FBLS-Based Fusion Method for Unmanned Surface Vessel Positioning Considering Denoising Algorithm

Abstract

Although a USV navigation system is an important application of unmanned systems, combining Inertial Navigation System (INS) with Global Positioning System (GPS) can provide reliable and continuous solutions of positioning and navigation based on its several advantages; the random error characteristics of INS and the instability derived from the GPS signal blockage represent a potential threat to the INS/GPS integration of USV. Under this background, a composition framework based on nonlinear generalization capability of support vector machines (SVM) and multi-resolution ability of wavelet transform is used to solve the difficulty that the INS suffers from the interference of stochastic errors, and the dynamic information of the USV is not influenced. An innovative fuzzy broad learning structure based on the broad learning (BL) method is utilized in the INS/GPS integration of USV, in which the navigation information of INS and GPS are deemed as the input of the Fuzzy Broad Learning System (FBLS) to train the network, and then the trained network of FBLS and navigation information of INS are applied for estimating the optimal navigation solution during the GPS signal blockage. Based on the USV platform, a sea trial was carried out to confirm the validity and feasibility of the proposed method by comparing with existing algorithms for INS/GPS integration. The experimental results show that the proposed approach could achieve the better denoising effect from random errors of INS and provide high-accuracy navigation solutions during GPS signal blockage.

1. Introduction

With the rapid development of intelligent technology, the wide application of intelligent technology in various fields means that unmanned vehicles and unmanned aerial vehicles (UAV) [1,2] have been gradually known by people. Unmanned Surface Vessel (USV) [3], as a branch of unmanned equipment manufacturing, has gradually appeared in people’s visual field and achieved rapid development. Unmanned ships are equipped with different sensors, which make it easy to complete the various tasks, including target recognition, routing plan and maritime search and rescue, underwater mapping based on integrating modern communication, information processing and perceptual control and other advanced technologies [4,5,6]. GPS and INS are regarded as important sensors of unmanned ships, which can obtain the ship’s position, velocity, attitude, and other navigational information to ensure that the ship navigation is safer and more reliable. GPS has been regarded as a satellite-based positioning system, which can output all-weather positioning information for the world. Moreover, the positioning accuracy is high, and the navigation accuracy does not change with time. However, the attitude information of the ship cannot be obtained by using GPS equipment alone, and GPS is vulnerable to electromagnetic interference and the data update rate of GPS is low [7]. INS has been deemed as a fully autonomous navigation system which has some advantages of high short-dated accuracy and high update rate of the data, but it has the disadvantage that navigation errors will accumulate over time. Therefore, in order to compensate for the shortcomings of INS and GPS, the combination of two sensors can update the speed and position components and improve the accuracy even at low data update rate.

Since the error of IMU increases due to random zero bias and bias drift, establishing a specific model to eliminate the influence of these errors on inertial sensors is hard to perform. The random errors of INS are composed of short-term errors and long-term errors, in which the short-term errors in INS random errors can be minimized by pre-filtering the original measurement, and the long-term errors can be compensated by the integration process. At present, the multi-resolution ability of wavelet transform denoising techniques is utilized to eliminate the short-term errors in IMU, and the results show that the noise is suppressed by reducing the frequency components with small correlation [8,9]. Unfortunately, the long-term errors of sensor associated with ship motion dynamics cannot be thoroughly removed by using the traditional denoising approached based on wavelet transform [10]. There are some common theories that can be utilized to pretreat the dynamic data from the original IMU measurement, for instance the Allan variance-based method [11,12]. Unfortunately, the complexity of computation associated with these approaches is ignored.

For a GPS/INS integrated system, the Kalman filter-based method is the common technique owing to its optimality in state estimation. However, there are many questions eager to be addressed in some aspects: (1) More precise random modeling of inertial sensors based on INS; (2) The accuracy decreases rapidly in the process of long-period GNSS interruption; (3) The prediction ability of modeling ship nonlinear behavior is relatively poor. (4) Unstable estimation can be caused by weak observability of error states. Considering the capability of artificial intelligence (AI) methods to address generalization and nonlinear problems, the focus of data fusion has shifted to the field of AI-based methods. In [13,14], artificial neural network (ANN) and multi-layer perceptron (MLP) were used to model the position errors of INS according to output data of INS and GNSS. Input-Delayed Neural Networks (IDNN) were proposed in [15], in which the networks attempted to model the velocity and position errors of INS according to current and past information derived from INS velocity and position. The artificial immune system (AIS) [16] method was explored to provide estimation errors of velocity and position of IMU. [17] had used the extreme learning machine (ELM) method and implemented both INS and GPS integrated navigation in high velocity applications with the help of the characteristics of fast learning speed and better generalization capability. In addition, [18] proposed the long- and short-term memory (LSTM) for a more stable and reliable navigation solution when GPS interruption occurs, and applied it to vehicle. A similar procedure could be seen in [19], where instead of utilizing LSTM, SVM was presented to integrate both IMU and GPS, and the results showed that the fusion algorithm has greatly improved the accuracy of the model.

As can be seen from the abovementioned research, there are still some problems even though many achievements have been obtained. Almost all the proposed algorithms to approximate the optimal solution in dynamic environments use a sliding window and its variants. However, most algorithms are limited to the computational complexity and training time for the choice of network structure. At present, it is still plagued by these problems.

In this article, a novel data fusion method for INS/GPS integration is proposed to improve the positioning accuracy and intensify reliability with less computing complexity, particularly when the GPS signal strength is low. The contributions of this article are as follows:

(1)

Aiming at the difficulty that the INS suffers from the interference of stochastic errors, this article proposes a composition framework based on nonlinear generalization capability of SVM and multi-resolution ability of wavelet transform without influencing the dynamic data of the ship.

(2)

Focusing on simple model structure and short training time of fuzzy broad learning theory, this article fuses uncertain sensory information derived from INS and GPS.

(3)

Verifying the validity and feasibility of the proposed method by comparing with current popular methods for INS/GPS integration.

The other parts of this article are arranged as follows: Section 2 describes the loosely coupled GPS/INS integration model, and the denoising method based on combine wavelet with SVM framework is introduced in Section 3 and Section 4, which describe the integrated navigation based on FBLS. The experiment results and analysis are presented in Section 5. Finally, Section 6 provides the concluding remarks.

2. Proposed Method

It can be observed in Figure 1 that the combination of denoising method and data fusion theory constitutes the system architecture of this paper. The denoising model is presented by using wavelet and SVM method to obtain the denoised IMU measurements. When the GPS signal is effective, the FBLS is trained to obtain the input-output mapping. However, if the GPS outages, the acceleration and angular rate data derived from INS are used as the input of the trained network to predict the corresponding position error, and finally obtain the positioning information of the USV.

• Analysis of Error Models of INS

The nonlinear model of attitude and velocity can be defined as [20]:

$$\{\begin{array}{l}\dot{\varphi }=({\omega }_{ie}^n+{\omega }_{en}^n)\times \varphi +(\delta {\omega }_{ie}^n+\delta {\omega }_{en}^n)-C_b^n{\epsilon }^b\hfill \\ \delta {\dot{V}}^n=f^n\times \varphi -(2\delta {\omega }_{ie}^n+\delta {\omega }_{en}^n)\times V^n-(2{\omega }_{ie}^n+{\omega }_{en}^n)\times \delta V^n+C_b^n{\nabla }^b\hfill \end{array}$$

(1)

where ϕ = [ϕ_E, ϕ_N, ϕ_U], δVⁿ = [δV_E, δV_N, δV_U] and fⁿ = [f_E, f_N, f_U] mean the attitude angle error, velocity error and the specific force vector of accelerometer, in which the subscript E, N, U denote the east, north and upper orientation, respectively. ${\omega }_{ie}^n$ and ${\omega }_{en}^n$ indicate respectively the angular rate caused by earth rotation and angular rate caused by vehicle motion, while $\delta {\omega }_{ie}^n$ and $\delta {\omega }_{en}^n$ indicate the corresponding errors. $C_b^n$ stands for the attitude matrix, ${\dot{\epsilon }}_i^b=0$ and ${\dot{\nabla }}_i^b=0$ (i = x, y, z) denote the constant drift of the gyro and accelerometer zero-bias.

The nonlinear model of position error can be defined as [20]:

$$\left[\begin{array}{c}\delta \dot{L}\\ \delta \dot{\lambda }\\ \delta \dot{h}\end{array}\right]=\left[\begin{array}{ccc}0& \frac{1}{R_M+h}& 0\\ \frac{\sec L}{(R_N+h)\cos \phi }& 0& 0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}\delta V_E\\ \delta V_N\\ \delta V_U\end{array}\right]+\left[\begin{array}{ccc}0& 0& \frac{-V_N}{{(R_M+h)}^2}\\ \frac{V_E\tan L\sec L}{(R_N+h)}& 0& \frac{-V_E\sec L}{{(R_N+h)}^2}\\ 0& 0& 0\end{array}\right]\left[\begin{array}{c}\delta L\\ \delta \lambda \\ \delta h\end{array}\right]$$

(2)

where δL, δλ, δh indicate errors of position. R_M and R_N represents the radius of curvature along the meridian circle and parallel to the prime vertical, respectively.

2.

State and Measurement Models

In this article, a loose combination of the navigation system is constructed based on the INS mechanization.

$$X={[{\varphi }_E,{\varphi }_N,{\varphi }_U,\delta V_E,\delta V_N,\delta V_U,\delta L,\delta \lambda ,\delta h,{\epsilon }_x,{\epsilon }_y,{\epsilon }_z,{\nabla }_x,{\nabla }_y,{\nabla }_z]}^{\mathrm{{\rm T}}}$$

(3)

Considering Equation (3) and INS error equations in (1) and (2), the state model can be expressed as:

$$X_{k+1}=F_k{X}_k+G_k{W}_k$$

(4)

where X represents the state vector, F_k and G_k mean the system matrix and system noise matrix, while W stands for the process noise vector.

The position observation model is constructed by the position difference between GPS and INS, and the velocity observation equation is constructed by the velocity difference. Then the observation model of GPS/INS integrated navigation system is:

$$Z_k=H_{k}X+D_k=\left[\begin{array}{c}{H}_P\\ H_V\end{array}\right]X+\left[\begin{array}{c}{D}_P\\ D_V\end{array}\right]$$

(5)

where $H_P=\left[\begin{array}{ccc}{0}_{3\times 6}& \mathrm{diag}\left(\left[R_M,R_N\cos L,1\right]\right)& 0_{3\times 6}\end{array}\right]$, $H_V=\left[\begin{array}{ccc}{0}_{3\times 3}& \mathrm{diag}\left(\left[1,1,1\right]\right)& 0_{3\times 9}\end{array}\right]$, D_P and D_V denote position observation errors and velocity observation errors of GPS, respectively.

3. Denoising of Combing Wavelet and SVM Method

3.1. SVM Approach

Based on the Vapnik–Chervonenkis dimension and structural risk minimization principle of statistical learning theory, Vapnik presented a new machine learning method, namely SVM [21]. SVM can not only effectively improve the generalization ability of learning machine, but also maximize the interval in feature space into a convex quadratic programming problem, so as to obtain the global optimal solution.

We assume that a training set {(x_i, y_i), i = 1, 2,…, n} is composed of n sample, where x_i and y_i denote the input data and the corresponding output data. So, the regression function can be written as:

$$f(x)=\langle \sigma ,\mathsf{\Phi }(x)\rangle +d$$

(6)

where Φ(x) represents the nonlinear function, which is mainly used to realize the mapping of training samples from low-dimensional space to high-dimensional feature space. σ and d mean the weight vector and bias vector, respectively. In order to extend the results obtained in the estimation indicator function (pattern recognition problem) to the estimation of real function (regression problem), an insensitive loss function L is introduced:

$$L_{\epsilon }=\{\begin{array}{cc}0,\hfill & \begin{array}{cccc}& \begin{array}{cc}& \end{array}& & \left|f(x)-y\right|\le \epsilon \end{array}\\ \left|f(x)-y\right|-\epsilon ,\hfill & \begin{array}{cc}& others\end{array}\end{array}$$

(7)

By introducing a variable that allows the deviation of the function interval, that is, the slack variables ${\xi }_i$ and ${\xi }_i^{\ast }$, the σ and d are calculated by addressing the quadratic programming (QP) problem [22]:

$$\{\begin{array}{l}\min \frac{1}{2}{\Vert \sigma \Vert }^2+C{\displaystyle \sum _{i=1}^n({\xi }_i,{\xi }_i^{\ast })}\hfill \\ s.t.\{\begin{array}{c}{y}_i-\langle \sigma ,\mathsf{\Phi }(x)\rangle -d\le \epsilon +{\xi }_i\hfill \\ -y_i+\langle \sigma ,\mathsf{\Phi }(x)\rangle +d\le \epsilon +{\xi }_i^{\ast }\hfill \\ {\xi }_i\ge 0,{\xi }_i^{\ast }\ge 0 (i=1,2,\cdots ,n)\hfill \end{array}\hfill \end{array}$$

(8)

where C means the regularization parameter to balance the maximum margin and classification error. The constrained optimization problem determined by Equation (8) is a typical QP problem, which can be solved by Lagrange multiplier method. Therefore, the dual optimization problem is:

$$\{\begin{array}{l}\max \left[-\frac{1}{2}{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n({\alpha }_i-{\alpha }_i^{\ast })({\alpha }_j-{\alpha }_j^{\ast })K(x_i,y_i)}-{\displaystyle \sum _{i=1}^n{\alpha }_i(\epsilon -y_i)-}{\displaystyle \sum _{i=1}^n{\alpha }_i^{\ast }(\epsilon +y_i)}}\right]\hfill \\ s.t.{\displaystyle \sum _{i=1}^n({\alpha }_i-{\alpha }_i^{\ast })=0,0\le {\alpha }_i,{\alpha }_i^{\ast }\le C (i=1,2,\cdots ,n)}\hfill \end{array}$$

(9)

where ${\alpha }_i$ and ${\alpha }_i^{\ast }$ denote Lagrange multipliers, and K(x_i, y_i) indicate the kernel function. The solution of Lagrange multipliers ${\alpha }_i$ and ${\alpha }_i^{\ast }$ is achieved by solving Equation (9), then $w={\displaystyle {\sum }_{i=1}^n({\alpha }_i-{\alpha }_i^{\ast })\mathsf{\Phi }(x_i)}$. Therefore, the support vector regression function f(x) in Equation (1) can be given by [22]:

$$f(x)={\displaystyle \sum _{i=1}^n({\alpha }_i-{\alpha }_i^{\ast })K(x_i,y_i)+d}$$

(10)

Figure 2 shows the process of SVM regression. The function of kernel is to ensure that SVM makes the data linearly indivisible in the low-dimensional space and linearly divisible in the high-dimensional space without inner product operations, enhance operational efficiency and avoid dimensional catastrophes. Therefore, the selection of kernel function largely determines the prediction accuracy. The radial basis function (RBF) is used as the kernel function of support vector regression (SVR), mainly because it has a wider scope of application and does not need to consider the size of data sets and feature dimensions in this research.

$$K(x_i,y_i)=\exp \frac{-{\Vert x_i-y_i\Vert }^2}{2{\gamma }^2}$$

(11)

where γ denotes the kernel function parameter that has an impact on the accuracy of prediction and complexity of data distribution.

Based on the nonlinear regression and high generalization ability derived from SVR, and if the data set representing the dynamics of vessel is given, it can be utilized to deal with the long-term noises of IMU. Therefore, the wavelet and SVR method are combined into a denoising framework, which is deemed as the preprocessed solution of original MEMS-IMU measurement.

3.2. Denoising Method Based on Wavelet and SVM

The denoising model is presented by using the wavelet and SVM methods in Figure 2. The latest set of original IMU output data x₁, x₂,…, x_n×k can be chosen, and its size is defined as n × k. It is worth to note that n and k are given as 10 to ensure the dynamics characteristics of denoising. In addition, the original measurement is preprocessed by using the four-level wavelet denoising algorithm based on the effect of noise reduction. After the sequence is denoised, it is decomposed into k smaller sequences, in which each smaller sequence is utilized as the input of the mean filter. Ultimately, the output sequence $x_1^{\prime }$, $x_2^{\prime }$,…, $x_k^{\prime }$, which is derived from mean filter, can be deemed as the input of SVM regression to obtain the accurate IMU measurement y.

When considering the training process of SVM, we use one group of the noisy data and its noise variance equivalent to the noise variance of sequence $x_1^{\prime }$, $x_2^{\prime }$,…, $x_k^{\prime }$. It is assumed that the measured noise of IMU follows the non-Gaussian distribution and satisfies the GED of non-zero state parameters. This assumption is helpful to improve the positioning accuracy according to the experimental results.

Taking the raw signal as the training norm and considering that the sine wave model can provide an infinite number of derivatives, the dynamic training model is appropriate, in which some data performs the training function, and the remaining data performs the testing function. Moreover, based on the predict consequences of the model, the optimum parameters of coefficient C and γ are calculated according to ergodic algorithm [23].

4. Fuzzy Broad Learning System

4.1. FBLS Structure

Fuzzy Broad Learning System (FBLS) is implemented based on the integrated structure of BLS and Takagi-Sugeno (TS) fuzzy subsystem in Figure 3. It mainly replaces the feature nodes of BLS with a set of TS fuzzy subsystems [24]. In order to reduce the computational complexity of BLS structure, the sparse automatic encoder used to fine-tune the weights in the feature layer is removed from the FBLS. Supposed a training data with n (n < N) fuzzy subsystems and m (m < M) enhancement nodes can be represented as

$$X=\left\{\left(\begin{array}{c}{x}_1\\ x_2\\ ⋮\\ x_N\end{array}\right)|x_s=[x_{s1},x_{s2},\cdots ,x_{sM}]\right\},s=1,2,\cdots ,N$$

(12)

The ith fuzzy system including K_i fuzzy rules has the following form

$$\begin{array}{l}\mathrm{If}{x}_{s1}is{A}_{k1}^i\mathrm{and}{x}_{s2}is{A}_{k2}^i\cdots x_{sM}is{A}_{kM}^i\\ \mathrm{then}{\upsilon }_{sk}^i=f_k^i(x_{s1},x_{s2},\cdots ,x_{sM}),k=1,2,\cdots ,K_i\end{array}$$

(13)

In this paper, the first-order TS fuzzy model is used to map the input x_s = (x_s1, x_s2,…, x_sN) to the ith fuzzy system, hence ${\upsilon }_{sk}^i$ can be represented as

$${\upsilon }_{sk}^i=f_k^i(x_{s1},x_{s2},\cdots ,x_{sM})={\displaystyle \sum _{t=1}^M{\alpha }_{kt}^i{x}_{st}}$$

(14)

where ${\alpha }_{kt}^i$ means the parameter derived from the ith fuzzy system, and its values are initialized by the uniform distribution in [0, 1]. The activation strength of kth fuzzy rule can be determined as

$${\tau }_{sk}^i={\displaystyle {\prod }_{t=1}^M{\mu }_{kt}^i(x_{st})}$$

(15)

where ${\mu }_{kt}^i$ corresponding to fuzzy set $A_{kt}^i$ is regarded as a Gaussian membership function, which can be presented as

$${\mu }_{kt}^i(x_{st})=e^{-{(\frac{x_{st}-c_{kt}^i}{{\sigma }_{kt}^i})}^2}$$

(16)

where ${\sigma }_{kt}^i$ and $c_{kt}^i$ denote the center and width, respectively. K_i clustering centers can be calculated by using k-means clustering method for the ith fuzzy subsystem of FBLS. ${\sigma }_{kt}^i$ is initialized by the cluster node. So, the weighted activation strength of each fuzzy rule can be denoted as

$${\omega }_{kt}^i=\frac{{\tau }_{sk}^i}{{\displaystyle {\sum }_{k=1}^{K_i}{\tau }_{sk}^i}}$$

(17)

4.2. FBLS-Aided Integrated Navigation System

Considering that the position errors of GPS/INS integration are mainly caused by errors of the gyroscope and accelerometer in INS, the outputs of the gyroscope and accelerometer are selected as the input of network while the position error of inertial navigation are chosen as the network output. The FBLS is trained when the GPS signal is effective, as shown in Figure 4, in which the P_INS denotes the output positioning data of inertial navigation solution, and P_GPS denotes the GPS positioning data. The positioning error δP estimated by EKF method and the GPS/INS integrated navigation positioning data are calculated by the formula P = P_INS − δP. In addition, the error estimates δP obtained by EKF are utilized as the expected output of the network, and the output $f_{ib}^b,{\omega }_{ib}^b$ of accelerometers and gyroscopes in INS are used as the input of the network. The training algorithm obtains the input-output mapping according to the parameters of the FBLS. Figure 5 shows the prediction process of the network when GPS outages. Due to the poor accuracy of gyroscopes and accelerometers, the navigation accuracy of the pure inertial navigation solution decreases sharply, which makes it difficult to achieve the required navigation accuracy. Therefore, the acceleration and angular rate data $f_{ib}^b,{\omega }_{ib}^b$ are used as the input of the trained network to predict the corresponding position error δP, so as to realize the compensation of INS error at that time and finally obtain the positioning information of the USV.

5. Experimental Results and Analysis

5.1. USV Platform Experiment

A sea trial was performed near the Lingshui port of Dalian, in which a navigation grade inertial measurement unit composed of gyroscopes and accelerometers was adopted for testing, and their specific parameters were shown in

Table 1. IMU Specifications.

Specifications	Gyroscopes	Accelerometers
Range	±100°/s	±19.6 m/s2
Bias	<±2.0°/s	<±0.294 m/s2
Scale Factor	<1%	<1%
Angle Random Walk	$<0.0375°/\mathrm{s}/\sqrt{Hz}$	$<0.0025\mathrm{m}/{\mathrm{s}}^2/\sqrt{Hz}$

. During the whole test, the test platform (see Figure 6) was in static condition within the initial 0~10 s. In different time periods of 10–20 s, 20–30 s and 30–50 s, the platform rotates clockwise at angular speeds of 1°/s, 5°/s and 9°/s, respectively. As shown in Figure 7, the measured values of three-axis accelerometer and x-axis and y-axis gyroscopes are almost noise, while many of the dynamic features derived from the platform can be displayed in the z-axis. The update rate of MEMS-IMU used in this test is 100 Hz.

Depending on a group of simulated data, SVM regression training is performed based on the denoising framework. Since the dominant motivation of the SVM-based algorithm is to combine wavelet denoising to keep the dynamic characteristics of USV when selecting the training model, more dynamic information should be included in the selected training model. When the dynamics of USV and noise features derived from IMU measurements are considered, taking six groups of non-Gaussian noises coexisting on the output signal as the input for the SVM regression training and a cosine wave as the corresponding output. Figure 8 shows the relationship between the availability of the SVM regression and the input signal. It can be seen that if the trained model is used, the raw sine wave signal can be estimated under six kinds of analog noise conditions.

The proposed hybrid denoising approach is utilized to denoise the original IMU measurement values based on the training model. To illustrate the validity of the presented method more clearly, the wavelet denoising method and combined algorithm of Allan analysis of variance and wavelet denoising (combined wavelet) were compared in this research, and the denoising results are shown in Figure 9, Figure 10 and Figure 11. As can be seen from Figure 9 and Figure 10, compared with the wavelet denoising method, the proposed approach can achieve better results under the condition of dealing with the noises with relatively low dynamic data. However, both combined wavelet algorithm and proposed approach can obtain similar effects. Figure 11 shows that the correct denoised effect when the signal mutation occurs suddenly cannot be achieved by using the wavelet denoising method under the condition of processing the original IMU measurement with high angular velocity dynamic data. However, the combined wavelet algorithm represents good dynamic performance and adaptability as compared with the wavelet method. Its defect is that it cannot adjust to the dynamic data derived from IMU measurements. Considering that the cosine wave training model can follow the dynamic of USV, the proposed method can achieve the better denoising effect while retaining the dynamic motion data. This result is further verified in

Table 2. RMS of different noise reduction method.

	RMS
	Wavelet	Combined Wavelet	Proposed Method
x-axis gyroscope	0.135	0.112	0.088
y-axis gyroscope	0.085	0.063	0.050
x-axis accelerometer	4.156	3.895	3.521
y-axis accelerometer	2.584	2.322	2.301
z-axis accelerometer	0.315	0.246	0.231

.

5.2. USV Sea Trial

(1)

Experiments Introduction

The raw data derived from sensing devices were gathered in a relatively open water area in which GPS signal is easy to capture, and the GPS/INS integration was investigated. Figure 12 shows the USV trajectory near the Lingshui port, where three simulated 60 s GPS outages (outages 1,2 and 5) and two simulated 120 s GPS outages (outages 3 and 4) are marked by the green circles with numbers. During the sea trial, the USV sails in various dynamics, including keeping speed and course, altering course, and changing speed. It should be noted that the traversal method is utilized to calculate the optimum penalty factor C and kernel function parameter γ during the SVM training to meet higher accuracy requirements.

(2)

Evaluation of Noise Reduction Effects

Figure 13 displays the noise reduction effects comparison between original IMU measurements and proposed denoising method on the y-acc. During the first few minutes, the USV is on standby mode. It can be seen that if the USV does not move, the proposed noise reduction effect is significant. In addition, we can conclude from the figure that the suggested denoising means is not only effective in removing the short-term noise, but also effective in retaining the dynamic information of the USV. This is mainly because the denoising method covers the superiority of wavelet denoising and SVM algorithm. The RMS of a different noise reduction method in a sea trial of USV is shown in

Table 3. RMS of different noise reduction methods in sea trial of USV.

	RMS
	Original IMU	Proposed Method
x-axis gyroscope	0.712	0.235
y-axis gyroscope	0.475	0.213
z-axis gyroscope	0.798	0.712
x-axis accelerometer	9.863	8.224
y-axis accelerometer	23.543	21.076
z-axis accelerometer	15.086	4.366

, and the RMS of three-gyroscope and three-accelerometer measurements can be improved from 67% to 10.8% and 16.6% to 71%, respectively.

(3)

Results Analysis of with Other Algorithms

To assess the performance of the proposed method, the intelligent methods of the current mainstream USV field are used for comparison and analysis. The algorithms used contain KF, BPNN and ELM. Note that for USV, the positioning errors represent the level difference between the reference position and the estimated position solutions. The performance evaluation of the horizontal positioning error of USV during the unavailability of GPS signal is presented in

Table 4. Positioning errors of different data fusion method in sea trial of USV.

No Outage	Maximum Error				RMS Error
	KF	BPNN	ELM	FBLS	KF	BPNN	ELM	FBLS
1	86.4	42.6	28.7	25.4	40.7	16.8	8.5	7.2
2	301.7	234.3	154.1	84.4	151.6	108.5	87.9	66.5
3	71.5	35.8	25.4	20.6	31.6	12.7	7.5	6.4
4	272.7	203.5	135.9	70.8	140.6	105.7	80.6	57.8
5	70.6	34.7	20.8	20.5	30.4	12.6	7.2	5.3

. Compared with the KF method, the proposed FBLS data fusion algorithm increases by 56–82% and 70–74% in RMS positioning and maximum positioning, respectively. The performance of the FBLS algorithm is 39–57% stronger than the BPNN method in RMS positioning, and 40–65% stronger than the BPNN method in maximum positioning. Through the comparison of ELM and FBLS methods, it can be seen that they can provide similar performance in outages 1, 3 and 5, but there are big performance differences in 120 s GPS outages (outages 3 and 4). This is because the positioning precision can be decided by dependability and generalization performance. The performance of the FBLS algorithm is 15–28% stronger than the ELM method in RMS positioning, and 11–48% stronger than the ELM method in maximum positioning. In addition, the FBLS approach presents good performance in the straight-line part, but when the USV performs the steering part (outages 2 and 4), the estimated positioning errors derived from the proposed approach appear relatively high because the precision of the model is restrained by the training data in these regions.

As shown in Figure 14, the USV trajectory of outage 1 along a straight line is given, and the average velocity is 9 kn. Compared with other methods, the proposed FBLS method has smaller drift and more superior performance, mainly because more appropriate network parameters are selected in the FBLS prediction model. Figure 15 shows the position trajectory of USV during GPS outage 4. The other approaches achieve better positioning solutions compared with the KF method. What is more, compared with the reference trajectory, the solutions of BPNN and ELM approaches display remarkable deviation, but the FBLS method provides the optimal solution of position.

Figure 16 shows that, during GPS fails, FBLS can achieve better solutions than other methods, and this is a process of deceleration and altering course, with an average velocity of 6kn. The maximum value of position error obtained by the FBLS structure improves by 20% and 12% compared with the BPNN and ELM methods. From Figure 17, the results of FBLS can provide the best positioning solution compared with other methods.

6. Conclusions

In this research, we propose a composition framework of SVM and wavelet transform to make the INS suffer from the interference of stochastic errors, and the dynamic information of the USV is not influenced. An innovative structure based on the BL network is utilized in an INS/GPS integration of USV, in which the navigation information of INS and GPS are deemed as the input of the BL network to train the network, and then the trained network of BL and navigation information of INS are applied to estimate the optimal navigation solution during the GPS signal blockage. The proposed method is compared with the KF, BPNN and ELM methods during the sea trial to verify the feasibility of this method. The experimental results confirm that the proposed approach could achieve better denoising effects from random errors of INS and provide high-accuracy navigation solutions during GPS signal blockage. In future study, the fusion strategy will be explored to further improve the navigation solution of USV.