Mathematical Problems in Engineering

Volume 2019, Article ID 9653237, 12 pages

https://doi.org/10.1155/2019/9653237

## A Robust EMD-Based RVFL Network Fusion Algorithm for Low-Cost GPS/INS Integrated System

Information Science and Technology College, Dalian Maritime University, Dalian 116026, China

Correspondence should be addressed to Jingbo Zhang; nc.ude.umld@obgnij_gnahz

Received 28 May 2019; Accepted 1 August 2019; Published 13 October 2019

Academic Editor: Luis Rodolfo Garcia Carrillo

Copyright © 2019 Da Liu et al. 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

Global positioning system (GPS) and inertial navigation system (INS) are commonly combined to overcome disadvantages of each and constitute an integrated system that realizes long-term precision. However, the performance of the integrated system deteriorates on which GPS is unavailable. Especially when low-cost inertial sensors based on the microelectromechanical system (MEMS) are used, performance of the integrated system degrades severely over time. In this study, in order to minimize the adverse impact of high-level stochastic noise from low-cost MEMS sensors, denoising technology based on empirical mode decomposition (EMD) is employed to improve signal quality before navigation solution by which significant improvement of removing noise is achieved. Moreover, a random vector functional link (RVFL) network-based fusion algorithm is presented to estimate and compensate position error during GPS outage such that error accumulation is suppressed quickly when INS is working standalone. Performance of the proposed approach is evaluated by experimental results. It is indicated from comparison that the proposed algorithm takes advantages such as better accuracy and lower complexity and is more robust than the commonly reported methods and is more appropriate for real-time and low-cost application.

#### 1. Introduction

Nowadays, navigation technology has attracted more attention than ever before on account of the increasing demand for positioning or location in various fields such as consumer electronics, displacement monitoring, and intelligent transportation. Global navigation satellite system (GNSS) and INS are two main positioning systems with high precision, high performance, and high reliability. GPS as a representative of GNSS has advantages of providing high long-term position accuracy and low cost. However, it suffers from obstruction and interference, leading to giving a continuous navigation solution in an urban canyon. On the contrary, INS could operate continuously with high bandwidth and presents low short-term noise, but its accuracy degrades with time elapse as the inertial instrument errors are accumulated fast. The complementary characteristics of INS and GNSS promote the integration of the two positioning systems, generating a new system possessing a continuous, complete navigation solution with high long- and short-term accuracy.

In the GPS/INS integrated system, Kalman filtering (KF) methods are commonly used for information fusion under assumption that the dynamic statistical model of the system and prior knowledge of the sensors in the system are known which limit the application area and degrade the performance of the system when low-cost sensors are used. Moreover, the accuracy of the integrated system deteriorates significantly on occasion of GPS outage because only the standalone INS system is working which makes the integrated system performance depend on poor long-term accuracy of INS.

To overcome the disadvantages of KF, a kind of effective solution based on an artificial neural network (ANN) is proposed to compensate integrated system deviation caused by GPS blockage, which utilizes the research results of the current popular artificial intelligence (AI). The purpose of applying AI is to bridge the relationship between vehicle motion dynamics and specific information of integrated system by making use of universal approximation capability of the neural networks or other similar models, which is an intrinsic regression method for fitting a nonlinear function with some signals of the system. Specifically, output data of sensors of the integrated system are employed for training an AI model when GPS is available so that extra information is predicted by a well-trained model to correct the accumulating errors produced by a standalone INS once GPS is blocked. Some scholars have investigated this field and their studies are reported. The radial basis function (RBF) is first introduced to predict position errors between GPS and INS by Sharafʼs team [1]. In their work, INS position and time were chosen as network inputs and output was INS error, and wavelet analysis was used to denoise the GPS and INS position signals for network training. In their later work, past samples of INS position and velocity were also utilized as network input to obtain better dynamics performance [2]. On this basis, Chen et al. used dynamical neural network to construct relation between multistep past INS errors and current INS error [3]. Then, Tan et al. developed a new model which combined increments of force and angular velocity rate as model inputs and chose the GPS position increments as model outputs, offering better performance than the traditional INS error output model [4]. Furthermore, Yao et al. selected current speed, specific force, angular velocity, and their past one-step delay as inputs of the multilayer perceptron network to predict GPS incremental output which was the measurement reference for correcting the estimated outputs of KF [5]. All these AI-based methods improved the accuracy of the GPS/INS integrating system in the case of GPS outage.

Various AI algorithms have been applied in compensating the precision loss due to GPS loss for the GPS/INS integrating system, such as the adaptive neuro-fuzzy inference system (ANFIS) [6], support vector machine (SVM) [7–9], feedforward network (FNN) [5], wavelet neural network (WNN) [3], and ensemble learning algorithm [10, 11]. AI-based methods proceeded remarkable prediction improvement in this field. However, they also have disadvantages that cannot be ignored. The parameter optimization process of ANFIS is a time-consuming work so that real-time implementation becomes a difficult task; for SVM, there is no uniform kernel function selection method, training for large samples is slow, and it is sensitive to data loss; the ANN methods including FNN and WNN have drawbacks on the local minimum and overfitting problems, while ensemble learning algorithm like LSBoost or Bagging suffer from disadvantages such as slow convergence and heavy and time-consuming computation. Kinds of new algorithms are proposed to solve these problems, including extreme learning machine (ELM), which is a relatively new method with fast convergence and good generalization ability to train a single-hidden layer feedforward neural network [12]. ELM is a feedforward neural network with single-hidden layer and random weight of hidden nodes, and output weights of ELM are analytically determined instead of being computed by gradient-based learning algorithms. The fast learning speed of ELM makes it suitable for real-time applications. For inertial sensors, especially that are comparatively low cost, preprocessing of the sensor measurements is comparative indispensable. The reason is that reliable data can be extracted from inertial sensor measurements mixed with a high level of stochastic noise and employed for training of a prediction model so that the model in the prediction mode will offer more actual and accurate output with a lower noise level of the INS data [13]. Wavelet analysis is a commonly efficient tool for signal denoising, which can be facilely and effectively implemented in the integrated navigation system to eliminate high-frequency noise via multiresolution features and improve system accuracy [14]. In this background, Abdolkarimi et al. proposed a wavelet-based ELM model to predict INS errors during GPS outage [15]. In their work, the wavelet denoising technique was adopted for improving signal-to-noise power ratio (SNR) of inertial sensor measurements and removing disturbance of high-frequency noise, ELM was used for quick learning and supply faster prediction update, and performance of the proposed model was evaluated in a real-time environment.

In recently reported investigation in the literatures, another feedforward network similar to ELM, termed as RVFL, has been proved possessing better performance in classification and regression issues [16, 17]. RVFL was first proposed to solve systems identification problem [18]. It is a single-hidden layer neural network with random weights and direct input-output connections between input and output neurons. The feature of direct links is the main difference between RVFL and ELM, without which the network may be unstable due to the randomly generated weights between the input and the hidden layer. To acquire superior performance of the GPS/INS integrating system with low-cost inertial sensors in the absence of GPS signal, we focus on the advantages of RVFL and investigate this promising network and evaluate its effectiveness in integrated navigation field. Moreover, a novel denoising method based on EMD was recently proposed to exceed the performance achieved by wavelet analysis [19, 20]. The new method is also complied with thresholding principle, whereas it exhibits better performance in the cases where the signal has a high noise level or high sampling frequency. Motivated by achieving and enhancing continuous high-precision operation performance even during the GPS outages, a novel AI-based methodology for the low-cost INS/GPS navigation system is proposed in this paper to solve the problems existing in the methods mentioned above, in which the high-frequency noise from low-cost sensors are suppressed by EMD denoising technology and high positioning accuracy, and real-time learning capability are obtained by taking advantage of the fast learning of RVFL. In this study, the superior performance of EMD denoising for low-cost inertial sensors is investigated compared to wavelet analysis denoising, and the integrated navigation model and algorithm utilizing RVFL is experimentally evaluated with some existing methods to demonstrate effectiveness and excellent performance of the proposed method.

The rest of this paper is organized as follows: Section 2 concisely describes the INS/GPS integrated navigation system with extended Kalman filter (EKF). Section 3 introduces theoretical details of EMD denoising technology. Section 4 presents an RVFL-based fusion algorithm and overall integration model. Experimental results on field test that verify the proposed methodology are illustrated and discussed in Section 5. Section 6 concludes this work in the end.

#### 2. INS/GPS Integrated Navigation System

In order to take advantage of the complementary characteristics of INS and GNSS, systems combining both technologies are established for a variety of applications. Integrated with GNSS, even low cost INS can be suitable for practical navigation solution. Integration is usually based on a Kalman filter, and INS solution is corrected by GNSS solution to form integration solution.

To describe the vehicle motion dynamics, continuous time state-space equations are constructed aswhere denotes the state transition process of the dynamic model which is formulized as nonlinear vehicle motion equations, is the state vector whose elements are variable of , is the system noise matrix, and are the process and observation noise vector, both of which are supposed to be zero mean white noise. represents the observation vector. is selected as follows:where , , , and are roll, pitch, and yaw errors in the navigation frame (*n*-frame) in which the *x*-*y*-*z* axes are set as East, North, and Up, respectively. , , and denote vehicle speed errors relative to referential orientation. , , and are position errors of vehicle resolved as longitude, latitude, and altitude. The subscripts *x*, *y*, and *z* represent the *x*, *y*, and *z* axis of the body frame (*b*-frame); thus, , , , , , and are expressed as accelerometer and gyros biases along the body-axis.

is the measurement model matrix that can be modeled aswhere the subscripts represent the matrix dimension. It is indicated that position variables are chosen as measurements which can be updated by sensors’ position information supply.

Matrix can be derived from INS navigation error propagation equations, which are formulated as follows [21]:where denotes the angular velocity of the *a*-frame with respect to the *b*-frame resolved in *c*-frame. The inertial frame is symbolized with subscript as . Likewise, represents the earth-centered earth-fixed frame. is a transformation matrix from *b*-frame to actual navigation frame (). and are referred as the meridian radius of curvature and the transverse radius of curvature; is a transformation matrix from *n*-frame to which is expressed aswhere represents the cosine operation and represents the sine operation. It is obvious that state variables are multiplied so that nonlinear couples exist in the state equations. When attitude angles are small quantities, it is commonly true to consider the system dynamic model is linear. However, if large system uncertainty exists, especially for yaw error, linear assumptions are not valid as a result of the elements coupled in [22]. In this case, KF, which is limited to be only suitable for linear system optimal estimation, is no more an effective fusion algorithm for the integrated navigation system. Therefore, EKF is chosen as the fusion algorithm when GPS is normally working. EKF essentially transforms the nonlinear model to a linear model by Taylor series approximation before applying the KF paradigm. After discretizing the state-space equation (1), first-order EKF is involved in the following two steps. Prediction: Update:where is the discretized nonlinear functions from continuous INS navigation error propagation equations. Subscript denotes the *k*th epoch in the iteration. is the predicted state covariance matrix, and are the process and measurement noise covariance matrix, is the filter gain matrix, and is the identity matrix. The Jacobian matrix is determined as

#### 3. EMD-Based Denoising

It is necessary to refine raw sensor measurements before applying to the integrated navigation system on account of the reasons that low-cost inertial sensors have high stochastic noise and highly complex nonlinearity which deteriorate the signal quality and decline the system performance.

As the development of signal-processing technology, a variety of denoising methods are developed such as basing on Fourier transform, short-time Fourier transform, and wavelet transform [15]. A new signal-processing technology termed EMD was developed and researched recently [23]. Signal can be decomposed to a few basic components as intrinsic mode functions (IMFs) via an iterative sifting procedure, the advantages of which are multiresolution analysis ability and free of difficulty in selecting basis. In this background, the signal denoising method based on EMD was proposed to enhance SNR performance, compared to wavelet denoising in a worsened noisy environment [19]. The same principle with thresholding according to wavelet denoising was used in this method, whereas special natures of decomposed signals resulting from EMD were considered to properly choose adaptive thresholding operation to obtain better signal noise reduction. Several denoising procedures were alternative, among which the clear iterative EMD interval-thresholding (EMD-CIIT) was proved to have better performance.

To avoid contaminated signal with the noise integrated navigation system from degrading performance of the integrated navigation system, the EMD-CIIT denoising method is adopted to remove harmful noisy signals for enhancing SNR of the raw measures of inertial sensors which are employed for dead reckoning of INS and training of the neural network, so that the precision of the system is improved. The fundamental procedure of EMD-CIIT is summarized in the following 3 phases.

##### 3.1. Redistributing Noise Signal

This phase is key operation of EMD-CIIT, which has the main difference compared to other EMD-based denoising algorithms such as EMD-IT and EMD-IIT.(1)The original noisy signal is decomposed by EMD to IMFs: , , , and .(2)Extract denoised signal from the first IMF via the thresholding method such as Bayesian wavelet denoising. The purpose of this operation is to avoid contamination results from altering the mixture of the noise signal and useful signal.(3)Separating actual noise signal from ,(4)Thus, a partial reconstruction signal excluding noise signal in first IMF is obtained:(5)Generate new noisy versions of the origin noisy signal by adding modified versions of whose sample positions are randomly altered. where is the altered version of and the relationship is expressed as in which the function often deals with the samples of in two forms: random circulation or random permutation.

##### 3.2. Thresholding Denoising

(6)Apply EMD expansion on to generate IMFs.(7)Employ EMD soft thresholding to process each IMF of and get a denoised version of , which is formulized as where is referred as the interval of the IMF component which is divided by zero crossings, and denotes the single extrema correspond to this interval. is an adaptive threshold depended on the noise level and is commonly determined as , where is the sample length and is the standard deviation of the noise and can be empirically estimated. In actual application, some low-order IMFs are excluded of reconstruction for flexibility and rationality which are handled empirically, and for more details, refer to [19].(8)Iterate times from Steps (5) to (7) and obtain different denoised versions of , i.e., , , , .

##### 3.3. Obtaining Denoised Signal

(9)Calculate the average of each denoised version of to get final denoised results of the origin signal.

After completing the denoising process between Phase 1 and Phase 3, refined signals of inertial sensors with higher SNR are obtained that are more suitable for the next prediction.

#### 4. Integrated System Based on RVFL

As mentioned above, RVFL is a single layer feedforward neural network (SLFN) with fast training algorithm, having favorable features on overfitting, local minima, and generalization, which is attributed to the characteristic network structure illustrated in Figure 1.