Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 854085, 10 pages

http://dx.doi.org/10.1155/2015/854085

## Adaptive Fusion Design Using Multiscale Unscented Kalman Filter Approach for Multisensor Data Fusion

^{1}School of Computer Science and Technology, Zhoukou Normal University, Zhoukou 466001, China^{2}School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, China

Received 28 July 2015; Revised 26 October 2015; Accepted 27 October 2015

Academic Editor: Fernando Torres

Copyright © 2015 Huadong Wang and Shi Dong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In order to improve the reliability of measurement data, the multisensor data fusion technology has progressed greatly in improving the accuracy of measurement data. This paper utilizes the real-time, recursive, and optimal estimation characteristics of unscented Kalman filter (UKF), as well as the unique advantages of multiscale wavelet transform decomposition in data analysis to effectively integrate observational data from multiple sensors. A new multiscale UKF-based multisensor data fusion algorithm is proposed by combining the UKF with multiscale signal analysis. Firstly, model-based UKF is introduced into the multiple sensors, and then the model is decomposed at multiple scales onto the coarse scale with wavelets. Next, signals decomposed from fine to coarse scales are adjusted using the denoised observational data from corresponding sensors and reconstructed with wavelets to obtain the fused signals. Finally, the processed data are fused using adaptive weighted fusion algorithm. Comparison of simulation and experimental results shows that the proposed method can effectively improve the antijamming capability of the measurement system and ensure the reliability and accuracy of sensor measurement system compared to the use of data fusion algorithm alone.

#### 1. Introduction

Multisensor data fusion is one of the key technologies for achieving intelligent measurement. Data measured with a single sensor are often incomplete, have great uncertainty, or even contain abnormal noise point due to the accuracy, resolution, measurement noise, and other factors of single sensor [1]. Meanwhile, susceptible to factors like measurement noise, sensor type, number of nodes, and monitoring location and influenced by formal uncertainties, diversity, quantitative enormousness, relational complexity, and redundancy of information detected, the sensor detection data are prone to be unreliable, incomplete, inaccurate, ambiguous, or even contradictory. Multisensor data fusion is a commonly used method of improving measurement accuracy and reliability. Multisensor data fusion technology has been widely used in military application domains such as automatic target recognition, battlefield surveillance, and traffic control, as well as nonmilitary application areas such as complex machine system monitoring, robotics, and medical diagnostics. Existing data fusion methods are divided into classic fusion methods and modern intelligent fusion algorithms [2, 3]. Weighted average method, least squares method, likelihood estimation, Kalman filtering, group-Bayes estimation, and D-S evidence reasoning are the representatives of classic fusion algorithms, whereas major modern intelligent fusion algorithms include expert system, cluster analysis, production rule, rough set theory, and neural network [4, 5]. The problem of data fusion for multisensor has been addressed by several exiting works in the context of data processing. In traditional simple multisensory data fusion algorithms, measurement accuracy is poor and there is low fusion efficiency, resulting in measurement uncertainty. How to design a high accuracy of the new algorithm has been the integration of multisensor data fusion research priorities. Zhao and Wang [6] proposed extended Kalman filter (EKF) for multisensors data fusion; experimental results show that the accumulated errors of inertial sensors are reduced by ultrasonic sensors and magnetometers, and EKF improves the accuracy of orientation and position measurements. Chiou and Tsai [7] presented a low-complexity and high-accuracy algorithm to reduce the computational load of the traditional data fusion algorithm with heterogeneous observations for location tracking. Not only can the proposed approach achieve an accurate location close to that of the traditional Kalman filtering data fusion algorithm but also it has much lower computational complexity. Ligorio and Sabatini [8] used a linear Kalman filter where the sensor fusion between triaxial gyroscope and triaxial accelerometer data was performed. A significant accuracy improvement was achieved over state-of-the-art approaches, due to a filter design that better matched the basic optimality assumptions of Kalman filtering. Vaccarella et al. [9] proposed a sensor fusion algorithm to compensate for the drawbacks of optical tracking systems (OTS) and electromagnetic tracking systems (EMTS) and achieve robust tracking of surgical instruments. The proposed algorithm increases the accuracy of EMTS in the presence of magnetic field distortion. Zhang et al. [10] takes the upper limb as our research subject and present a novel upper limb movement estimation algorithm to cope with these two challenges by adaptive fusion of sensor data and human skeleton constraint. Zheng et al. [11] proposed a new framework for sequential Bayesian estimation in sensor networks; the proposed scheme outperforms the one that ignores missing data information and the one that selects sensors randomly for information transmission. Mosallaei and Salahshoor investigate the application of centralized multisensor data fusion (CMSDF) technique to enhance the process fault detection. The measurement fusion methods directly fuse observations or sensor measurements to obtain a weighted or combined measurement and then use a single Kalman filter to obtain the final state estimate based upon the fused measurement [12]. These authors presented a Particle Filter (PF) based multisensor data fusion (MSDF) technique in an integrated Navigation and Guidance System (NGS) design based on low-cost avionics sensors [13]. Wang et al. addressed the problem of tracking multiple targets using multisensor bearings-only measurements in the presence of noise and clutter. The Rao-Blackwellized Monte Carlo Data Association (RBMCDA) scheme and the unscented Kalman filter (UKF) were applied to solve the problems of uncertain association and nonlinear filtering [14]. Wang et al. proposed a multisensor data fusion technique for the online volume concentration measurement of coal/biomass pulverized-fuel flow in cofired power plant. The techniques combine electrostatic sensors with capacitance sensors and incorporate a data fusion technique based on an adaptive wavelet neural network (AWNN), and gradient descent learning algorithm and genetic learning algorithm are used for training of the network parameters [15].

At present, the wavelet transformation, combining with Kalman filter, is the most used algorithm in multisensor data fusion technology. However, wavelet transformation and Kalman filter have two aspect problems in algorithm. One aspect of the problem consists in the multiresolution analysis (MRA) method of wavelet transformation. It only subdivides the approximate signal of low-frequency band step by step effectively, which causes the precision in low-frequency band to be more and more high and that the detail signal of the high-frequency band is invariable. Therefore, MRA method has low resolving ability in frequency. The other aspect of the problem is that some system has nonlinear character in practice measuring, which makes Kalman filter precarious and even causes no convergence. So the filter effect is not very good.

In order to overcome the shortcoming described above, a new multiscale UKF-based multisensor data fusion algorithm is proposed by combining the UKF with multiscale signal analysis. The improved data fusion way is used to fuse multiresolution data in the sensor measurement system, which can fuse multisensors data in different resolution.

The main contributions of this paper are summarized as follows:(1)A new multiscale UKF-based multisensor data fusion algorithm is proposed by combining the UKF with multiscale signal analysis.(2)We provide extensive numerical results to demonstrate the usage and efficiency of the proposed multisensor data fusion algorithm.(3)We evaluate the performance of the proposed algorithms by comparing them with the use of data fusion algorithm alone. The proposed method can effectively improve the antijamming capability of the measurement system and ensure the reliability and accuracy of sensor measurement system.

#### 2. System Description

By the dynamic equation and observation equation of the Kalman filtering algorithm, which can get sensor signal at a scale of () system model,wherein, in formula (1), is -dimensional matrix, , is a system matrix, , and is the systematic noise, , and satisfies the following statistical properties:The general observation equation iswhereinwhere, in formula (3), the observed value represents the observed values of the th sensor on the scale (), , the sampling rate of the sample between the two dimensions of the sensor vector is 2 : 1, namely, , is observation matrix, and observation noise is Gauss white noise sequence. At the same time,Here we assumed that , , and are uncorrelated.

#### 3. Unscented Kalman Filter and Wavelet Transform

##### 3.1. Unscented Kalman Filter

Unscented Kalman filter (UKF) is a Gaussian filter which calculates the mean and covariance of nonlinear transformation using unscented transform (UT). Based on the principle that the approximate probability distribution is easier than the approximate arbitrary nonlinear transformation, the UT characterizes certain characteristics, such as mean and covariance, of a probability distribution by deterministically selecting a set of sample points; propagates this set of sample points through the nonlinear transformation; and calculates the mean and covariance of propagated sample points. Estimation accuracy of UKF depends on the accuracy of mean and covariance calculated by UT. Compared to the extended Kalman filter (EKF), UKF offers better performance at the same amount of calculation and does not require the calculation of Jacobian matrix. It can be interpreted as random linear regression, thereby revealing the reason why UKF is superior to EKF. Existing UKF algorithm is essentially a second-order UT-based nonlinear filtering method, which can only match the second-order Taylor expansion terms of nonlinear function, and therefore has a limited accuracy.

Implementation steps of the unscented Kalman filter are as follows:(1)Calculating weights corresponding to sample points using and given previously, , here , is the dispersion degree of sample points, is the weight coefficient of the first-order statistical properties, and is a function of second-order statistical properties of the required weight coefficients.(2)Propagation function of the state evolution equation related to the sample points should be calculated as follows: .(3) The statistical characteristic functions and should be calculated assisted with forecast sampling points and weights ,(4)Calculation of dispersion function derived from measurement equation of sample points that are obtained by utilizing UT transformation, .(5)The predicted value and the measured value of the statistical characteristics should be calculated by , Here is the measurement error covariance matrix, is the covariance matrix of the state vector and the measured values.(6) Amplification of unscented Kalman filter should be calculated; simultaneously, it is required to update system characteristic function ,

It can be seen from the implementation process of UKF that its estimation of mean and variance is actually accurate to the Taylor expanded quadratic polynomial of function , while EKF can only be accurate to linear item generally, and other higher-order nonlinear polynomials are all ignorable. Therefore, UKF is easy to implement, has higher estimation accuracy than EKF, and can be applied to any linear model.

Although UKF has been widely used in the estimation of dynamic systems, it is established based on the dynamic model and observation model of target in the time domain, which does not take into account the multiscale characteristics of target and is unable to conduct multiscale analysis on target data. Wavelet transform, as a powerful multiscale analytical tool, just makes up for the deficiency of UKF in multisensor multiscale analysis.

##### 3.2. Wavelet Transform

In recent years, wavelet analysis has become a rapidly developing emerging discipline. Wavelet transform offers a multiresolution, microscopic way of image representation that is suited to the human vision principle [16]. After many years of development, a series of remarkable theoretical and practical achievements have been made on wavelet transform, which has been widely used in the scientific and technological fields such as signal processing, image processing, speech recognition and synthesis, radar, CT imaging, pattern recognition, machine vision, and machine fault diagnosis [17, 18]. Wavelet transform makes localized temporal (spatial) frequency analysis on signals gradually refine function in a multiscale manner through stretching and translation operations and thereby ultimately achieve temporal subdivision of signals at high frequencies and frequency subdivision of signals at low frequencies, which can automatically adapt to the requirements of time-frequency signal analysis [19, 20]. In this paper, multiscale stochastic dynamic models at different scales are built using combined multiscale signal representation and data fusion technologies based on a dynamic system with different characteristics at different scales where multiple sensors are used to observe the same random phenomenon (target state) to obtain some effective state estimation and reconstruction algorithms.

Define , when it meets the allowable conditions,wherein is Fourier transform; then call based wavelet. The wavelet function generated by can be expressed aswhere is the translation factor and is the scale factor.

Define ; then the based wavelet function continuous wavelet transform is as follows:

After expanding , , frequency spectrum of any time with any precision can be obtained. For actual operation, its data size is too big, so parameters , are discretized to obtain discrete wavelet transform. Its corresponding discrete wavelet function can be expressed asDiscrete wavelet transform coefficients can be expressed asThe reconstruction formula isIf the discrete point is , , which is called the binary wavelet transform.

Considering signal sequence , () with scale , the analysis and integrated form of discrete orthogonal wavelet transform are , , and , where and are, respectively, smooth signal and detail signal of , and , respectively, correspond to the low-pass filter and high-pass filter. In the wavelet transform, the processing procedure is as follows: firstly, original signal is decomposed into the low-frequency approximate section and the high-frequency detail section; what follows are all further decompositions of low-frequency approximate section of signal, while high-frequency detail section is not considered.

#### 4. Multiscale Representation Method of Signal

Assuming that the signal sequence is divided into data blocks with length (),The dynamic relationship between status variable data block and can be described as has statistical properties ,

Meanwhile, with regard to scale value , observation value and error, symbolled as and , respectively, can be written in the form of data blocks as (9) shows; then we have the following equalities is a matrix of dimension, where the ultimate columns compose a single matrix and other elements are zero. has statistical properties ,

#### 5. Multiscale Information Fusion Estimation Algorithm

The initial values of data block are and ; they can be calculated by the following equation:

Assuming that estimation value of the th state vector and estimation covariance error matrix corresponding to have been obtained, both of them are based on global information fusion; therefore, the following equations can be concluded:The following steps are for multiscale multisensor data fusion:(1)A sensor signal with a given length of the time step was defined. Firstly, UKF was applied to it, and filter estimation was made based on the observational data in UKF to obtain the estimation sequence . However, filtering effect was not obvious due to the substantial amount of noise contained in the data acquired from original sensors. The signal sequence obtained from filter estimation was defined as the initial sequence , and further correction and multiscale analysis were made on its estimated value on the scale axis.(2)Multiscale wavelet decomposition was performed on the initial sequence onto the coarsest scale to obtain the low-frequency and high-frequency decomposition sequence . Then, the wavelet decomposed low-frequency signals were further decomposed while ignoring the high-frequency detail section, and after reconstruction and were obtained. Afterwards, the wavelet decomposed low-frequency approximation section was further decomposed. Finally, the low-frequency signals obtained were reconstructed to obtain . Multilevel decomposition and reconstruction procedures of collected sensor signals by UKF and wavelets are shown in Figure 1.(3)Adaptive data fusion was performed on the sensor signals obtained by multiscale analysis using adaptive weighted least squares (WLS) [21], the adaptive weights . . Achievement of weighted adaptive multisensor fusion avoids the unreliability of sensor detection data resulting from the representational uncertainty, diversity, complexity, and redundancy of detection information in the sensor networks. Multiscale multisensor adaptive weighted data fusion technology adopted in this paper avoids the uncertainty of single sensor measurement and improves the measurement accuracy and fusion efficiency. Flowchart of multiscale multisensor adaptive weighted data fusion algorithm is shown in Figure 2.