , 2 2 10 km The speed threat index of target j can be expressed as: In the formula, 3 5 10 / s m The route shortcut threat index of target j can be expressed as: In the formula, 3 2 5 10 km , j l is the shortcut of the target relative to the defensive route.
Therefore, the comprehensive threat degree of target j can be expressed as: In the formula, 1 w , 2 w , 3 w , 4 w , 5 w are the weight coefficients of each threat element index.
The calculation of the weight is analyzed by the Interval AnalyticHierarchy Process(IAHP). According to the obtained weight W and the threat index of each threat element of the target, the total threat degree of each target can be calculated, and the expression is: In the formula, W is the weight of threat elements calculated according to the IAHP method, and i P is the calculated target threat index matrix.

Fitness function
When faced with targets with different threat levels, the multi-sensor network pays different attention to the target, allocates different sensor resources to form a multi-sensor detection alliance, so that the sensor network resource utilization efficiency is the highest, and the solution is the optimal solution. The expression of fitness value is: In the formula,   N i is the number of targets tracked by sensor i .
The purpose is to maximize   X  , then the objective function is:

Basic particle swarm algorithm
The particle swarm algorithm [8] regards the process of solving the optimal solution or approximate solution of the problem as a process of predation by a flock of birds. Each bird is equivalent to a particle, which is a feasible solution to the problem. Since the particle swarm algorithm requires fewer analysis parameters and variables in the solution process, and has a strong local search ability, this paper uses the particle swarm optimization algorithm to solve the problem of selecting members of the sensor alliance. The particle swarm algorithm sets a population composed of n particles, its position is . In each iteration, the particle adjusts its speed and position according to the positions of i P and g P , so that the particle can approache g P , and finally finds the optimal solution or approximate solution. The update formula for its speed and position is： In the formula, 1 c and 2 c are learning factors, generally random numbers uniformly distributed between   0 2 ， , 1 r and 2 r are random numbers between   0,1 , and w is the inertia weight.

Improved particle swarm algorithm
In the basic particle swarm algorithm, although the algorithm has few parameters and strong local search ability, it has the problem that the particles are easy to fall into the local optimum and the speed of convergence is slow.
In response to this problem, the negative reinforcement factors 1  , 2  are introduced to enable the particles to move away from the current poor solutions of individuals and groups, indirectly narrowing the optimization range and increasing the speed of optimization. At the same time, the collision factors 3 3 c r , 4 4 c r are introduced. When particles fall into the local optimum and lose their vitality, collisions can increase the diversity of the particles so that the particles still have the ability to search while maintaining the current optimum solution, which helps to avoid falling into the local optimum. The particle velocity update formula becomes：  When the deviation is greater than the threshold, the collision factor is assigned to change the current position of the particle, and the fitness value is calculated. If the fitness value of the new position is greater than the historical optimal value, the position is replaced, otherwise. Otherwise, continue to collide, calculate and compare fitness values, until the end of the iteration.

Simulation conditions
Suppose that in an air defense operation, there are 7 targets, and the defender has 10 sensors join the detection mission. The target parameters and parameter indexes are shown in Table 1, and the detection accuracy and energy consumption of the sensor to the target are shown in Table 2.  According to the weight calculation model, the importance of the target parameters is judged, and the target parameter interval threat judgment matrix is constructed, as shown in Table 3. Then the consistency test is carried out, and the random consistency index is found to be 1.12, and then 0.227 CR    and 0.390 CR   are calculated. The mean value is 0.081 0.1 CR   , and the consistency test is passed. According to formulas (10) and (11)

Comparison of results
The basic algorithm and improved algorithm are used to solve the objective function. The simulation parameters are set as follows: the number of populations is set to 60, the inertia weight is set to 0.  Figure 1, and the alliance scheme is shown in Table 4.   Figure 1 that the algorithm can be stabilized before and after the improvement, and the solution of the multi-sensor detection alliance can be obtained. The basic particle swarm algorithm is stable after 25 iterations, with a fitness value of 9.511. The improved particle swarm algorithm reached stability after 13 iterations, with a fitness value of 10.63, which improved the convergence speed and fitness. Table 4. Comparison of alliance allocation plans.

Comparison and analysis of different algorithms for solving alliance schemes
The ant colony algorithm and the improved bee colony algorithm and the improved particle swarm algorithm are used to solve the problem. After 200 iterations, the comparison of the three algorithm results is shown in Figure 2. It can be seen from Figure 2 that the three algorithms finally reached stability, and the ant colony algorithm reached stability after 42 iterations, with a fitness value of 8.634. The improved bee colony algorithm is stable after 31 iterations, with a fitness value of 9.063. The improved particle swarm algorithm reached stability in 17 iterations, with a fitness value of 10.66. It can be seen that the improved particle swarm algorithm has better solution quality and convergence speed than the ant colony algorithm and the improved bee colony algorithm in solving the multi-sensor alliance scheme.

Conclusion
This paper proposes a multi-sensor alliance scheme based on NC-PSO. The simulation analysis shows that in the process of NC-PSO solving the sensor detection alliance, the convergence speed and accuracy of the algorithm are improved compared with the previous improvement and the comparison algorithm, which proves the rapidity and effectiveness of the algorithm, and algorithm can quickly get a better multi-sensor alliance program.