Application of multi-sensor state fusion estimation in radar tracking

Abstract: Carlson optimal data fusion criterion is adopted to apply the multi-sensor state fusion estimation method based on Kalman filtering to the radar tracking system. Simulation experiments show that the state fusion estimation error of multi-sensor Kalman filtering is smaller than the state estimation error obtained by single sensor Kalman filtering, which verifies the effectiveness of the method for radar tracking.

With the development of science and technology, especially the development of microelectronics technology, integrated circuit technology, computer technology, signal processing technology and sensor technology, multi-sensor information fusion has developed into a new research field and has been widely used in both military and civilian fields.

The basic principle of multi-sensor information fusion is like the process of comprehensive information processing by the human brain, that is, making full use of multiple sensor resources, through the rational control and use of various sensors and their observation information, combining the complementary and redundant information of various sensors in space and time according to a certain optimization criterion, so as to draw more accurate and reliable conclusions.

The diversity and complexity of modern warfare have put forward higher requirements for information processing. Information fusion can optimize and comprehensively process the various observation information provided by multiple sensors, so as to obtain the target state, identify the target attributes, analyze the target intention and behavior, and provide combat information for electronic countermeasures and precision guidance. This paper applies the multi-sensor state fusion estimation method based on Kalman filtering to the radar tracking system. The simulation experiment shows that the estimated values ​​obtained by the fusion of the three sensors are closer to the target signal, thus improving the tracking accuracy of the radar system.

1 Kalman filter

One of the main tasks of multi-sensor information fusion is to use multi-sensor information to estimate the state of the target. At present, there are many methods for state estimation, and Kalman filter is a commonly used method. Kalman filter has good performance in maneuvering target tracking. It is the best estimate and can perform recursive calculation, that is, it only needs a current measurement value and the predicted value of the previous sampling period to perform state estimation.

Consider a discrete-time dynamic system of the following form:

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2 Multi-sensor state fusion estimation algorithm

The research methods of single sampling rate multi-sensor state fusion estimation mainly include methods based on probability theory, methods based on Kalman filtering, methods based on inference networks, methods based on fuzzy theory, methods based on neural networks, and methods based on wavelets, entropy, class theory, random sets, biological inspiration, Choquet integral, etc. [2]. The method based on Kalman filtering has been the most widely studied due to its advantages such as simple operation, small amount of calculation, and strong real-time performance.

The following focuses on the distributed data fusion state estimation algorithm based on Kalman filtering. Assume that the multi-sensor system has the following form [3]:

The Kalman filter estimator based on the i-th sensor information is shown in Figure 1. The flow chart of the Carlson federated fusion estimation algorithm is shown in Figure 2.

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3 Radar Tracking System Simulation

Consider a radar tracking constant acceleration model with three sensors [5], whose discrete state equation is:

Assuming the number of sensor sampling points is 600, the statistical results of 10 Monte Carlo simulations are shown in Table 1. Table 1 gives the comparison of the absolute mean of the estimation error. The comprehensive estimation error of the fusion of three sensors is the smallest.

The state estimation curves of the first sensor, the second sensor, the third sensor and the fusion of the three sensors are shown in Figure 3, Figure 4, Figure 5 and Figure 6 respectively. The horizontal axis in the figure is the number of simulation steps, and the time for each step is 0.01 s. If you look closely at these state estimation curves, the state estimation curves of the single sensor are all insufficient. For example, Figure 3 is not very good for velocity tracking, Figure 4 is not very good for acceleration tracking, and Figure 5 is not very good for velocity tracking. Only Figure 6 has good tracking of displacement, velocity and acceleration. It can be seen that compared with the results of the single sensor Kalman filter, the estimated values ​​obtained by the fusion of the three sensors are closer to the target signal, which proves the effectiveness of the algorithm in this paper.

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Information fusion technology has the advantages of improving the reliability and stability of the system, and state fusion estimation is one of the research hotspots. In this paper, the multi-sensor state fusion estimation method based on Kalman filtering is applied to the radar tracking system. The simulation experiment shows that the state estimation error obtained by fusing the information of three sensors is smaller than the state estimation error obtained by Kalman filtering using any single sensor. Therefore, this method is very effective for tracking the radar system. This method can be extended to application fields such as integrated navigation, signal processing, image processing, fault detection and fault tolerance.

References

[1] Chen Xinhai. Best Estimation Theory[M]. Beijing: Beijing University of Aeronautics and Astronautics Press, 1987.

[2] Pan Quan, Yu Xin, Cheng Yongmei, et al. Basic methods and progress of information fusion theory [J]. Acta Automatica Sinica, 2003, 29(4): 599-615.

[3] YAN LP, LIU BS, ZHOU D H. The modeling and estimation of asynchronous multirate multisensor dynamic systems, Aerospace Science and Technology, 2006, 10(1):63-71.

[4] CARLSON N A. Federated square root filter for decentralized parallel processors[J]. IEEE Transactions on Aerospace and Electronic Systems, 1990, 26(3):517-525.

[5] SUN S L. Multi-sensor optimal information fusion Kalman filters with applications[J]. Aerospace Science and Technology, 2004, 8(1):57-62.