^{1}

^{2}

^{3}

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Modern information fusion systems essentially associate decision-making processes with multi-sensor systems. Precise decision-making processes depend upon aggregating useful information extracted from large numbers of messages or large datasets; meanwhile, the distributed multi-sensor systems which employ several geographically separated local sensors are required to provide sufficient messages or data with similar and/or dissimilar characteristics. These kinds of information fusion techniques have been widely investigated and used for implementing several information retrieval systems. However, the results obtained from the information fusion systems vary in different situations and performing intelligent aggregation and fusion of information from a distributed multi-source, multi-sensor network is essentially an optimization problem. A flexible and versatile framework which is able to solve complex global optimization problems is a valuable alternative to traditional information fusion. Furthermore, because of the highly dynamic and volatile nature of the information flow, a swift soft computing technique is imperative to satisfy the demands and challenges. In this paper, a nonlinear aggregation based on the Choquet integral (NACI) model is considered for information fusion systems that include outliers under inherent interaction among feature attributes. The estimation of interaction coefficients for the proposed model is also performed via a modified algorithm based on particle swarm optimization with quantum-behavior (QPSO) and the high breakdown value estimator, least trimmed squares (LTS). From simulation results, the proposed MQPSO algorithm with LTS (named LTS-MQPSO) readily corrects the deviations caused by outliers and swiftly achieves convergence in estimating the parameters of the proposed NACI model for the information fusion systems with outliers.

In the modern world, to make optimum decisions in economics, industry, science, aeronautics, manufacturing, traffic control, and many other military and civilian applications we are extremely dependent on useful and crucial information which is drawn from messages or data via transformation, classification and/or some other processing. Therefore, multi-sensor systems providing these messages or data are becoming increasingly important in meeting the goals of optimum decision-making. Besides, a feasible model to elaborate on information fusion and a soft computing technique to perform the heavy computations required are also critical.

Within the consideration of a feasible model, traditionally, the most common forms are the weighted average model and the linear regression model. These models are all linear and assume that there is no interaction among feature attributes (^{n}

Confirming the feasible model and from previous analysis, to efficiently and swiftly estimate the model’s parameters satisfying specific criteria is the next challenge. That is, a timesaving soft computing technique is necessary for the information fusion system with contaminated attributes. In the literature, there are many outstanding soft computing techniques that qualify for this task; they are neural network (NN) [

The rest of paper is organized as follows: in Section 2, we introduce the NACI model and characterize the information fusion system. Section 3, the least trimmed square estimator and the QPSO algorithm are briefly described. Next, we propose the LTS-MQPSO algorithm in detail. Section 5, is shown the results of numerical simulation and then the paper is concluded in Section 6.

In traditional linear aggregations, the most frequent model used to describe the relation between feature attributes _{0} is a constant, _{s}^{2}. This linear model always performs a good approximation based on a fundamental assumption that there is no interaction among feature attributes. However, in many real-world systems, the inherent interaction among feature attributes must be considered circumspectly. To reasonably describe the inherent interaction among feature attributes, Wang and Klir [

Besides, a nonlinear integral is also introduced to aggregate the feature attributes. That is, whenever we deal with information fusion systems where information possesses some inherent interactions, the nonlinear integral with respect to the NGM is the most reasonable tool. In practical applications, there are many kinds of nonlinear integrals such as the Choquet integral [_{1}), _{2}),⋯_{n}_{α}_{1},_{2},⋯,_{n}

Compared to the linear aggregation model shown in _{i}_{i}_{1},_{2},⋯,_{n}_{1},_{2},⋯,_{n}

In the NACI model, constants ^{n}

Because the kernel of the performance index of optimization is the LS estimator, it always suffers from atypical observations which arise from outliers in real world systems. That is, the LS method deviates seriously in estimations of a model’s parameters where outliers are present. Hence, it is also a major objective of this study to propose a feasible method for resolving this issue. The proposed method has to achieve not only precise model’s parameters but also remarkable capability of rejecting outliers. In general, these kinds of problems are also called robust regressions and many high breakdown value regression estimators have been proposed for this [

In

The LTS estimator is formulated as:
_{i}_{th}^{2} (_{i}_{th}_{1},_{2},⋯,_{h}_{ini}_{new}_{ini}

After drawing observations without contaminations, a proper soft computing technique is essential and can help us to efficiently estimate the parameters of the NACI model. In the literature there are many outstanding soft computing techniques that qualify for this work. The QPSO algorithm is one of these soft computing techniques, and possesses significant global and local search abilities. In the QPSO algorithm, particles move in a quantum multi-dimensional space, the state of particles is usually depicted by normalized wave function Ψ(^{2} is then interpreted as the corresponding probability density function which satisfies the follow equation:
^{2} is the Laplacian operator. In an environment with a potential field, the particles are then attracted to the center of field through the optimization process, and this attraction leads to the global optimum. Based on the assumption that the attractive potential field is time-independent (the co-called stationary state), the solution of the time-independent Schrödinger equation has the form [^{cnt}_{1}, _{2} are constriction coefficients and
^{gol}_{th}

Within empirical applications, however, the QPSO algorithm usually represents a stagnating phenomenon for searching the global optimal solution in multi-mode problems and systems. Meanwhile, it is also strongly influenced by the creative coefficient _{ini}

The other improvement of the modified MQPSO algorithm is the mechanism to overcome prematurity. Inspired by the mechanisms of mutation and elite crossover in the GA, an index of conquering stagnation (named ^{gol}^{gol}^{gol}^{gol}

For observations without outliers, the MQPSO algorithm offers superior performance for estimating parameters than the GA [

^{n}

^{gol}

^{cnt}

_{i}_{2}(_{1} − _{2}) denotes the distance between _{1} and _{2}.

^{gol}^{gol}^{gol}

^{gol}

^{gol}

The multi-sensor-based intelligent security robot (ISR) [

In the smoke sensor module, the kernel is a TG135 ionization smoke sensor. When smoke occurs, an ionizing radioactive source is brought close to the plates and the air itself is ionized. In other words, it will generate a tiny current. For the flame sensory module, the R2868 ultraviolet sensor is used for detecting the flame. Its peak wavelength is 200 μm and its sensing wavelength is 185–260 μm. For the temperature sensory module, the AD590 semiconductor sensor is adopted to detect the temperature of fire. This sensor has a positive temperature coefficient of about 0.7, and its linearity is within 0.5% for a temperature range between −65 °C and 150 °C. The standard output of the AD590 is 1 mA/°K. In general, these sensory signals are all tiny values and have to be converted to a standardized voltage output by an amplifier circuit. Besides, the relations of input sensory signals and output voltage signals must be made linear by tuning the calibration circuits. Finally, these sensory signals that are converted to binary digital signals are transmitted to the IPC. In this experiment, these three modules are integrated together and the resulting 3-in-1 fire detection sensor is shown in

_{true}_{cont}

In this example, the termination criteria of the program are that the iterations reach a maximum of 1,500 times or the mean square error is less than 10^{−5}. After performing the proposed LTS-MQPSO algorithm for many times, the average results of estimating the model parameters and comparisons are shown in ^{−4}. Besides, it is intuitive that the LTS-MQPSO algorithm is able to make quite precise estimations of model’s parameters.

In this paper, the NACI model association with the LTS-MQPSO algorithm is considered and developed to deal with a non-additive system with outliers. Whenever atypical observations are present, the parameter estimation method based on the LS estimator is no longer feasible. Therefore, replacement of the LS estimator with the LTS estimator is an excellent alternative. That is, we successfully integrate the mechanisms of the SA, and the GA into the QPSO algorithm to estimate parameters of the NACI model; meanwhile, the LTS estimator is also introduced to filter out outliers before performing the modified MQPSO algorithm. From the simulation results, the proposed LTSMQPSO algorithm can precisely estimate parameters of the NACI model for observations contaminated with outliers; meanwhile, it still maintains high coincidence between the estimated and original objective attributes.

This work was supported by the National Science Council of Taiwan, R. O. C. under Grand NSC99-2221-E-224-060 and NSC96-2221-E-150-070-MY3.

Block diagram of the proposed structure for the parameters estimation of the NACI model via MQPSO and LTS in the training state.

Block diagram of the proposed structure for information fusion systems.

A typical curve of the creative coefficient

The flow chart of the proposed LTS-MQPSO algorithm.

The hierarchy structure of the sensory systems used for the ISR.

The 3-in-1 fire detection sensor used for the fire detection subsystem of the ISR.

Shown the results for the contaminated objective attributes and the estimated objective attributes.

Zoom in the curve marked by a dotted circle in

Shown the results for the original objective attributes and the estimated objective attributes.

Zoom in the curve marked by a dotted circle in

Tanning data with and without contaminations used for verifying the proposed NACI model and LTS-MQPSO algorithm.

_{1} |
_{2} |
_{3} |
_{4} |
_{true} |
_{cont} | |
---|---|---|---|---|---|---|

01 | 0.760 | 0.900 | 0.790 | 0.930 | 5.67253 | 5.67253 |

02 | 0.930 | 0.210 | 0.440 | 0.260 | 5.39280 | 5.39280 |

03 | 0.680 | 0.850 | 0.070 | 0.750 | 5.28559 | 5.28559 |

04 | 0.260 | 0.940 | 0.900 | 0.030 | 5.49294 | 5.49294 |

05 | 0.860 | 0.790 | 0.630 | 0.690 | 5.56252 | 5.56252 |

06 | 0.670 | 0.120 | 0.420 | 0.710 | 5.41806 | 5.41806 |

07 | 0.190 | 0.760 | 0.460 | 0.210 | 5.30678 | 5.30678 |

08 | 0.920 | 0.180 | 0.400 | 0.040 | 5.33158 | 5.33158 |

09 | 0.650 | 0.680 | 0.450 | 0.920 | 5.48550 | |

10 | 0.050 | 0.710 | 0.210 | 0.010 | 5.13252 | 5.13252 |

11 | 0.290 | 0.640 | 0.600 | 0.290 | 5.39438 | 5.39438 |

12 | 0.270 | 0.040 | 0.940 | 0.650 | 5.60023 | 5.60023 |

13 | 0.970 | 0.400 | 0.080 | 0.290 | 5.25339 | 5.25339 |

14 | 0.450 | 0.460 | 0.890 | 0.810 | 5.64319 | 5.64319 |

15 | 0.730 | 0.020 | 0.910 | 0.330 | 5.58932 | 5.58932 |

16 | 0.650 | 0.120 | 0.160 | 0.210 | 5.21480 | 5.21480 |

17 | 0.490 | 0.790 | 0.150 | 0.910 | 5.31462 | 5.31462 |

18 | 0.530 | 0.900 | 0.820 | 0.720 | 5.62050 | 5.62050 |

19 | 0.170 | 0.580 | 0.070 | 0.620 | 5.17635 | |

20 | 0.870 | 0.820 | 0.790 | 0.030 | 5.50912 | 5.50912 |

⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |

385 | 0.820 | 0.120 | 0.250 | 0.680 | 5.35888 | 5.35890 |

386 | 0.480 | 0.240 | 0.160 | 0.200 | 5.19002 | 5.19003 |

387 | 0.960 | 0.110 | 0.830 | 0.140 | 5.55050 | 5.55042 |

388 | 0.880 | 0.370 | 0.210 | 0.660 | 5.35336 | 5.35336 |

389 | 0.710 | 0.650 | 0.350 | 0.330 | 5.34275 | 5.34284 |

390 | 0.420 | 0.840 | 0.130 | 0.430 | 5.23067 | 5.23077 |

391 | 0.680 | 0.650 | 0.390 | 0.400 | 5.36962 | 5.36974 |

392 | 0.330 | 0.320 | 0.810 | 0.640 | 5.55438 | 5.55440 |

393 | 0.650 | 0.790 | 0.340 | 0.710 | 5.40430 | 5.40440 |

394 | 0.840 | 0.030 | 0.250 | 0.580 | 5.34598 | |

395 | 0.300 | 0.940 | 0.480 | 0.520 | 5.39375 | 5.39379 |

396 | 0.770 | 0.770 | 0.200 | 0.810 | 5.36578 | 5.36589 |

397 | 0.520 | 0.980 | 0.760 | 0.010 | 5.44782 | 5.44787 |

398 | 0.580 | 0.920 | 0.870 | 0.900 | 5.68322 | 5.68323 |

399 | 0.790 | 0.910 | 0.720 | 0.370 | 5.53678 | 5.53670 |

400 | 0.370 | 0.560 | 0.890 | 0.210 | 5.52618 | 5.52621 |

The average results of model parameters estimated by the proposed LTS-MQPSO algorithm.

Estimated | Original | Estimated | Contaminated | Original | ||
---|---|---|---|---|---|---|

_{1} |
0.202630 | 0.20 | d(1) | 5.67262 | 5.67253 | 5.67253 |

_{2} |
0.119595 | 0.12 | d(2) | 5.39267 | 5.39280 | 5.39280 |

_{1,2} |
0.352183 | 0.35 | d(3) | 5.28556 | 5.28559 | 5.28559 |

_{3} |
0.399180 | 0.40 | d(4) | 5.49297 | 5.49294 | 5.49294 |

_{1,3} |
0.561244 | 0.56 | d(2) | 5.56263 | 5.56252 | 5.56252 |

_{2,3} |
0.498894 | 0.50 | d(6) | 5.41794 | 5.41806 | 5.41806 |

_{1,2,3} |
0.601077 | 0.60 | d(7) | 5.30686 | 5.30678 | 5.30678 |

_{4} |
0.298500 | 0.30 | d(8) | 5.33147 | 5.33158 | 5.33158 |

_{1,4} |
0.451280 | 0.45 | d(9) | 5.48563 | 5.48550 | |

_{2,4} |
0.379223 | 0.38 | d(10) | 5.13246 | 5.13252 | 5.13252 |

_{3,4} |
0.601223 | 0.60 | ⋮ | ⋮ | ⋮ | ⋮ |

_{1,2,4} |
0.728169 | 0.73 | d(391) | 5.36962 | 5.36974 | 5.36974 |

_{1,3,4} |
0.900233 | 0.90 | d(392) | 5.55438 | 5.55440 | 5.55440 |

_{2,3,4} |
0.828266 | 0.83 | d(393) | 5.40430 | 5.40440 | 5.40440 |

_{1,2,3,4} |
1.000000 | 1.00 | d(394) | 5.34598 | 5.34591 | |

_{1} |
0.661194 | 0.67 | d(395) | 5.39375 | 5.39379 | 5.39379 |

_{2} |
0.299558 | 0.30 | d(396) | 5.36578 | 5.36589 | 5.36589 |

_{3} |
1.000000 | 1.00 | d(397) | 5.44782 | 5.44787 | 5.44787 |

_{4} |
0.430799 | 0.43 | d(398) | 5.68322 | 5.68323 | 5.68323 |

4.999999 | 5.00 | d(399) | 5.53678 | 5.53670 | 5.53670 | |

1.202177 | 1.20 | d(400) | 5.52618 | 5.52621 | 5.52621 |

The average results of objective attributes estimated by the LTS-MQPSO, the LTS-MQPSO-LB and the MQPSO algorithm.

Original | Contaminated | Estimated by LTS-MQPSO | Estimated by LTS-MQPSO-LB | Estimated by MQPSO | |
---|---|---|---|---|---|

d(1) | 5.67253 | 5.67250 | 5.67253 | 5.67356 | 5.68501 |

d(2) | 5.39280 | 5.39280 | 5.39280 | 5.39319 | 5.33520 |

d(3) | 5.28559 | 5.28560 | 5.28559 | 5.28591 | 5.31600 |

d(4) | 5.49294 | 5.49290 | 5.49294 | 5.49304 | 5.46360 |

d(2) | 5.56252 | 5.56250 | 5.56252 | 5.56237 | 5.61565 |

d(6) | 5.41806 | 5.41810 | 5.41806 | 5.42090 | 5.38345 |

d(7) | 5.30678 | 5.30680 | 5.30678 | 5.30770 | 5.32974 |

d(8) | 5.33158 | 5.33158 | 5.33157 | 5.24508 | |

d(9) | 5.48550 | 5.48550 | 5.48550 | 5.48373 | 5.52952 |

d(10) | 5.13252 | 5.13250 | 5.13252 | 5.13101 | 5.17121 |

d(11) | 5.39440 | 5.39440 | 5.39438 | 5.39677 | 5.42818 |

d(12) | 5.60020 | 5.60020 | 5.60020 | 5.60104 | 5.58952 |

d(13) | 5.25340 | 5.25340 | 5.25353 | 5.25332 | 5.41922 |

d(14) | 5.64320 | 5.64320 | 5.64318 | 5.64338 | 5.66970 |

d(15) | 5.58930 | 5.58930 | 5.58939 | 5.58941 | 5.52346 |

⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |

d(386) | 5.30790 | 5.30790 | 5.30781 | 5.309731 | 5.31757 |

d(387) | 5.47460 | 5.47460 | 5.47471 | 5.476158 | 5.47223 |

d(388) | 5.30380 | 5.30380 | 5.30377 | 5.303276 | 5.25468 |

d(389) | 5.59290 | 5.59290 | 5.59300 | 5.594471 | 5.61154 |

d(390) | 5.57300 | 5.57300 | 5.57296 | 5.573292 | 5.55016 |

d(391) | 5.36974 | 5.46760 | 5.36974 | 5.464645 | 5.37275 |

d(392) | 5.55440 | 5.52800 | 5.55440 | 5.529859 | 5.52020 |

d(393) | 5.40440 | 5.38750 | 5.40440 | 5.387559 | 5.44484 |

d(394) | 5.34591 | 5.29230 | 5.34591 | 5.29274 | 5.33559 |

d(395) | 5.39379 | 5.39379 | 5.337529 | 5.30333 | |

d(396) | 5.36589 | 5.19230 | 5.36589 | 5.192462 | 5.20087 |

d(397) | 5.44787 | 5.30860 | 5.44787 | 5.307585 | 5.28206 |

d(398) | 5.68323 | 5.61440 | 5.68323 | 5.614041 | 5.61254 |

d(399) | 5.53670 | 5.65030 | 5.53670 | 5.651546 | 5.65586 |

d(400) | 5.52621 | 5.53400 | 5.52621 | 5.533216 | 5.44066 |

The average results of model parameters estimated by the LTS-MQPSO, the LTS-MQPSO-LB and the MQPSO algorithm.

Original | Estimated by LTS-MQPSO | Estimated by LTS-MQPSO-LB | Estimated by MQPSO | |
---|---|---|---|---|

_{1} |
0.20 | 0.202630 | 0.220264 | 0.999814 |

_{2} |
0.12 | 0.119595 | 0.101039 | 0.205399 |

_{1,2} |
0.35 | 0.352183 | 0.355931 | 0.000001 |

_{3} |
0.40 | 0.399180 | 0.446918 | 0.209780 |

_{1,3} |
0.56 | 0.561244 | 0.617110 | 0.000134 |

_{2,3} |
0.50 | 0.498894 | 0.542382 | 0.044604 |

_{1,2,3} |
0.60 | 0.601077 | 0.660831 | 0.002942 |

_{4} |
0.30 | 0.298500 | 0.249854 | 0.251532 |

_{1,4} |
0.45 | 0.451280 | 0.430170 | 0.000009 |

_{2,4} |
0.38 | 0.379223 | 0.337117 | 0.000087 |

_{3,4} |
0.60 | 0.601223 | 0.578540 | 0.289889 |

_{1,2,4} |
0.73 | 0.728169 | 0.718593 | 0.389799 |

_{1,3,4} |
0.90 | 0.900233 | 0.905735 | 0.347362 |

_{2,3,4} |
0.83 | 0.828266 | 0.827270 | 0.000376 |

_{1,2,3,4} |
1.00 | 1.000000 | 1.000000 | 1.000000 |

_{1} |
0.67 | 0.661194 | 0.689136 | 0.163266 |

_{2} |
0.30 | 0.299558 | 0.330364 | 0.163267 |

_{3} |
1.00 | 1.000000 | 1.000000 | 1.000000 |

_{4} |
0.43 | 0.430799 | 0.584927 | 0.269410 |

5.00 | 4.999999 | 4.999316 | 5.1152898 | |

1.20 | 1.202177 | 1.075533 | 2.0519762 | |

MSE | 8.0154e-005 | 0.0018 | 0.455776 | |

Elapse | 1059 seconds | 1496 seconds | 1580 seconds |