An Improved Multi-Sensor Weighted Fusion Algorithm

An Improved Multi-Sensor Weighted Fusion Algorithm

　introduction

　　Multi-sensor data fusion is an information processing technology that has developed rapidly in recent years. It processes information and data from multiple sensors or multiple sources to obtain more accurate and reliable conclusions. The application of this technology can not only improve the accuracy and reliability of the system, but also improve the measurement range of the system, increase the credibility of the system, and shorten the response time of the system. In data fusion, the weighted fusion algorithm is a relatively mature fusion algorithm. The optimality, unbiasedness, and minimum mean square error of the algorithm have been proven in many research results. The core problem of the weighted fusion algorithm is how to determine the weights. The selection of weights directly affects the fusion results.

　　Commonly used methods include weighted average method. Weighted average is the simplest and most intuitive method, which is to take the weighted average of redundant information provided by multiple sensors as the fusion value. This method can process dynamic raw data in real time, but the determination of weights is subjective. In practical applications, the effect is not optimal. This paper adopts the method of quadratic weighting and introduces the concept of optimal proportional weights. First, a single sensor is weighted, then the whole is weighted and the weighted fusion formula based on the improved algorithm is derived. The effectiveness of the algorithm is verified by simulation and comparison with the equal weight fusion algorithm used in the weighted average fusion algorithm.

　　Multi-sensor data weighted fusion

　　Weighted data fusion is the process of multiple sensors measuring the data of the same characteristic parameter in a certain environment, taking into account the local estimation of each sensor, assigning a weight to each sensor according to a certain principle, and finally obtaining a global optimal estimate by weighted integration of all local estimates.

　　Weighted average fusion algorithm

　　Assume that in a fusion system of n sensors, sensors s1, s2, …, sn perform state estimation on the same target, and the local state estimation value of the i-th sensor at the k-th time is (i=1, 2, …, n). It is assumed that it is an unbiased estimation, and the local estimation errors of any two sensors are uncorrelated.

　　Assume that the weights of each sensor are w1, w2, …wn, then the fused state estimate is and the condition that the weights satisfy is:

　　Improved weighted fusion algorithm

　　The improved weighted fusion algorithm proposed adopts the quadratic weighting method and introduces the concept of optimal proportional weight. First, a single sensor is weighted and then the whole is weighted, in order to achieve the optimal algorithm performance.

　　Single sensor once weighted

　　The method of obtaining observation data is generally to use a single sensor. Since the system variance of the sensor is fixed, the only way to reduce the estimated mean square error is to increase the observation data. Increasing the observation data will increase the amount of calculation and reduce the convergence speed. Multi-sensor data fusion can solve this problem. However, among multiple sensors, if one or more sensors have large observation noise or divergent estimated values, data fusion will also make the fusion system performance unstable and cause serious estimation errors. Therefore, before multi-sensor data fusion, the state estimation value of a single sensor should be weighted to make the estimation value converge quickly. The purpose is to input stable fusion data into the fusion system so that the fused estimation value reaches the optimal state.

　　The idea of ​​single sensor weighting is: when the variance is minimum at a certain moment, the ratio of the state estimate at this moment to the sum of the observed value at this moment and the state estimate at this moment is used as the weight, and it is defined as the optimal proportional weight. The purpose of using this weight to weight is to correct those estimates that are divergent or have large estimation deviations, so that they converge and provide a good and stable data source for the multi-sensor data fusion system.

　　Wk is the optimal proportional weight when the variance is minimum at the kth moment; vj is the sum of the observation value and the state estimate at t moments; and is the weighted state estimate at t moments.

4. The fusion weight ai can be calculated from the variance of each sensor according to formula (11), and the weighted state estimation values ​​of each sensor in the previous step are fused, and the fusion value is calculated according to formula (12).

　　From the above operation flow, it can be seen that for each sensor, the optimal proportional weight can be calculated only when its variance is minimized. Then, the fusion weight is calculated based on their fixed variance.

　　Through simulation, by comparing FIG1 and FIG2 , it can be seen that the estimation accuracy of a single sensor weighted by using the optimal proportional weight is higher than that of a single sensor weighted by not using the optimal proportional weight. This method can improve the estimation accuracy.

　Simulation comparison of the two algorithms

　　Consider a 2D tracking system with three sensors:

　　Where T is the sampling period, x(t)=[xl(t), x2(t)]T, xl(t), x2(t) and w(t) are the position, velocity, and acceleration of the moving target at time tT, respectively, and z(t) is the observation signal of x(t), and v(t) is the observation noise.

　　Assume w(t) and vi(t) are independent Gaussian white noises with zero mean and variance matrices respectively.

　　Matlab is used to simulate and generate 200 cycles of state estimation data of the three sensors tracking the target and the fusion data of the two algorithms.

　　Figure 3 is a comparison of the estimated values ​​of the three sensors and the estimated values ​​of the improved fusion algorithm and the average weighted fusion algorithm with the true values, and Figure 4 is a comparison of the state filtering error curves of the improved fusion algorithm and the average weighted fusion algorithm. It can be seen from Figures 3 and 4 that after multi-sensor fusion, no matter which fusion algorithm is used, the target track is greatly improved compared with the original single sensor tracking.

　　The fusion effect of the improved weighted fusion algorithm proposed in this paper is obviously better than that of single sensor tracking. The comparison of the fusion estimation values ​​and variances of the two fusion algorithms in Figures 3 and 4 also shows that the improved fusion algorithm is better than the average weighted fusion algorithm.

　Conclusion

　　In multi-sensor data fusion, the large variance of the sensor system will have an adverse effect on weighted fusion. To address this problem, this paper introduces the concept of optimal proportional weights and proposes an improved weighted fusion algorithm using the quadratic weighting method. On this basis, the calculation formula of the improved weighted fusion algorithm is obtained, and the effectiveness of the improved fusion algorithm is proved by computer simulation experiments and comparison with the average weighted algorithm.