1. Introduction
In recent years, underwater acoustic sensor networks (UASNs) have been proposed to explore the ocean and realize aquatic applications, such as safety systems, oil platform monitoring, navigation [
1,
2]. In [
3,
4], the UASNs are used for the protection of offshore platforms and energy plants. In UASNs, the target localization, which aims to estimate the location of unknown target, is an important task. In advance, the target localization systems are divided into two categories: passive localization [
5,
6,
7] and active localization [
8,
9]. For instance, a passive localization was presented in [
10] to analyse the received acoustic signals based on Energy Detection and extended Kalman Filter (EKF) algorithm. In [
11], an optimal long-term robot motion planning algorithm was proposed to realize the active source localization. In addition, an asynchronous localization algorithm with mobility prediction in [
12] is presented to realize collaboratively localize an underwater target. In this paper, we investigate the active localization system in UASNs, where the target transmits localization request message actively and the receivers of the sensor nodes estimate the distances to the target.
Difficulty of the underwater target localization is the constrained underwater environment. Firstly, the limited bandwidth capacity and limited battery power [
13] make long-distance communication pattern inefficient in the process of communicating between target and sensor nodes.To optimize the limited communication capacity of sensor nodes, the sensor nodes were divided into several subnetworks in [
14] to realize short-distance transmissions instead of the long-distance, improving the sensing accuracy of each sensor node. However, the short-distance pattern is only implemented in the process of data aggregation rather than the process of communicating between the target and sensor nodes.Thus, how to realize the low-cost and short-distance pattern in the process of communicating between the target and sensor nodes is one of the pivotal issues to be addressed in this paper. Base on the classification property of SVM [
15], SVM algorithm was applied to discriminate whether the target lies in the region near the location of a sensor node. Motivated by classification this character, we propose a node-selection strategy to structure a low-cost and communication-efficient sensor networks by selecting fractional sensor nodes within the efficient range from the entire sensor networks to communicate with the target.
Subsequently, sensor networks are required to achieve the underwater target localization task. In [
16,
17], the state-space approach based on particle filter method has been employed to realize target localization in UASNs. The particle filter recursively estimates the probability density of the unknown target location conditioned on all measurement data up to the current frame. Using a sequential Monte Carlo method, the probability density is represented by a set of random particles with associated weights which are updated by the likelihood function of observation. In [
18], the time of arrival (ToA) measurement model which relies on precise time synchronization and the speed of sound was adopted to construct the likelihood function. The time synchronization has been improved in [
19,
20,
21]. However, the ToA is vulnerable to the sensing noises from the speed of sound which is affected by many factors such as water temperature, pressure, and salinity [
22]. The sensing noises will distort the likelihood function, which makes the particles cannot be weighted accurately and leads to “particle degeneracy” problem. In order to solve this problem, various methods such as human memory model [
23], adaptive method [
24] and mean-shift method [
25] were applied to establish the likelihood function. Specially, learning-based methods have been incorporated into particle filter to deal with sensing noise problem. In [
26], the least-square support vector regression (LSSVR) was used to obtain the accurate observation in the noise conditions owe to its black-box model. However, considering that the unique underwater circumstances where the target is occluded by objects results in excessive sensing noise, the method cannot be effective in target localization.
In this paper, we investigate a support vector learning-based particle filter algorithm in communication-efficient UASNs to improve the localization accuracy. A node-selection strategy is first proposed, using support vector machine (SVM) algorithm to train all sensor nodes and judge whether the sensor node locates within the communication-efficient range to the target, to select fractional sensor nodes to participate in the sensing process. Since the node-selection strategy provides the short-distance communication pattern, it has advantages of the communication cost and measurement accuracy compared to the analog long-distance particle filter method [
27]. Next, based on the raw data obtained from the selected sensor nodes, a LSSVR-based observation model, where an iterative regression function is proposed to deal with distorted raw data, is established to yield accurate observation against the sensing noises. At the same time, we integrate the observation to formulate the likelihood function of the particle filter. Compared with the ToA-based particle filter [
28], where the ToA measurement model was adopted to construct the likelihood function, this approach has a better performance against the sensing noise and effectively update the weights of particles to solve the “particle degeneracy” problem. Based on the above solutions, the communication efficiency and localization accuracy are improved. The main contributions of this paper are threefold.
A node-selection strategy, where the discrimination criteria is the distance to target so as to realize the short-distance communication, is proposed to select fractional number of sensor nodes from the sensor networks. The pattern where less sensor nodes participate in the sensing process by the way of short-distance communication enhances the communication property and reduces the sensing noises.
A learning-based observation model coupled with an iterative regression function is proposed to yield an accurate observation against the sensing noise.
A likelihood function integrating the accurate observation is formulated to effectively update the weights of particles, avoiding the “particle degeneracy”. The solution yields an accurate localization result.
The rest of this paper is organized as follows. In
Section 2, the problems for particle filter estimation in UASNs are formulated. In
Section 3, the detailed solutions for the problems are presented. Then,
Section 4 shows the simulation results and analysis of them. Finally, conclusions are given in
Section 5.
4. Results and Discussion
In this section, we deploy a simulation environment with 20 sensor nodes to a region of 100 m × 100 m × 100 m. First, we investigate the communication-efficient network architecture. According to the
Section 3.1, the optimized network architecture in this paper can pick fractional sensor nodes by the node-selection strategy to improve the communication efficiency. The distance parameter is set
to train the monitored region. We set the communication-efficient range as
= 10 m, 40 m, 50 m, 60 m, 70 m, 80 m and 100 m respectively. When the target locates in (40,50,60), we give the
Table 1 to show the discriminant performance of node-selection strategy in the case of different communication-efficient range. According to the
Table 1, the node-selection strategy has a great performance in discriminating and selecting sensor nodes in the different communication-efficient range.
Meanwhile, considering that if the number of selected sensor nodes is too small, the obtained observation in
Section 3.2 will degrade because of the lack of data information. Thus, in the following simulated experiments, we set the communication-efficient range as
m, avoiding the shortage of information. An example with target locating in (51.08,40.95,60.75) is shown in
Figure 3. It can be shown that the node-selection strategy select appropriate sensor nodes, that means
.
Next, this section is devoted to the experimental study for the verification of the localization performance of the proposed support vector learning-based particle filter (SVL-PF) in sensing noise condition. According to [
26,
28], the least-square support vector regression and ToA are used to establish the observation function of particle filter respectively, improving the accuracy of the measurement data. In Consensus Estimation [
14], a regional optimal solution is proposed to avoid the occurrence of no-solution situation and improve the localization accuracy. These algorithms have been demonstrated to be effective when handling the universal sensing noise. In this paper, we propose a support vector learning-based particle filter (SVL-PF) scheme to solve the excessive sensing noise on the basis of the universal sensing noise. Thus, we compare the proposed SVL-PF algorithm with Consensus Estimation [
14], LSSVR-PF [
26] and ToA-PF [
28] in two different simulated scenarios from both universal sensing noise and excessive sensing noise.
For all the simulated experiments, the gain of propagation loss
in (
25) is selected to be
. The parameters
and
in (
27) are set to 1 and 0.2, guaranteeing the convergence performance. Since the underwater target is usually assumed to be moving slowly, the CV model is employed for the state model
where
T representing the time period in seconds between the previous and current time step;
is the motion velocity and
is the target state.
is a Gaussian random variable with zero mean and unit variance. We set the initial state
and initial particles are drawn uniformly around the workspace.
A. Scenario 1: A localization example in the universal sensing noise condition
In this scenario, we check the localization performance in the case where the universal sensing noise is mingled in raw data. A Gaussian noise with a standard deviation of
of the raw data is added to the raw data. The sensing noise is mainly caused on account of the insufficient communication ability of sensor node.
Figure 4 shows the localization trajectories of four algorithms. In the figure, the green curve (SVL-PF estimation ) preferably follows the blue curve (real state) than the red curve (ToA-PF), black curve (Consensus Estimation) and purplish red curve (LSSVR-PF).
To show more clearly, a localization error function is defined as
, where
is the estimated location of the target and
is the real location of the target at time frame
k. The localization errors using the proposed SVL-PF algorithm in this paper and the compared algorithms are shown in
Figure 5.
As shown, even though the localization errors of SVL-PF are larger than the compared algorithms at certain time frames such as and 66, it is obvious that the SVL-PF presents better localization accuracy as a whole.
Moreover, considering that the particle filter recursively estimates target location conditioned on all measurement data up to the current time frame, the prior results have an effect on the current time frame. Thus, the average of accumulated error function is defined to show the average localization error from the initial time frame to present time frame
k.
where
is the localization error at time frame
k and
represents the current time frame. When the current time frames are
, the average localization errors of all test algorithms are shown in
Table 2.
Based on the
Table 2, the SVL-PF in this paper has smaller average localization error at different time frames. The significance of the different results among the algorithms (SVL-PF, ToA-PF, LSSVR-PF and Consensus Estimation) illustrates that the SVL-PF using the support vector learning-based measurement model is efficient against the sensing noise.
According to the results, we can easily verify that the proposed SVL-PF algorithm in this paper presents better localization performance, although the compared algorithms have a good localization performance in the universal sensing noise. It means that the proposed algorithm in this paper has a better localization accuracy in the situation of universal sensing noise.
B. Scenario 2: A localization example in the excessive sensing noise condition
As described in
Problem 2, the excessive sensing noise will lead to particle degeneracy and accuracy loss. In this scenario, we check the localization performance in the case where the excessive sensing noise arises. On the basis of the universal sensing noise, a Gaussian noise with a standard deviation of
of the raw data is additional added to the raw data
. Similarly, the localization trajectory and the corresponding localization errors are described in
Figure 6 and
Figure 7. Taking
Figure 7 as an example, the localization errors of the ToA-PF, LSSVR-PF and Consensus Estimation are larger than the proposed SVL-PF in this paper. Moreover,
Table 3 shows the average localization errors of all test algorithms in the excessive sensing noise condition. The compared algorithms (ToA-PF, Consensus Estimation and LSSVR-PF) contain the larger average localization errors which reach to
m,
m and
m. It is obvious that the SVL-PF has a smaller average localization errors from the initial time frame to the final time frame. The results declare that the LSSVR-based and ToA-based cannot effectively handle the excessive sensing noise problem, and the the excessive sensing noise results in the no-solution situation, causing the localization accuracy loss of the Consensus Estimation algorithm. Besides, compared with the
Table 2 and
Table 3, the average localization error of LSSVR-PF algorithm has a great increase from universal condition to excessive condition. The reason is that the LSSVR model closely related to the raw data cannot obtain satisfactory measurement data in excessive noise condition and the correlation character of particle filter among all measurement data up to the current time frame aggravates the localization accuracy.
As shown, SVL-PF is the most effective algorithm in terms of excessive sensing noise. It demonstrates that SVL-PF can solve the excessive sensing noise problem by means of the iterative regression function and improve the localization accuracy.
It is found from the aforementioned results that the proposed SVL-PF algorithm in this paper has a better performance against the sensing noise from both universal sensing noise and excessive sensing noise. Specially, in the face of the sensing noise, SVL-PF algorithm can solve this problem and improve the localization accuracy.