Professor Wang Shaoping’s Team: Active Tensor in Sensor Networks

In recent years, multi-sensor network technology has developed rapidly and is increasingly applied in various fields. Target detection and tracking are one of the important applications of multi-sensor networks. As technology continues to evolve, the movement patterns of incoming targets have become more diverse and complex, leading to uncertainty in the target motion models. This raises higher requirements for the performance of target detection and tracking in multi-sensor networks. In this context, scientifically and accurately assessing the performance of target detection and tracking in sensor networks has become particularly important.

However, research on the performance evaluation of target detection and tracking in sensor networks is still lacking, and the impact of sensor measurements on target detection and tracking performance is not well understood. There is limited research on how to more reasonably optimize sensor scheduling and deployment, and how to more effectively acquire and utilize measurement information, which lacks systematic theoretical guidance. In many application areas, the performance of target detection and tracking in sensor networks is crucial and requires effective evaluation methods for sensor network performance analysis and evaluation, enabling rational assessments of existing networks or optimization of their designs.

Information geometry theory can deeply explore and understand the structure and characteristics of sensor network systems, providing new ideas for analyzing the performance of target detection and tracking in sensor networks. This paper analyzes sensor networks using information space, treating sensor information as geometric objects, extending the theory and applications of information geometry, and proposing information Lagrangian and information active tensors to characterize the dynamic characteristics and manifold structure of sensor network information space. Based on this, performance analysis and target detection and tracking research for sensor networks are conducted.

This paper analyzes information systems using the Lagrangian and active tensors, where the Lagrangian function describes the overall state of the information space, helping researchers gain a deeper understanding of the characteristics and behaviors of the information space, while the active tensor reflects the intrinsic properties of the sensor network information space, which are the properties inherent to the information space itself.

This paper starts from the sensor measurement model and constructs the information space of a certain angle sensor network, conducting in-depth research based on this:

1) Deriving the Lagrangian of the sensor network information space , as shown in Figure 1, the Lagrangian of the angular sensor network changes as shown in Figure 2. It can be seen that the Lagrangian of the angular sensor is symmetric, and it is noteworthy that the position of the sensor is a singular point of the information space.

Figure 1 Spatial Position of Angular Sensor Network and Target

Figure 2 Lagrangian of the Angular Sensor Space

2) Defining and deriving the active tensor of the information space , and analyzing its properties. Figure 3 illustrates the single-step optimization problem for the maneuver of target detection and tracking sensors. The angular sensor located at the origin O observes the target at point P. To maximize the acquisition of measurement information, the sensor needs to maneuver.

Assuming that the single-step maneuvering radius of the sensor is r, it can appear at any point A on a circle with radius r centered at O in the next moment to obtain measurements of the target, thereby using the two observations to estimate the target state. When the maneuvering direction of the sensor is different, the accuracy of the two observations for estimating the target state varies. To obtain the maximum amount of information and achieve the highest estimation accuracy, it is necessary to find the optimal maneuvering direction angle . In this paper, this problem is transformed into fixing one sensor and the target position, while optimizing the position of another sensor, allowing the sensor network to obtain the maximum active tensor at the target point. The variation of the active tensor value with the maneuver distance (radius) – angle is shown in Figure 4.

Reviewed by: Cai Fei, Fan Zhenzhen