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In a precise positioning system, weak signal errors caused by the influence of a human body on signal transmission in complex environments are a main cause of the reduced reliability of communication and positioning accuracy. Therefore, eliminating the influence of interference from human crawling waves on signal transmissions in complex environments is an important task in improving positioning systems. To conclude, an experimental environment is designed in this paper and a method using the Ultra-Wideband (UWB) Local Positioning System II (UWB LPS), called Bayesian Compressed Sensing-Crawling Waves (BCS-CW), is proposed to eliminate the impact of crawling waves using Bayesian compressive sensing. First, analyse the transmission law for crawling waves on the human body. Second, Bayesian compressive sensing is used to recover the UWB crawling wave signal. Then, the algorithm is combined with the maximum likelihood estimation and iterative approximation algorithms to determine the label position. Finally, through experimental verification, the positioning accuracy of this method is shown to be greatly improved compared to that of other algorithms.

With the continuous improvement of wireless technologies such as Bluetooth, ZigBee, and Wi-Fi and the rapid development of ad hoc networks and the Internet of Things, wireless networks have attracted increasing attention from academic circles. Location-based services (LBS) are generally considered to be indispensable key technologies [

The channel model and ranging error model are important foundations for location algorithms and system performance evaluation can provide simulation data for research on ranging and positioning algorithms [

Current UWB positioning is generally divided into Line-of-Sight (LOS) and Non-Line-of-Sight (NLOS) cases, and most are based on AOA estimation. If the base stations were able to perform both TOA estimation and Direction-of-Arrival (DOA) estimation at the same time, only one base station would be needed for positioning. Previous studies [

The remainder of this paper is structured as follows: Section

In the classical Saleh–Valenzuela channel model, multipath components arrive in a cluster and the arrival time of rays in a cluster follows a Poisson distribution. The channel impulse response can be modelled as follows:

where

Saleh–Valenzuela channel model.

Human body occlusion is a special scenario in non-line-of-sight (NLOS) propagation. Under human body occlusion, when the transmitting antenna and the receiving antenna are both on the same side of the human body, they are not blocked and pass directly through each other during propagation. Thus, signal path energy loss detection can accurately obtain the direct path signal [

Figure

Signal propagation path in a human-occluded application scenario.

A real signal

where

where

The process of recovering x from the measurement sequence y is called sparse reconstruction. However, this model is an NP-hard problem. Nevertheless, Chen and Candes [

In the above formula, when

In the standard CS framework, the signal reconstruction problem is mainly solved by convex optimization methods such as basic tracking (BP) and greedy algorithms such as matching pursuit (MP) and orthogonal matching pursuit (OMP).

Compression sensing is used to recover the signal through a small number of measurements, and compression sensing can accurately restore the original signal when it is sparse. In other words, after the influence of human body occlusion, the original propagation signal can still be accurately restored. The compressed-sensing signal model is similar to the traditional signal model. Assuming that a is the signal to be perceived, the perceptual process of this signal is described by

where

Based on the above theoretical description, sparse representation is used in this paper to represent the signal. The sparsity here involves our understanding of the signal transmission strength. The sparse definition derived from mathematical experience is that a vector contains at most k non-zero sparse elements and is calculated by the k-norm, defined as follows.

A vector is called k sparse signal if

All the k sparse vector geometries are represented as

Assuming that

Then, for any

Let

The k-sparse signal can be considered more extensive, while the structure sparsity is based on the signal structure plus some other structural. Let

Vector

At the same time, a sparse fusion frame concept was also proposed in [

where

Based on statistical information of the measurement signal, prior knowledge of the signal in the sparse domain and CS is represented in the Bayesian framework. Compression measurements should also consider measurement noise and additional noise, expressed as follows:

where

As mentioned above, the coefficients are sparsely constrained. The previously widely used sparsity is the Laplacian density function:

Therefore, the solution in (

However, the Laplacian prior is not conjugate with Gaussian likelihood, and the associated Bayesian inference may not be performed in closed form. An associated vector machine (RVM) has been applied that has similar properties to the Laplacian prior but allows convenient conjugate index analysis. Thus, zero-mean Gaussian priors are considered for each element of

where

By marginalizing the hyperparameter

Based on the above discussion, the Bayesian linear model considered on the RVM is essentially a simplified model for Bayesian model selection. We can express the posterior of

where

In the above formula,

where

To solve the signal compression sensing recovery problem, commonly used effective solutions include greedy iterative algorithms, nonconvex optimization-based iterative algorithms, convex optimization algorithms, and graph theory-based information transfer algorithms. Considering the propagation characteristics of UWB signals under human occlusion, for this study, we chose a simple and effective greedy algorithm.

The greedy algorithm solves the problem iteratively. The core idea is to find the relevant columns of measurement matrix A using a greedy approach and then find the corresponding sparse solution. In each iteration, the algorithm selects a column in the measurement matrix related to y and minimizes the mean square error at each step. Then, the corresponding row contribution subtracts the remaining residual from

Input measurement matrix A, measurement y, and the error threshold

Set k = 0, initialize

Let k = k + 1 and select

As calculated by Step

Calculate the residual

If

The above algorithm provides a basic definition of the OMP algorithm.

The measurement matrix

Then, the OMP algorithm can completely recover the UWB signal

For the OMP algorithm, when one of the following two conditions is met:

The mutual relationship number satisfies A

The measurement matrix A satisfies the M+1-order RIP condition, where the constant

Then, the OMP algorithm will completely recover the k sparse signal from

For this study, we conducted experiments in both indoor and outdoor environments and included a laboratory, a Meeting-Room, and a corridor. The outdoor environments included a soccer field and an area outside a school building. For each venue, we placed laptops in more than 10 places and placed tags in several different locations. During the experiment, one or more people moved within the environment, for example, students walking on the football field or in the research lab. Diagrams of the experimental environments are shown in Figures

Actual experimental environment diagram.

Laboratory

Meeting-Room

corridor

Experimental environment plan.

Laboratory

Meeting-Room

corridor

The hardware system used in this paper is the I-UWB LPS positioning system. At present, the system has achieved 5cm positioning accuracy for a single-label. Figure

Hardware testbed [

Base station

Power supply

Network diagram

PC-side

When a signal passes through a human body, a certain degree of attenuation occurs due to the blocking effect, and the signal forms a crawling wave. To express the effect of crawling waves intuitively, they are represented by a carrier signal and a modulated signal, as shown in Figure

Carrier signal and spectral density of carrier and modulation signals.

Carrier signal

Modulation signal

As shown by the carrier signal diagram in Figure

Under the premise of reducing the impact of human crawling waves, we studied the effects of Bayesian compressive sensing algorithm on signal transmission by analysing the modulated signal, as shown in Figure

Carrier signal and spectral density for signal modulation and filtering gain response.

Signal modulation

Filtering gain response

From Figure

From the Bayesian compressive sensing signal obtained as described above, the crawling wave is demodulated using two methods, as shown in Figure

Two ways of crawling wave demodulation.

Envelope detection

Synchronous product detection

An analysis of Figure

The waveform and frequency of the signal before filtering are shown in Figure

The waveform and frequency of the signal.

The waveform and frequency before filtering

The gain response of the filter

By comparing the signal waveform before, after filtering and the spectrum change law, we can see that the scheduling value m plays a crucial role in signal modulation. The effect of the scheduling value m on the modulation of the crawling waves is shown in Figure

Effect of the scheduling value m on the modulation of crawling waves.

As can be seen from the analysis in Figure

At the end of these experiments, we studied the influence of the modulation degree on the waveform. When the modulation degree is zero, the modulation signal has no waveform, and as the modulation degree increases, the waveform becomes increasingly obvious. However, when the modulation degree exceeds 1, signal distortion occurs and unwanted waveforms appear. This indicates that the value of the modulation degree is between 0 and 1; it cannot be 0, and the maximum value is 1. A higher carrier frequency f can be selected, and the time sampling interval needs to be designed to be larger.

After completing the above signal processing, the influence of the crawling waves is successfully eliminated, and the signal weakness generated when the signal is blocked by the human body is effectively reduced.

After exploring the effects of human body occlusion and the Bayesian algorithm on the signal transmission effect, this study performed experiments on the proposed algorithm combined with Bayesian compressive sensing and obtained the transmission effect, positioning error, and sample numbers of the processed UWB signal. The relationship between these values is shown in Figure

Error analysis.

Signal frequency diagrams on the x, y, and z-axes.

Figure

The signal frequency diagrams on the x, y, and z-axes, respectively, are shown in Figure

Figure

Comparison of positioning accuracy in simple and complex environments.

Simple environment

Complex environment

From Figure

In this paper, by combining the advantages of previous positioning methods, we propose a BCS-CW method that uses the local positioning system II-UWB LPS in conjunction with Bayesian compressive sensing to eliminate the effects of crawling waves under an environment with four base station tags. By analysing the transmission law of crawling waves on the human body, we obtained the main reason for the influence of human body occlusion on UWB signal transmission. Bayesian compressive sensing can recover the obtained UWB crawling wave signal; then, maximum likelihood estimation and the iterative approximation algorithm are combined to determine the tag’s location. Finally, combined with actual environmental experiments, the proposed positioning accuracy after eliminating the impact of human crawling waves is greatly improved compared to other algorithms. The problem to be solved in future work is how to completely eliminate debilitated signals under human body occlusion. We plan to conduct further research in future work.

This experiment was obtained in a real experimental environment, all data is actually available, and the relevant data has been described in the article.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Li Beibei contributed to algorithm creation and to the analysis. As the supervisor of Hao Zhanjun, he proofread the paper several times and provided guidance throughout the entire manuscript preparation process. Dang Xiaochao contributed to the algorithms, the analysis, and the simulations and wrote the paper. Li Beibei and Hao Zhanjun revised the equations, helped write the introduction and related works sections, and critically revised the paper. All the authors have read and approved the final manuscript.

This work was supported by the National Natural Science Foundation of China under Grant nos. 61762079 and 61662070; the Key Science and Technology Support Programme of Gansu Province under Grant nos. 1604FKCA097 and 17YF1GA015; and the Science and Technology Innovation Project of Gansu Province under Grant nos. 17CX2JA037 and 17CX2JA039.