A novel indoor localization method using passive phase difference fingerprinting based on channel state information

Abstract

The device-free channel state information indoor fingerprint localization method may lead to phase offset errors, strong fingerprint noise and low sampling classification accuracy. In light of these characteristics, this article presents an indoor localization algorithm that is based on phase difference processing and principal component analysis. First, during the offline phase, this algorithm calculates phase differences to correct for random phase shifts and random time shifts in communication links. Second, the principal component analysis method is used to reduce the dimensionality of the denoised data and establish a robust fingerprint database. During the online phase, the algorithm trains a back-propagation neural network using the fingerprint data and determines the modelled mapping relationship between the fingerprint data and the physical localization after carrying out the phase difference correction and the principal component analysis–based dimensionality reduction. The experiments show that compared with existing fingerprint location methods, this algorithm has the advantages of significant denoising effectiveness and high localization accuracy.

Introduction

In recent years, location-based service (LBS) has greatly increased the convenience of our daily lives. ¹ According to previous studies, 80% of a human life is spent indoors. ² Thus, there is a need for more accurate localization service indoors for staff monitoring, supermarket commodity localization, hospital patient calling localization, human traffic condition monitoring and other device-free localization applications. Information on the locations of people has gradually become an urgent problem in the field of indoor location research. The localization accuracy of traditional radio frequency (RF) signals depends on the receiver’s signal quality. Meanwhile, the signals usually used for localization contain noise and various errors. The outdoor line-of-sight (LOS) transmission conditions are vastly superior to those of indoor environments, and these conditions are very important in permitting the linear path propagation of the signal and thus achieving greater accuracy. Therefore, the global positioning system (GPS) has achieved excellent positioning effect in outdoor environment. However, GPS cannot achieve continuous localization in complex indoor environments, as it can outdoors, and it is easily affected by the multi-path effect and increased localization errors.

The wide deployment of indoor Wi-Fi has led to the rapid development of an indoor localization method based on the traditional received signal strength information (RSSI). However, the numeric value of this signal comes from the estimated result in the medium access control (MAC) layer, which causes unstable numerical fluctuations and serious errors; thus, high localization accuracy cannot be achieved using this method. Compared with RSSI, channel state information (CSI) can also be obtained from normal commercial Wi-Fi. Under the surrounding conditions, CSI has a more fine-grained awareness degree and contains a multi-path effect, power attenuation and other information. CSI has been found to be much more stable than RSSI for a given location. ³ In this situation, the indoor localization technique based on CSI signals has become a good choice in solving indoor localization problems. In modern communication techniques based on 802.11n orthogonal frequency division multiplexing (OFDM), some commercial network interface controllers (NICs) that use the 20/40 MHz bandwidth can extract the sub-carrier amplitude and sub-carrier phase from the CSI signal features, and they illustrate the effects of reflection, refraction, attenuation and other superposition errors on every transmission links.

Traditional indoor localization systems using CSI can be divided into two types: first is the geometric location method based on distance and ⁴ the second is to use the fingerprint database as the standard feature data. The fingerprint-based localization method is divided into two phases: the offline phase and the online phase. The offline phase builds the fingerprint information in the database and compares it with the test point. In the online phase, real-time sampling values are matched with the fingerprint database, which enables us to calculate their precise locations. For example, the fine-grained indoor fingerprinting system (FIFS) ⁵ exploits a weighted average of CSI amplitudes over three antennas to achieve fine-grained localization, while the amplitudes and calibrated phase information of CSI are exploited by DeepFi ⁶ and PhaseFi, ⁷ respectively. Xie et al. ⁸ propose a CSI-based indoor signal propagation model to estimate the distance between a transmitter and a receiver. Spot-Fi ⁹ conducts trilateration localization using multiple receivers. The geometric location method has the characteristics of low algorithm complexity and fast computing speed, but it requires at least two nodes to assist in the localization, and its accuracy is entirely dependent on the LOS transmission distance (the quality of the distance accuracy). The fingerprint-based localization method represents another method that is not dependent on the LOS transmission-based measurements and requires only one Wi-Fi access point to complete the localization. Wang et al. ¹⁰ uses only amplitude information to conduct the localization, primarily because the signal may display random time offsets and random phase offsets during its transmission in space. PinLoc ¹¹ represents a data-processing method that is intended to reduce the phase offset, but it does not consider the co-existence of random time offsets and random phase offsets. They use a simple transform to achieve sanitization results. For every received channel response, the slope they calculate is the correlation of the difference between the current phase function and the first data when the measurement noise $(Z_f)$ is infinitesimal. The difference with our method is that we first reduce the noise of data packets from previous packet, and second, for a single packet, then sanitize the sub-carrier from previous sub-carrier. Log likelihood distance (LLD) ¹² achieves excellent noise reduction through the reduction of secondary noise to the sub-carrier time interval. This interval exceeds $(2/3)\pi$ , based on the Intel 5300 NIC condition. However, this method does not effectively reduce the localization errors because the corrections are executing when the attenuation is greater than $(2/3)\pi$ , when the phase less than $(2/3)\pi$ and the phase noise reduction loses its effect. Besides, the localization arithmetic model is based on the distance of the signal, but the proposed method in this article using a back-propagation (BP) neural network model to achieve positioning results. The fast orthogonal search (FOS) algorithm ¹³ calculates the weight of the original CSI signal, and the noise and numerical error in the original data directly affect the localization performance of the system. Y Chapre ¹⁴ propose a multiple-input multiple-output (MIMO) system; this approach incorporates MIMO information and extracts relatively robust fingerprints, and the phase values are subtracted for subsequent sub-carriers.

An indoor fingerprint localization algorithm that is based on principal component analysis (PCA) and phase difference (PD) corrections, that is, the principal component analysis and phase difference sanitization (PCA-PD) algorithm, is proposed in this article. First, the offline phase is used to correct phase information in the communication link. Second, based on PD filtering, the system uses the PCA method to reduce the dimensionality of the data and establish a robust fingerprint feature database. A mapping relationship model between the sampling signal and physical locations is established using a BP neural network in the last step of the offline phase. During the online phase, the final location was estimated through network model computing based on differential phase pre-processing. The final location estimation is obtained by computing real-time sampling values and fingerprint values.

System model and relevant definitions

The localization methods based on fingerprint databases obtain accurate localization results by finding one-to-one correspondences between physical locations and the fingerprint databases, which are constructed using the signal features in real-time sampling. Device-free fingerprint localization means localization without carrying any devices. A BP neural network is employed as the model used in training and classification based on the fingerprint data. This neural network includes an array of mapping collections $L=\{L_1,L_2,\dots ,L_N\}$ between the signal and the physical locations, and many transmission targets $U_i(i\in \{1,2,\dots ,M\})$ exist along the communication links from the transmitter to the receiver. The targets are the CSI data sets received by the signal receiver. Alternatively, the Atheros-CSI tool ¹⁵ driver source code, which supports the IEEE 802.11n standard at the kernel level, can be modified to support NICs, and its applications can be rewritten to perform more advanced extraction of CSI. The signal communication model of CSI can be illustrated as follows

$${U^{\prime }}_i=H{U}_i+N$$

(1)

where matrix N refers to additional white gaussian noise, whereas H refers to the channel frequency response (CFR); therefore, the CSI matrix can be illustrated as

$$H=\left(\begin{array}{cccc}{H}_{1,1}\hfill & H_{1,2}\hfill & \cdots \hfill & H_{1,j}\hfill \\ \multicolumn{1}{c}{H_{2,1}}& H_{2,2}\hfill & \cdots \hfill & H_{2,j}\hfill \\ \multicolumn{1}{c}{⋮}& ⋮\hfill & \ddots \hfill & ⋮\hfill \\ \multicolumn{1}{c}{H_{i,1}}& H_{i,2}\hfill & \cdots \hfill & H_{i,j}\hfill \end{array}\right)$$

(2)

H is the CSI matrix between the transmitter $U_i$ and the receiver $U{\prime }_i$ , and $H_{i,j}$ stands for each sub-carrier. In addition, i and j represent the serial numbers of the communication link and the sub-carrier, respectively. The data set $U_i$ is a type of sequence set of inter-data group sequences. We need to reduce the noise of the phase in the CSI feature information to decrease the signal errors received by the signal receiver. The IEEE 802.11n protocol stipulates the sub-carrier number in different bandwidths; when the bandwidth is 20 MHz, j is 30 in group 2, and when the bandwidth is 40 MHz, j is 114 in group 1. We can define the $j\mathrm{th}$ sub-carrier of the $i\mathrm{th}$ link as

$$H_{i,j}=\left|H_{i,j}\right|e^{j\prime \sin \angle H_{i,j}}$$

(3)

Figure 1 shows 100 measurements of 114 sub-carrier phases in channel 1 of the 3 × 1 antenna beams (including one transmitting antenna and three receiving antennas) for a communication system employing the 40 MHz bandwidth. The raw phases of locations 1 and 2 are represented in Figure 1(a) and (b), and their unwrapped phases can be found in Figure 1(c) and (d). From these four panels, we conclude that the CSI phase shows different curves in different propagation environments, which also verifies the localization feasibility and shows that the CSI phase can be used as a signal feature fingerprint.

Figure 1.

Raw phase and unwrapped phase for two locations: (a) raw phase for location 1, (b) raw phase for location 2, (c) the unwrapped phase for location 1 and (d) the unwrapped phase for location 2.

The noise reduction process includes three stages, specifically inter-group data noise reduction, intra-group data noise reduction and very large reductions in the dimensionality of the data. Inter-group data noise reduction involves removing errors due to continuous sampling, and intra-group data noise reduction involves removing the set $U_i$ and the frequency offset error among the sub-carriers. To build the robust fingerprint feature database after the noise reduction is complete, the PCA method is applied in this article. The reduction in the dimensionality of the data is intended to reduce the redundancy of the information in the fingerprint data, reduce the dimensionality of the fingerprint data, reduce the complexity of the calculations and increase the operation speed of the subsequent recognition step. The extraction of fingerprint feature data from the communication links between the transmitting antenna and the receiving antenna is carried out after omni-directional matching. Each link includes representative information on the environments of the sub-carriers. However, each one-dimensional fingerprint within the data includes a large number of sub-carriers. In essence, the PCA algorithm extracts data in a high-dimensional space into a low-dimensional space through orthogonal transformation. This procedure both reduces the dimensionality of a large quantity of fingerprint data and preserves the original characteristics of the fingerprint data to the greatest possible extent, thus permitting the data to contribute to the construction and comparative analysis of the BP neural network model.

Definition 1

Suppose ${\varphi }_{\varsigma ,\rho }=[{\varphi }_i{\varphi }_2\cdots {\varphi }_j]$ is the phase without error offsets when there are j sub-carriers. Thus $\varsigma$ of ${\varphi }_{\varsigma ,\rho }$ represents the measurement times, and $\rho$ represents the sub-carrier serial numbers.

Definition 2

Defining ${\theta }_{m,n},m=1,\dots ,\varsigma ,n=1,\dots ,\lambda$ as the phase gained from actual measurements, m represents the measurement times, and n represents the sub-carrier serial numbers.

Definition 3

We define the measured phase value $\epsilon \mathrm{th}$ as

$${\theta }_{\epsilon }=[{\theta }_{1,1}{\theta }_{1,2}\cdots {\theta }_{1,n}]$$

(4)

Definition 4

The random time offset and random phase offset of the $\epsilon \mathrm{th}$ measurement are defined as ${\alpha }_{\epsilon },{\beta }_{\epsilon }$ . Thus, the phase error is given by ${\theta }_{\epsilon }={\varphi }_{\epsilon }+2\pi f*{\alpha }_{\epsilon }+{\beta }_{\epsilon }$ , and f represents the frequency interval of the adjacent sub-carrier.

Definition 5

We define the phase value difference of the adjacent sub-carrier as $\Delta {\theta }_{\epsilon ,n}$

$$\Delta {\theta }_{\epsilon ,n}={\theta }_{\epsilon ,n+1}-{\theta }_{\epsilon ,n}$$

(5)

Definition 6

We define the sub-carrier phase correction as

$$\theta {\prime }_{\epsilon }=\varphi {\prime }_{\epsilon }+2\pi f*\alpha {\prime }_{\epsilon }+\beta {\prime }_{\epsilon }$$

(6)

PCA-PD indoor localization system

Localization system architecture

The proposed rules of PD relate to noise reduction between the CSI phase sampling data, and noise reduction of the CSI sub-carriers are very important to the system. As shown in Figure 2, the PCA-PD processing of the characteristic data is conducted in both offline and online phase simultaneously. This processing includes removing errors (specifically inter-group errors) generated during successive data sampling, correcting outliers among each communication link among the sub-carriers (intra-group errors) and PCA reduction of the dimensionality of the fingerprint data. The obtained fingerprint feature information is stored in the database for use in training the BP neural network. The mapping between the phase information and the physical location fingerprints is established through continuous learning and calculation. Finally, during the online phase and after the aforementioned PCA-PD processing has been performed, the real-time test point values of the phases yield estimates of physical locations by supplying inputs to and analysing the outputs from the BP neural network model.

Figure 2.

Position system operation framework.

Noise reduction for inter-group errors

The signal received by the receiver changes due to the multi-path transmission effect of the signal, and continuous CSI phase sampling at the same physical position over a short period of time also produces errors. The range of phase values after unwrapping the raw phase is $\Delta \partial (\Delta \partial \in [-\pi ,\pi ])$ , and a $2\pi$ jump in the phase is produced with real linear variations. To avoid the inter-group errors that affect the processing results of the intra-group errors, the inter-group errors must be removed first. The sampling values of the single phase are recorded as a set. The above two errors actually exist after continuously sampling 100 sets of data at the same position and carrying out a comparative analysis. Samples 14, 15, 16, 17 and 18 in the sampled data set are regarded as typical representatives for processing, as shown in Figure 3. As shown in Figure 3(a), sample 17 displays the same change in phase as samples 16 and 15, and the measured values of samples 17 and 18 differ substantially from those of the above three groups. Figure 3(b) illustrates the differences between pairs of sub-carriers. Figure 3(c) is the result of the denoised PD value data, and Figure 3(d) is that we restore the denoised PD result to the raw phase value. The results show that the differences in the curves with the same trend are horizontal straight lines, while the PD with different trends displays a certain angle. During processing, the phase represented by the non-parallel sampling difference must be removed from the overall fingerprint data set. The specific steps are as follows:

• Step 1: The phase information ${\theta }_{\epsilon }$ is extracted through unpacking the $\epsilon$ CSI data, and the raw phase information of each link is recorded in sequence.

• Step 2: The unwrapped phase ${\omega }_{\epsilon ,n+1}$ is obtained by applying the unwrapping method to the raw phase data. The following rules are used to process each ${\omega }_{\epsilon ,n+1}$

  $${\omega }_{\epsilon ,n+1}=\{\begin{array}{c}{\omega }_{\epsilon ,n}+\Delta f_{\epsilon ,n}-2\pi ,\Delta f_{\epsilon ,n}>\pi \hfill \\ \multicolumn{1}{c}{{\omega }_{\epsilon ,n}+\Delta f_{\epsilon ,n}+2\pi ,\Delta f_{\epsilon ,n}<-\pi }\\ \multicolumn{1}{c}{{\omega }_{\epsilon ,n},-\pi <\Delta f_{\epsilon ,n}<\pi }\end{array}$$
  (7)

• Step 3: The set of recorded $\Delta {\theta }_i$ values is $(X_i,Y_i)$ , and the curves reflecting the relation between Y and X are fitted using the least-squares method. Let

$$Q=\sum _{i=1}^n{[Y_i-({\sigma }_0+{\sigma }_1{X}_i)]}^2$$

(8)

When Q reaches the minimum value, the following condition is satisfied

$$\{\begin{array}{c}{\sigma }_0=\frac{\sum _{i=1}^n(X_i-\overline{X})Y_i}{\sum _{i=1}^n{(X_i-\overline{X})}^2}\hfill \\ \multicolumn{1}{c}{{\sigma }_1=\overline{Y}-{\sigma }_0\overline{X}}\end{array}$$

(9)

• Step 4: Let ${\sigma }_0=0$ and set a threshold range of angles $[-(1/8)\pi ,(1/8)\pi ]$ for ${\sigma }_1$ , the phase data that are not contained within this range are removed.

Figure 3.

Inter-group data denoising process: (a) the sampled phase, (b) the phase difference, (c) the valid phase and (d) the valid phase difference.

From the previous four steps, the error produced between the sampling point values of the phase is removed. By analysing and comparing the differences between the data of the sub-carriers, the incorrect data packets and error packets are removed. This method achieves remarkable results in reducing the noise in the sampled data from the perspective of global optimization.

Noise reduction for intra-group errors

Because the denoising range of the intra-group data depends on the error condition between the sub-carriers, different phases display diverse inter-group error values. The phase error of the offset also exists for all of the data packets. The differences among the sub-carriers in six consecutive data samples are shown in Figure 4(b)–(g), which show the error offset. The error fluctuation point marked by the circle indicates the location where the abnormal phase offset is generated.

Figure 4.

Intra-group data denoising process: (a) the unwrapped phase, (b) unstable phase difference in 30th phase, (c) traps point of inverse tangent in 31th phase, (d) unstable phase difference in 32th phase, (e) traps point of inverse tangent in 33th phase, (f) unstable phase difference in 34th phase and (g) traps point of inverse tangent in 35th phase.

At the same time, as shown in Figure 5, sub-carriers 55 and 58 display $2\pi$ jumps. The unwrapping method can only address $|{\varphi }_{\epsilon ,n+1}-{\varphi }_{\epsilon ,n}|>\pi$ . When there is a offset delay error in the phase, and the produced offset satisfies $|{\varphi }_{\epsilon ,n+1}-{\varphi }_{\epsilon ,n}|<\pi$ , the error phase is not corrected. In this case, the correct phase is assumed to have been found, and this step can be ignored.

Figure 5.

Wrapped phase produced $2\pi$ jump in exceptional circumstances.

The specific steps used to reduce the above phase error in intra-group data and clearly demonstrate the noise reduction filtration algorithm are as follows:

• Step 1: Based on a previous study, ¹⁶ the error between the sub-carriers is recorded as ${\theta }_{\epsilon }={\varphi }_{\epsilon }+2\pi f*{\alpha }_{\epsilon }$ . The serial number of difference j sub-carrier is $j-1$ , and the PD set $T=\{T_1,T_2,\dots ,T_{j-1}\}$ is set to 0 in advance.

• Step 2: The CSI difference for each package is calculated as

  $$T_i={\theta }_{i+1}-{\theta }_i$$
  (10)

• Step 3: The difference is added to the set according to the serial number, and the new sets are obtained. A threshold $\delta$ is set as the weight factor of the difference correction method

  $$\begin{array}{c}{T}_i=T_i-(T_i-\frac{\sum _{j=0}^n{T}_j}{n})\times \delta \hfill \\ \multicolumn{1}{c}{=T_i(1-\delta )+\frac{\delta \sum _{j=0}^n{T}_j}{n}}\end{array}$$
  (11)

• Step 4: On the basis of the initial values, the original values are recast using the differences

  $${\theta }_{m,j}={{\theta }_{m,}}_{j+2}-(T_j+T_{j+1})$$
  (12)

• Step 5: The known parameters ${\alpha }_{\epsilon }$ to get ${\beta }_{\epsilon }$ determined via linear fitting are employed, resulting in the final phase expression

$$\theta {\prime }_{\epsilon }=\varphi {\prime }_{\epsilon }+2\pi f*\alpha {\prime }_{\epsilon }+\beta {\prime }_{\epsilon }$$

(13)

Dimension reduction and BP neural network model

After noise reduction in inter-group data and in intra-group data, the phase pre-processing method can effectively eliminate noise, and its performance is better than that of other methods. The original phase values are subjected to noise removal in inter-group data and noise removal in intra-group data. The specific steps used to apply PCA to the fingerprint data set to reduce its dimensionality are as follows:

• Step 1: The whole pre-processed fingerprint data matrix is obtained. In total, there are L locations, and the size of each sample is $M\times N$ . Each training sample matrix is then the $L=[l_1,l_2,\dots ,l_n{]}^T$ , the size of the entire data matrix is $n\times (M\times N)$ , and n is the serial number of the sub-carriers. The original feature vector is mapped to the P-dimensional subspace.

• Step 2: Calculate the training average and the difference

  $$\Psi =\frac{1}{n}\sum _{i=1}^{i=n}{l}_i,d_i=l_i-\Psi$$
  (14)

• Step 3: Construct a covariance matrix

  $$C=\frac{1}{n}\sum _{i=1}^n{d}_i{d}_i^T=\frac{1}{n}A{A}^T$$
  (15)

  where the A expressed as $[d_1,d_2,\dots ,d_n]$ .

• Step 4: Solve for the eigenvalues and eigenvectors of the covariance matrix and obtain the eigenvalues and eigenvectors of $A{A}^T$ by solving for the eigenvalues and eigenvectors of $A{A}^T$ .

• Step 5: Select the appropriate principal components, sort the obtained eigenvalues, and take the top P eigenvectors and eigenvalues. Find the original eigenvector of the covariance matrix as

  $$D_i=\frac{1}{\sqrt{\lambda }}A{v}_i(i=1,2,\dots ,p)$$
  (16)

The linear transformation matrix composed of the first P largest eigenvectors can then be obtained as W

$$W=[D_1,D_2,\dots ,D_p]$$

(17)

• Step 6: Projecting the original input feature vector into a P-dimensional subspace yields

$${\Omega }_i=W^T{d}_i(i=1,2,\dots ,n)$$

(18)

The system uses a standard BP neural network with a three-layer model structure. This structure includes an input layer, a hidden layer and an output layer. The input layer includes P neuronal cells and represents a simplification of the normalized phase values of the sub-carriers. The output layer includes 25 neuronal cells that represent 25 grid cells at the corresponding locations in the physical grid space. BP neural networks adopt gradient-correction methods to learn their weights and thresholds. Two important aspects that affect the learning efficiency of the BP neural network model are the number of hidden nodes and the learning rate. The level of learning efficiency determines the speed with which the error decreases in the initial stage. At the same time, gradual learning based on the fingerprint data set leads to non-convergence of the learning process and cannot meet the requirements of localization. The system compares the final errors through the choice of parameters and after 3000 epochs for different values of the learning rate and the number of hidden nodes. The 25-grid-cell model training process is as follows:

• Step 1: Network initialization: based on the number of test point value sub-carriers in the system and the grid sequence identity Y, the number of nodes in the input layer n; the number of nodes in the hidden layer l; the number of nodes in the output layer m; the neuronal cell link weights of the initialized input layer ${\omega }_{\mathrm{ij}}$ , ${\omega }_{\mathrm{jk}}$ ; the hidden layer and the output layer; the initialized hidden layer threshold a and the output layer threshold b are determined, given the learning rate and excitation functions of the neurons.

• Step 2: Calculation of the output of the hidden layer: based on the input variable X, the link weights ${\omega }_{\mathrm{ij}}$ of the input layer and the hidden layer, and the hidden layer threshold a, the output of the hidden layer H is calculated

  $$H_j=f(\sum _{i=1}^n{\omega }_{\mathrm{ij}}{X}_i-a_j)$$
  (19)

  where l is the number of nodes in the hidden layer, and f is the hidden layer. The algorithm chooses the following function

  $$f(x)=\frac{1}{1+e^{-x}}$$
  (20)

• Step 3: Calculation of the output from the output layer: based on the output from the hidden layer H, the link weight ${\omega }_{\mathrm{jk}}$ and the threshold b, the predictive output of the BP neural network is calculated as O

  $$O_k=\sum _{j=1}^l{H}_j{\omega }_{\mathrm{jk}}-b_k$$
  (21)

• Step 4: Error calculation: based on the network prediction output O and the expected output Y, a network prediction error e is calculated

  $$e_k=Y_k-O_k$$
  (22)

• Step 5: Weight updating: based on the network prediction error e, the network link weights ${\omega }_{\mathrm{ij}}$ , ${\omega }_{\mathrm{jk}}$ can be updated

  $${\omega }_{\mathrm{ij}}={\omega }_{\mathrm{ij}}+\eta H_j(1-H_j)x\left(i\right)\sum _{k=1}^m{\omega }_{\mathrm{jk}}{e}_k$$
  (23)
  $${\omega }_{\mathrm{jk}}={\omega }_{\mathrm{jk}}+\eta H_j{e}_k$$
  (24)

  where $\eta$ is the learning rate.

• Step 6: Threshold upgrading: based on the network prediction error e, the network node thresholds a and b can be updated

  $$a_j=a_i+\eta H_j(1-H_j)\sum _{k=1}^m{\omega }_{\mathrm{jk}}{e}_k$$
  (25)
  $$b_k=b_k+e_k$$
  (26)

• Step 7: Determine whether the iterative evaluation of the algorithm has completed. If not, return to Step 2.

The performance of the model can be determined by comparing the output of a given standard physical location grid number with the output corresponding to the physical location of the grid cell after the BP neural network has been trained. The feasibility of the proposed localization algorithm is verified.

Experimental study

Experimental configuration

The verification of the performance of the algorithm is carried out in an actual experimental scenario. To collect CSI data, three desktop computers are used to realize the functionality of an entire localization system, and these machines are used to represent a transmitter, a receiver and a data processing machine. Two of these machines are equipped with Atheros 9380 NICs and run version 16.04 LTS of the Ubuntu operating system. To transmit to the receiver desktop, the transmitter uses one antenna in the injection mode. The receiver desktop works in monitoring mode to receive data using all three antennas. The data-processing desktop is connected to the router through a cable, and the antenna is connected using a 1.5-m external antenna. The length and width of the experimental site are 15 m × 10 m, and the site contains 5 × 5 grid cells with lengths and widths of 0.96 m × 1.1 m, respectively. These features of the experimental site are shown in Figure 6(a) and (d), respectively. The height of the antenna from the ground is 1 m. The position of the antenna is shown in Figure 6(b) and (c). The parameters of the tool are modified, ¹⁷ and the data packet transmission rate of the transmitter is adjusted to 1500 packages per second. A total of 3000 CSI data samples are collected at each position, and the final error is determined after 1500 learning epochs. Finally, the best network learning efficiency is determined according to the error. The different nodes and learning rates used in the actual learning process influence the final error of the BP neural network algorithm. Based on the final error and learning time, the following conclusions can be drawn by analysing the actual data. The number of hidden nodes in this system is set to 21, and the learning ability of the BP neural network is optimized.

Figure 6.

Experimental scene diagram and antenna placement: (a) an overview of laboratory layout, (b) the height of receiver antenna, (c) the height of transmitter antenna and (d) the real experiment scene.

Experimental analysis

Impact of the threshold $\delta$ on the localization performance

In the PCA-PD noise reduction algorithm, the slope of the curve threshold is preset as the variable point. The size of the variable reflects the degree of data filtering among the sampled values. Changes in this threshold have an impact on the localization performance of the system. When the threshold is set to 0, 0.2, 0.4, 0.6 and 0.8, the filtering effect between single links is shown in Figure 7. As the threshold value increases, the unstable peak of the data shown in Figure 7(b)–(f) reflects a gradual change in the strength of the data in sub-carrier error filtering. Moreover, the data demonstrate a shift from a completely random state to the loss of signal characteristics . This figure indicates that, while the size of the threshold is proportional to the removal of the noise, it is not necessarily proportional to the localization performance of the system. When the threshold is gradually increased, the noise reduction graph of the intra-group error is shown in Figure 7. The error value tends to be flat as the threshold increases, for example, the error fluctuation is extremely slight in the case where the threshold is 0.8. The increase in the threshold illustrates the effect of error value noise reduction; namely, the inter-group error becomes larger. Nevertheless, the enhancement of the effect of noise reduction does not necessarily improve the localization performance of the system. In Figure 8, when the threshold is gradually changed from 0.1 to 0.6, the localization error of the system gradually decreases. While the localization error displays a small increase at 0.4, the overall localization error tends to decrease. In the situation in which the threshold is 0.6, the minimum localization error is 1.15 m and the localization error increases slightly after 0.6.

Figure 7.

The influence of the diverse threshold on the error filtering strength: (a) the phase difference for 30th phase, (b) phase difference for $\delta =0$ , (c) phase difference for $\delta =0.2$ , (d) phase difference for $\delta =0.4$ , (e) phase difference for $\delta =0.6$ and (f) phase difference for $\delta =0.8$ .

Figure 8.

The influence of the threshold on localization error.

According to the overall localization performance of the system, this phenomenon shows that the noise generated during the period of continuous data sampling is more important than the data reduction among the sub-carriers.

Effects of different sample sets on the localization results

The training sample set size of the CSI phase data also affects the localization performance of the system. Given the same environmental parameters, different sample sets are selected to conduct the training. The sampling frequency of the system sample data is 1500 pacakages per second. As shown in Figure 9, the number of samples is set to 1000, 2000, 3000, 4000, 5000 and 6000. The system localization error is shown in Figure 9, which considers threshold values of 0.2, 0.4 and 0.6 and the effects of different training times. When the number of training sets is the same, the localization error with a threshold of 0.2 is always greater than when thresholds of 0.4 and 0.6 are used. As the number of training samples increases, the difference in the localization error between the thresholds of 0.4 and 0.6 is greater. In particular, when the scale of the training sets is 3000, the localization error corresponding to the three thresholds reaches its minimum, and the localization error is 1.15 m when the threshold is 0.6. In summary, when the system selects 3000 sets of sample data, the localization performance of the system is optimized.

Figure 9.

The influence of the sampling numbers.

Impact of PCA

A communication link has only 114 sub-carrier values in total. The process of reducing the dimensionality of the data via PCA involves selecting representative values for the 114 sub-carriers. As shown in Figure 10, we select latitudes of 15, 25, 33, 41, 48 and 55 to measure the location performance of the system at different thresholds. In the scenarios in which different thresholds are used, the location accuracy decreases as the dimensionality of the data increases . When p<33 (p is the reduced dimensionality of the data), the localization accuracy achieved for a threshold value of 0.2 is greater than the localization accuracy obtained for threshold values of 0.4 and 0.6. Meanwhile, the localization accuracy represented by the threshold values of 0.2 and 0.4 has an approximate value when p=33. In the cases in which p=41 and p=48, the position accuracy curve represented by the threshold value 0.4 displays a small increase compared to the threshold of 0.2. As p is gradually increased, the three positioning accuracy curves all display decreasing trends, and the localization accuracy also decreases gradually. When p=48, the minimum localization accuracy is obtained for the threshold in all cases, and the minimum localization accuracy is 1.15 m when the threshold is 0.6. For the case in which the threshold is 0.2 and p=33, the localization accuracy is reduced by the maximum degree. When p=48 and the threshold is 0.4 or 0.6, we obtain the largest reduction in the localization error. Compared with p=48, the localization performance of the system for a threshold of 0.6 and p=55 is not obviously reduced; instead, it shows a slight increase.

Figure 10.

The influence of the principal component parameter p.

Overall performance of the algorithm

According to the CSI phase information extracted from the communication links of the system, we select uniform environmental parameters for use in the localization methods to verify the performance of the algorithm proposed in this article. As shown in Figure 11, we compare the performance of the proposed system with FIFS, ¹⁰ DeepFi, ¹⁵ FOS algorithm, ¹⁸ PinLoc ¹¹ and LLD method. ¹² CSI values are collected from 3000 packages at each position. At the same time, we set the error removal threshold to 0.6 in intra-group data. The cumulative distribution function (CDF) of the distance error is presented in Figure 11, and the mean and standard deviation of the location errors are presented in Table 1. From the Figure 11, it can be concluded that, with the proposed system, approximately 67.2% of the test samples have an error under 1 m and 99.9% have an error under 2 m, while FOS ensures that approximately 53.4% of the test samples have an error under 1 m and 92.6% have an error under 2 m. The localization performance achieved by the PCA-PD noise reduction algorithm is better than that of the FOS noise reduction algorithm. The error cumulative probability of the FOS, DeepFi and FIFS algorithms is 79.2%, 77.8% and 63.7%, respectively, when the localization error is 1.5 m. PinLoc in the existing test experimental environment with movable desktop base, 1-m antenna and 9380 network card achieves 33.4% probability of acuracy when positioning error less than 1 m. Compared with PCA-PD, the LLD method achieves good positioning accuracy when the positioning error is less than 0.7 m, but the positioning accuracy is only 85.6% when the positioning error is less than 1.5 m. Therefore, generalize from overall performance, these localization methods are not able to perform as well as the proposed system. Compared with FOS, the proposed algorithm displays a 12.7% improvement in accuracy. This result shows that the proposed system is efficient in improving the system performance. In the FIFS, the cumulative probability of error is only 63.7% within 1.5 m and less than 80% within 2 m. The aforementioned experiment shows that the proposed algorithm yields better localization performance than the other five algorithms.

Figure 11.

The systems overall localization performance.

Table 1.

Comparison of method overall localization performance.

Localization method	Average error (m)	Standard error (m)	Localization accuracy (1 m)
PCA-PD	1.4223	1.1511	67.7%
FOS	1.5955	1.4126	53.4%
DeepFi	1.7932	1.3113	40.04%
FIFS	2.3601	1.0186	37.78%

PCA-PD: principal component analysis and phase difference sanitization; FOS: fast orthogonal search; FIFS: fine-grained indoor fingerprinting system.

Table 1 compares the overall localization performance of the four localization algorithms. From the table, it can be concluded that the average errors of FOS, DeepFi and FIFS are 1.5955, 1.7932 and 2.3601 m, while the average error corresponding to this algorithm is 1.4223 m and the standard error is 1.1511 m. Compared with other algorithms, the average localization error of the proposed algorithm is reduced by 10.86%, 20.68% and 39.73%. The algorithm features higher localization accuracy and smaller errors, and it can be effectively applied to indoor localization. The proposed algorithm has a localization accuracy of 67.7% at 1 m, which corresponds to an improvement in localization accuracy of 14.3%, 27.66% and 29.92% when compared to the other methods.

Related works

The literature on wireless localization based on RF fingerprinting is wide; hence, we will only discuss the major results on the topic. Several wireless systems have been used to apply the concept of RF fingerprinting for localization, including the most common Wi-Fi networks, ¹⁹ but also radio-frequency identification (RFID) technologies,^18,20 bluetooth^17,21 and ultra-wideband (UWB).^22,23 A combination of wireless technologies can be used to improve localization accuracy. ²⁴ RF fingerprinting can be carried out using received signal features, in particular signal strength, such as RSSI, reference signal received power (RSRP), reference signal received quality (RSRQ) and CFR/CSI or equivalently the channel impulse response (CIR).^4,6,25,26 Time of arrival (TOA), timing advancing (TA), time difference of arrival (TDOA) and angle of arrival (AOA) are less frequently used in fingerprinting-based approaches.^27,28 In addition to using wireless signal processing methods, many researchers have tried a variety of approaches to improve positioning problems in the field of indoor localization. As with all communication mediums, there are other mediums, such as geomagnetism,^29,30 visible light ³¹ and simultaneous localization and mapping (SLAM). ³²

Conclusion

In this article, an indoor fingerprinting localization algorithm that is based on PCA-PD and BP neural networks is proposed. The algorithm uses the PCA-PD data sanitization method as the pre-processing method to denoise the original position feature information and obtain good data with localization features. In the online phase, the real-time measured CSI values are classified using a BP neural network model. The back propagation neural network and phase difference (BP-PD) algorithm is verified experimentally in a 5 × 5 grid space in a real environment. The performance of the PCA-PD, FOS, DeepFi, FIFS, PinLoc and LLD methods are compared, and the impact of the threshold $\delta$ and different numbers of sampling sets and principal components p on the performance of the algorithm are studied. Compared with other localization systems based on BP neural networks, the overall performance of the algorithm has higher classification accuracy and achieves a localization accuracy of 96.2% within 1.5 m and 67.7% within 1 m. In this article, the test target is one person standing in a specific area. The follow-up studies will consider the case in which multiple individuals are to be localized simultaneously.