Figures
Abstract
The common track fusion algorithms in multi-sensor systems have some defects, such as serious imbalances between accuracy and computational cost, the same treatment of all the sensor information regardless of their quality, high fusion errors at inflection points. To address these defects, a track fusion algorithm based on the reliability (TFR) is presented in multi-sensor and multi-target environments. To improve the information quality, outliers in the local tracks are eliminated at first. Then the reliability of local tracks is calculated, and the local tracks with high reliability are chosen for the state estimation fusion. In contrast to the existing methods, TFR reduces high fusion errors at the inflection points of system tracks, and obtains a high accuracy with less computational cost. Simulation results verify the effectiveness and the superiority of the algorithm in dense sensor environments.
Citation: Xu L, Pan L, Jin S, Liu H, Yin G (2015) A Reliability-Based Track Fusion Algorithm. PLoS ONE 10(5): e0126227. https://doi.org/10.1371/journal.pone.0126227
Academic Editor: Ian McLoughlin, The University of Science and Technology of China, CHINA
Received: July 3, 2014; Accepted: March 31, 2015; Published: May 7, 2015
Copyright: © 2015 Xu et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited
Data Availability: All relevant data are within the paper.
Funding: The work described in this paper is supported by the National Natural Science Foundation of China under Grant No. 61201084, No. 11301110, and No. 61100030; the China Postdoctoral Science Foundation under Grant No. 2013M541346; Heilongjiang Postdoctoral Special Fund (Postdoctoral Youth Talent Program) under Grant No. LBH-TZ0504; Heilongjiang Postdoctoral Fund under Grant No. LBH-Z13058; the Fundamental Research Funds for the Central Universities under Grant No. HEUCF100604; the Program for Innovation Research of Science in Harbin Institute of Technology under Grant No. A201401; the Natural Scientific Research Innovation Foundation in Harbin Institute of Technology, Postdoctoral Science-research Developmental Foundation of Heilongjiang Province under Grant No. LBH-Q13072; and the Open Project Program of Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University under Grant No. 93K172014K08.
Competing interests: The authors have declared that no competing interests exist.
Introduction
In the field of track fusion, Measurement Fusion (MF) [1], Simple Fusion (SF) [2]and Weighted Covariance Fusion (WCF) [3] are the most representative track fusion algorithms. MF possesses the advantage of simple idea and small computational cost, but lower accuracy. SF was proposed by Siger and has a notable advantage, high efficiency. However, the accuracy of SF is still not high. WCF was proposed by Bar-Shalom, which is also a classical algorithm. It is characterized by high accuracy, but heavy computational cost. Until now, some performances of them are still the objectives pursued. So, many new algorithms were compared with them on performance. In recent years, many new approaches appeared in the field of track fusion. For examples, Yuan, Dong and Wang gave a fusion algorithm based on an adaptive neuro-fuzzy inference system, which combines the merits of fuzzy logic and neural network [4]. Stienne, Reboul, Azmani, Choquel and Benjelloun assumed the error of angular measurements follow a von Mises distribution and proposed a multi-sensor fusion operator [5]. Duan and Li presented two optimal distributed fusion algorithms by taking linear transformation of the raw sensor measurements [6]. Hu, Duan and Zhou proposed a distributed asynchronous fusion algorithm by reconstructing the optimal centralized fusion result [7]. Beugnon, Singh, Llinas and Saha gave an adaptive track fusion algorithm [8], which is based on the requirements of the current system to select adaptively a track fusion algorithm. Li, Cheng, Zhang and Shen added the feedback structure on the basis of the adaptive track fusion algorithm [9]. Hao, Fawzi, Lefaudeux and Pollard proposed a new track fusion architecture using the split covariance intersection filter-information matrix filter [10]. Duraisamy, Schwarz and Wohler presented an overview of the track fusion algorithms to fuse two homogenous sensor systems [11]. Besides, scholars put forward many solutions to the track fusion problems under different environments. Chen and Bar-Shalom modified several track fusion algorithms accounting for the model mismatch among some of the local tracks [12]. Aziz proposed a new multiple decisions fusion rule in the distributed multiple sensor systems. The proposed fusion method derives the overall decision based on the multiple decisions from each individual sensor assuming that the probability distributions are not known [13]. Zhu, Zhai, Yu and Han addressed the estimation fusion when the cross-correlation of local estimation errors is partially known [14].Chen and Li focused on the tradeoff between the bandwidth and the tracking accuracy for the track fusion with communication constraints [15]. Watson, Rice and Alouani developed the solution for fusing multiple tracks from an arbitrary number of asynchronous measurements with a low complexity [16]. Chang, Chong and Mori focused on scalable fusion algorithms and conducted the analytical performance evaluation under different operating conditions [17]. Aeberhard, Schlichtharle, Kaempchen and Bertram presented a novel approach in a high-level sensor data fusion architecture for the automotive surround environment perception [18]. Quaranta and Balzarotti proposed an algorithm for the fusion of data originated by a bidimensional radar and infrared search [19]. Besides, the works in [20–26] contribute to the research of the information fusion problems.
Due to the complexity of targets and environments, track fusion requires multiple aspects of information. However, this does not mean that increasing the amount of information being fused always yields better results. In 1997, Hall and Llinas pointed out that the fusion of some sensor data may actually produce worse results than could be obtained by tasking the most appropriate sensor in sensor suite. This is caused by the attempt to combine the accurate data with inaccurate or biased data [27]. In dense sensor environments, there is a large amount of redundant information and the contribution of each sensor track to the system track is different. In some cases, some sensors at fault may increase the fusion time greatly, even lead to opposite results. However, most of the existing multi-sensor systems fuse all the available sensor tracks and treat all sensor data equally without regard of their different quality and different contribution to the system tracks. Actually, no matter what kinds of fusion technologies we adopt, the use of reliable information is the precondition of a successful fusion. If the quality of the data provided by the local sensors is different, the accuracy of system tracks will be different. In the dense sensor environments, the high-quality data is vital important to the validity of the fusion system. So a track fusion algorithm based on the reliability in dense sensor environments is proposed in this paper.
Track Association
Throughout this paper, assume that M sensors observe T targets in clutter. The observation obtained in the discrete time is made up of several measurements, and some are from targets and the others from the clutter.
In the multi-sensor environments, each sensor detects all the targets in the surveillance region and forms the local tracks of these targets. The central node fuses the local tracks from the same target to acquire system tracks. So the track association should be considered at first to judge whether the local tracks from different sensors derive from the same target.
Assume the state estimation of a sample point from sensor i at time k is:
(1)
where pm(1≤m≤n) is the feature of local tracks, and n is the number of features.
The corresponding distinguishing rate of sensor i is:
(2)
where δm is the corresponding distinguishing rate of each feature.
Define the statistical distance of two sample points:
(3)
Namely,
(4)
If dij≤min(dii,djj), the two sample points are associated, which means they are from the same target and should be fused.
The State Estimation Fusion Based on the Reliability
Outlier elimination
In order to improve the quality of local tracks, outliers are detected at first.
The expectation of the state estimation of target t at time k can be expressed as:
(5)
where
.
The average distance of the state estimation of target t at time k is:
(6)
Compare
with
. If
(7)
then the value is reasonable. Otherwise, the sample point is regarded as an outlier and its value is replaced by
.
Reliability calculation
In the multi-sensor track fusion systems, the trust level of the measurement results from the local sensors is called the reliability of the sensor. TFR constructs multi-sensor reliability judgment matrices for different targets, and acquires reliability of all local sensors for each target. If the interference is different, the reliability of the data provided by local sensors is different, and the accuracy of the system tracks will also be different, even if the local sensors have the same error. Based on this fact, TFR assumes that most of the local sensors are reliable. Then, the closer the measurement results from a local sensor is to the average value, the higher their reliability ratio is, and the larger the corresponding elements in the judgment matrix is. For the target, the sensor is more reliable.
The ratio of the state estimation distance of target t from sensor i and from sensor j at time k is defined as:
(8)
For target t, the reliability judgment matrix of local sensors is:
(9)
Normalize Rt, get
, where
(10)
Add the element of
by row, and get the transition vector
, where
, i,j = 1,2,…,M. And
is the reliability of the state estimation of target t from sensor i.
Repeat this process, establish the reliability vector for each target, and get T reliability vectors, Vt(t = 1,2,…,T).
State estimation fusion
Select [M/2] state estimations with high reliability in Vt(t = 1,2,…,T) for each target. Fuse the selected state estimations to acquire the system tracks, and abandon the rest state estimations with low reliability.
The global state estimation at k is:
(11)
The global error covariance is:
(12)
where
is the local state estimation and
is the local error covariance of target t from sensor i at time k.
Experiments
System description and initial settings
Let x(k) be the state vector at time k. The target model is expressed as:
(13)
where F(k) is a state transition matrix, G(k) is an input control matrix, u(k) is a mobile acceleration input matrix, and v(k) is a discrete-time white noise sequence, which satisfies E(v(k)) = 0.
The measurement equation of sensor i is expressed as:
(14)
where H(k) is an observation matrix, and wi(k) is a Gauss observation noise with zero mean and variance Ri(k). All the targets in the experiments are generated randomly according to the above target model.
In order to facilitate the problem discussion, assume all the state estimations sent into the fusion center are in the same coordinate system, all the sensors sample synchronously, and the delay time of data transmission is 0. The parameters of the sensors adopted in the experiments are exhibited in Table 1.
Experimental results and analysis
The first experiment is designed to model four sensors to observe 5 targets at the same time, in which the first four sensors in Table 1 are adopted. The sampling interval is 1 second, and the target-tracking lasts 100 seconds. The targets run at a variable speed in the three-dimensional space. The target tracks are shown in Fig 1, and the observational data from local sensors are shown in Fig 2.
In order to validate the performance, the algorithm is simulated 100 times by Monte Carlo method. Comparisons of error between the cases with reliability analysis and without reliability analysis in x-axis, y-axis and z-axis of target1 are respectively shown in Fig 3a, 3b and 3c. By the reliability analysis, the error of the system tracks is reduced greatly, which verifies that the reliability analysis can improve the accuracy of system tracks. For the other targets, there are similar conclusions. Namely, the reliability calculation of local tracks is a useful preliminary step to improve the accuracy of the track fusion.
(a) In x-axis, (b) In y-axis, and (c) In z-axis.
Comparisons of error covariance among MF, SF, WCF and TFR at inflection points in x-axis, y-axis and z-axis of target1 are respectively exhibited in Fig 4a, 4b and 4c. We see TFR obtains the highest accuracy at the inflection points in general.
(a) In x-axis, (b) In y-axis, and (c) In z-axis.
The average errors in x-axis, y-axis and z-axis of each target gained by MF, SF, WCF and TFR are exhibited in Table 2 and Fig 5. And Table 3 shows the average time for the fusion of all targets by MF, SF, WCF and TFR. From Table 2, Table 3 and Fig 5, we see that MF and SF have a fast speed, but a low accuracy. WCF possesses the highest accuracy, but with a relatively heavy computational cost. While, TFR balances the conflicts between the fusion accuracy and the computational burden.
(a) In x-axis, (b) In y-axis, and (c) In z-axis.
Another experiment is done on larger datasets, in which 30 targets enter the surveillance space. The sampling interval is 1 second, and the target-tracking lasts 20 seconds. The targets run at a variable speed in the three-dimensional space. The tracks with 30 targets are shown in Fig 6.
Two cases are set in the experiment. Case1 is the dense sensor environment, in which six sensors observe the targets at the same time. The parameters of the six sensors are exhibited in Table 1. And Case2 is the sparse sensor environment, in which two sensors observe the targets at the same time. The first two sensors in Table 1 are adopted.
In order to validate the performance, the algorithm is simulated 100 times by Monte Carlo method. Fig 7a and 7b show the comparisons of average error by 100 times simulation for fusing all targets by MF, SF, WCF and TFR in Case1 and Case2. Table 4 shows the comparisons of the fusion time by 100 times simulation for fusing all targets by MF, SF, WCF and TFR in Case1 and Case2.
(a) Case1, and (b) Case2.
From the simulation results, we find that in the dense sensor environment, MF, SF and WCF all have the serious imbalance between the accuracy and the computational cost. Compared with them, TFR acquires a higher fusion accuracy with an acceptable computational cost. The success of TFR lies in that it excludes some low-reliability local tracks, which both reduces the fusion time and improves the fusion accuracy. In the sparse sensor environment with two sensors, TFR degenerates into MF, and costs more time. Thus, we draw a conclusion that TFR suits for dense sensor environments with a large amount of redundant information, and does not suit for sparse sensor environments with "poor" sensor information.
Conclusion
At present, most track fusion algorithms take into account the adaptation and the completeness of the fusion strategies, with little thinking over the information quality provided by the local sensors. This paper differs from such approaches by introducing a track fusion algorithm based on the reliability from the view of improving the quality of local tracks. By abandoning the tracks with low reliability, the algorithm not only reduces the fusion complexity, but also facilitates the process of the fusion. The simulation results show the reliability analysis plays a significant role in improving the accuracy of system tracks, especially at inflection points, and TFR balances the conflicts between the accuracy and the computational cost in dense sensor environments.
Author Contributions
Conceived and designed the experiments: LX HL. Performed the experiments: LX. Analyzed the data: LX SJ. Contributed reagents/materials/analysis tools: GY. Wrote the paper: LX LP. Designed the algorithm: LX.
References
- 1.
Willner D, Chang CB, Dunn KP (1978) Kalman filter algorithms for a multi-sensor systems. In Proceedings of the IEEE Conference on Decision and Control(ICDC’1978), Clearwater, FL, USA: 570–574.
- 2. Singer RA (l970) Estimating optimal tracking filter performance for manned maneuvering targets. IEEE Transactions on Aerospace and Electronic Systems 6(4): 473–483.
- 3. Bar-Shalom Y, Campo L (1986) The effect of the common process noise on the two-sensor fused-track covariance. IEEE Transactions on Aerospace and Electronic Systems 22(6): 803–805.
- 4. Yuan Q, Dong CY, Wang Q (2009) An adaptive fusion algorithm based on ANFIS for radar/infrared system. Expert Systems with Applications 36(1): 111–120.
- 5. Stienne G, Reboul S, Azmani M, Choquel JB, Benjelloun M. (2014) A multi-temporal multi-sensor circular fusion filter. Information Fusion 18: 86–100.
- 6. Duan ZS, Li XR (2011) Lossless linear transformation of sensor data for distributed estimation fusion. IEEE Transactions on Signal Processing 59(1): 362–372.
- 7. Hu YY, Duan ZS, Zhou DH (2010) Estimation fusion with general asynchronous multi-rate sensors. IEEE Transactions on Aerospace and Electronic Systems 46(4): 2090–2102.
- 8.
Beugnon C, Singh T, Liaas J, Saha RK (2000) Adaptive track fusion in a multisensor environment. In Proceedings of the 3th International Conference on Information Fusion(ISIF’00), Paris, France: 24–3l.
- 9. Li H, Cheng K, Zhang A, Shen Y (2006) Adaptive algorithm for multisensor track fusion with feedback architecture. Chinese Journal of Computers 29(12): 2232–2237.
- 10.
Hao L, Fawzi N, Lefaudeux B, Pollard E (2013) Track-to-track fusion using split covariance intersection filter-information matrix filter(SCIF-IMF) for vehicle surrounding environment perception. In 16th International IEEE Conference on Intelligent Transportation Systems(ICITS’13), La Hague, 6 pages.
- 11.
Duraisamy B, Schwarz T, Wohler C (2013) Track level fusion algorithms for automotive safety applications. In 2013 International Conference on Signal Processing Image Processing & Pattern Recognition (ICSIPR’13), Coimbatore: 179–184.
- 12.
Chen HM, Bar-Shalom Y (2007) Track association and fusion with heterogeneous local trackers. In Proceedings of the 46th IEEE Conference on Decision & Control(ICDC’07), New Orleans, LA: 2675–2680.
- 13. Aziz AM (2014) A new multiple decisions fusion rule for targets detection in multiple sensors distributed detection systems with data fusion. Information Fusion 18: 175–186.
- 14. Zhu HY, Zhai QZ, Yu MW, Han CZ (2014) Estimation fusion algorithms in the presence of partially known cross-correlation of local estimation errors. Information Fusion 18: 187–196.
- 15.
Chen HM, Li XR (2007) On track fusion with communication constraints. The 10th International Conference on Information Fusion(ICIF’07), Quebec, Que:1–7.
- 16.
Watson AG, Rice TR, Alouani AT (2000) An IMM architecture for track fusion. In Proceedings of SPIE on signal Proceeding, Sensor Fusion and Target Recognition, Orlando, FL: 2–13.
- 17. Chang K, Chong CY, Mori S (2010) Analytical and computational evaluation of scalable distributed fusion algorithms. IEEE Transactions on Aerospace and Electronic Systems 46(4): 2022–2034.
- 18. Aeberhard M, Schlichtharle S, Kaempchen N, Bertram T (2012) Track-to-track fusion with asynchronous sensors using information matrix fusion for surround environment perception. IEEE Transactions on Intelligent Transportation Systems 13(4): 1717–1726.
- 19. Quaranta C, Balzarotti G (2013) Technique for radar and infrared search and track data fusion. Optical Engineering 52(4): 04640.
- 20. Zhong BN, Yao HX, Chen S, Ji RR, Chin TJ, Wang HZ (2014) Visual tracking via weakly supervised learning from multiple imperfect oracles. Pattern Recognition 47(3):1395–1410.
- 21.
Zhang JM, Ma SG, Sclaroff S. (2014) MEEM: Robust tracking via multiple experts using entropy minimization. 13th European Conference on Computer Vision(ECCV’2013). LNCS 8694, PART 6, Zurich, Switzerland: 188–203.
- 22.
Yoon JH, Kim DY, Yoon KJ (2012) Visual tracking via adaptive tracker selection with multiple features. 12th European Conference on Computer Vision(ECCV’2012). LNCS7575, PART 4, Florence, Italy: 28–41.
- 23. Sun QC, Hou YQ, Tan QC, Li GN (2014) A flexible calibration method using the planar target with a square pattern for line structured light vision system. PLOS ONE 9(9): e106911. pmid:25203507
- 24. Jin SL, Tan RJ, Jiang QH, Xu L, Ma R, Peng JJ, et al. (2014) A generalized topological entropy for analyzing the complexity of DNA sequences. PLOS ONE 9(2): e88519. pmid:24533097
- 25. Li XT, Yin MH (2012) Application of differential evolution algorithm on self-potential data. PLOS ONE 7(12): e51199. pmid:23240004
- 26. Zhao XW, Zhang WY, Xu X, Ma ZQ, Yin MH (2012) Prediction of protein phosphorylation sites by using the composition of k-spaced amino acid pairs. PLOS ONE 10(7): e46302.
- 27. Hall DL, Llinas J (1997) An introduction to multisensory data fusion. In Proceeding of the IEEE, 85(1): 6–23.