Research on 3D Localization of Indoor UAV Based on Wasserstein GAN and Pseudo Fingerprint Map

Abstract

In addition to outdoor environments, unmanned aerial vehicles (UAVs) also have a wide range of applications in indoor environments. The complex and changeable indoor environment and relatively small space make indoor localization of UAVs more difficult and urgent. An innovative 3D localization method for indoor UAVs using a Wasserstein generative adversarial network (WGAN) and a pseudo fingerprint map (PFM) is proposed in this paper. The primary aim is to enhance the localization accuracy and robustness in complex indoor environments. The proposed method integrates four classic matching localization algorithms with WGAN and PFM, demonstrating significant improvements in localization precision. Simulation results show that both the WGAN and PFM algorithms significantly reduce localization errors and enhance environmental adaptability and robustness in both small and large simulated indoor environments. The findings confirm the robustness and efficiency of the proposed method in real-world indoor localization scenarios. In the inertial measurement unit (IMU)-based tracking algorithm, using the fingerprint database of initial coarse particles and the fingerprint database processed by the WGAN algorithm to locate the UAV, the localization error of the four algorithms is reduced by 30.3% on average. After using the PFM algorithm for matching localization, the localization error of the UAV is reduced by 28% on average.

1. Introduction

Geospatial awareness has emerged as a pivotal concern within the realm of intelligent spaces, particularly in scenarios involving the flight of the unmanned aerial vehicle (UAV) [1,2], also known as a drone. Presently, the predominant method for location sensing relies on the Global Navigation Satellite System (GNSS), such as the Global Positioning System (GPS), BeiDou navigation satellite system (BDS), GLONASS, and Galileo [3]. However, the reception of these signals, which emanate from satellites, encounters challenges when situated indoors or amid densely populated urban landscapes. Consequently, extensive studies of indoor localization have been directed toward elucidating methodologies utilizing signals derived from prevailing wireless infrastructures, including cellular networks [4], Ultra-Wideband (UWB) [5], Bluetooth [6], and Wi-Fi [7]. Among these technologies, Wi-Fi is undoubtedly the most likely to be combined with UAV to achieve indoor localization purposes. The widespread deployment of Wi-Fi access points (APs) and the pervasive integration of the Received Signal Strength (RSS) sensing capability in UAVs underscore Wi-Fi’s suitability for the development of such location systems [8].

Fingerprint localization is the most practicable way for balancing localization precision and efficiency in an RSS-based Wi-Fi indoor localization system. Compared with fingerprinting, ranging methods tend to be less complex. However, the choice of the fingerprinting method in this paper is justified due to its superior accuracy and robustness in complex indoor environments, particularly for 3D localization. Fingerprinting methods excel in environments with multipath effects, signal interference, and non-line-of-sight (NLoS) conditions, where ranging methods typically struggle. Moreover, 3D localization requires higher precision, and fingerprinting allows the incorporation of more diverse environmental features, making it more suitable for such applications. Therefore, fingerprinting is selected to achieve the desired accuracy and robustness in 3D indoor positioning tasks. In RSS-based fingerprint indoor localization systems, there exist two fundamental phases: an offline training phase and online localization phase [9]. The main task of the offline phase is to generate reference points (RPs), or fingerprints. The RP is generally the center of a certain grid after a uniformly gridded field, which includes a known location coupled with an RSS vector collected from the active Wi-Fi APs in the field. All RP fingerprints on the site are combined to form a fingerprint database. In the online localization phase, real-time RSS vectors from the target are matched using RPs with the fingerprint database established in the offline phase [10].

Fingerprinting stands out as a widely embraced technology for indoor localization, proficiently delineating the intricate electromagnetic environment through the meticulous collection of numerous location fingerprints during the offline phase. Nevertheless, the precision of localization hinges upon the deployment of an extensive and densely distributed array of RPs [11,12]. Especially when the target that needs to be positioned is a UAV, the entire indoor space is measured in 3D space, and the number of RPs increases exponentially compared with 2D plane localization. This necessitates a substantial investment in labor and time for a comprehensive site survey conducted by a skilled surveyor. Furthermore, alterations in the Wi-Fi environment, including disruptions caused by human movement or adjustments in the configuration of Wi-Fi APs, can potentially influence the temporal accuracy of the fingerprint database. This requires timely updates to the database to address environmental changes, making the maintenance workload larger and more challenging [13,14]. Methods for addressing this issue vary depending on different purposes, but algorithms based on machine learning are the most common and effective, such as deep neural network (DNN) [15], Gaussian process regression (GPR) [16], and generative adversarial networks (GANs) [17,18]. Among these algorithms, GANs, with their outstanding capabilities in data augmentation and model generalization, are increasingly being employed by scholars for the purpose of transforming fingerprint signals.

GANs represent an unsupervised machine learning algorithm comprising a generator G and a discriminator D. The generator G, fueled by random noise inputs, produces synthetic data, while the discriminator D assesses the authenticity of the provided data. Both components undergo simultaneous optimization during adversarial training. The generator’s objective is to craft realistic data, rendering them indistinguishable for the discriminator, which, in turn, strives to continuously enhance its capacity to discern between real and fabricated elements. This adversarial training engenders an enduring feedback loop, ultimately enabling the generator to generate synthetic data that are nearly indiscernible from authentic datasets [19]. GANs represent formidable generative models proficient in producing lifelike examples utilizing a stochastic vector r. GANs obviate the necessity for explicit knowledge of a true data distribution or reliance on predetermined mathematical assumptions. These inherent advantages render GANs highly versatile for applications across diverse domains, including image processing, data construction, and sensing communication [20,21].

Different variations of the GAN model have been used in RSS-based indoor fingerprinting localization systems. WiGAN, an automatic scheme for constructing fine-grained indoor ratio maps and an adaptation approach empowered by GPR-conditioned least-squares GANs (GPR-GANs) with a mobile robot, is proposed in [22]. However, GPR algorithms are commonly used for regression tasks, and their performance may be limited by the dimension and complexity of the data. When combining GANs, it can increase the complexity of the overall system, leading to problems that are difficult to interpret or optimize. An Amplitude-Feature Deep Convolutional GAN (AF-DCGAN) model is proposed to extend the Channel State Information (CSI)’s, not RSS values’, fingerprint database [18], and the same case also includes [23,24]. Although a GAN-based method is introduced to increase the amount of training RSS data collected at each RP in [25], it is based on a Bluetooth low-energy (BLE) landmark. The above methods are all general smart device localizations in the 2D plane, and as far as we know, the GAN algorithm has not been used to realize UAV localization in a 3D indoor space.

The Wasserstein GAN (WGAN)-based estimation proposed in [26] is extended in this paper to complement and enrich RSS fingerprint data. WGAN outperforms traditional GANs in generating higher-quality and more realistic samples, making it more advantageous for later target localization when augmenting fingerprint databases. Focusing on WGAN and the WGAN inversion model (WGAN-IM), a localization strategy is presented in this paper incorporating a corrections-based fingerprint model. During the online phase, the fine-grained fingerprint database is upgraded by using the data imputation function of WGAN according to the 3D initial fingerprint database of coarse particles or the UAV crowd-sensing signals. In the online phase, the pseudo fingerprint map (PFM) plane information is generated using WGAN-IM based on the single fingerprint information of the located target UAV combined with its inertial measurement unit (IMU) information during flight. Finally, the fine-grained fingerprint database is matched with a suitable matching algorithm to realize the localization of the UAV.

The overall structural block diagram of this study is shown in Figure 1, and the key contributions are as follows:

(1)

In the offline phase, the WGAN algorithm is used to supplement and complement the data in a coarse-grained fingerprint database. The generator and discriminator are trained using the initial RSS dataset, and the synthesized RSS data are generated using the generator and fed into the discriminator along with the real data for adversarial training. During the training process, the weights of the generator and discriminator are adjusted so that they are balanced. The feasibility and effectiveness of the proposed method are verified by algorithm derivation and simulation test.

(2)

In an indoor environment where UAVs are operating, the 3D spatial volume is divided into small cubic cells, with each cell serving as a collection point for fingerprint data. The enhanced fingerprint database generated by WGAN is then used in the UAV localization system. In addition to using the RSS value of Wi-Fi, it relies on the inertial measurement unit (IMU) system of the UAV to revise 3D position coordinates in localization, which avoids the defect that visual localization is easily blocked in indoor environments.

(3)

In the online localization stage, the PFM generated by the WGAN-IM is used for matching and positioning. The generator takes a single set of RSS values as input to locate the target and produces multiple sets of similar RSS values as output. The discriminator takes a set of RSS values as input and outputs a ratio indicating the probability that the input data are real. The Wasserstein distance (W-distance) is used as the loss function of the generator, so that the distribution of the generated data is close to the distribution of the offline fingerprint database. By training the generator and discriminator, the generator can generate data similar to real offline fingerprint data. The gradient clipping technique is used to ensure the stability of the Wasserstein distance during training. In this way, the point location of the target is extended to plane matching, and the experimental results show that this method improves the localization accuracy.

The remainder of this paper is organized as follows. In Section 2, related materials and methods are described. The UAV indoor localization system is then presented in Section 3. In Section 4, the role of the WGAN algorithm in both offline and online phases is discussed. Section 5 provides the design of simulations and analyzes the results. Finally, the paper is concluded in Section 6.

2. Materials and Methods

2.1. Current Research on UAV Indoor Localization Systems

Most of the localization for UAVs is carried out outdoors at present, which is related to the wide application range of UAVs outdoors. The methods used for outdoor drone localization mainly include IMU [27], visual [28], ultrasound [29], and lidar [30].

Indoor UAV applications encompass security surveillance, search and rescue, logistics management, building inspections, delivery services, entertainment activities, and environmental monitoring among various sectors. The application demand drives the emergence of research, and more and more scholars have begun to study the localization of UAVs in indoor environments. iDROP relies on ultrasonic signals generated by speakers to mitigate ranging errors and errors caused by the relative geometry between transmitters and receivers, providing an indoor 3D localization solution for UAVs [31]. AIM also uses the acoustic characteristics of UAVs to estimate their positions and derive their movements, achieving excellent localization results even in indoor NLoS environments [32], and similar ultrasonic indoor localization systems include PILOT [33]. By using image processing technology based on DNN, reference [34] realizes autonomous navigation of UAVs with onboard cameras in indoor corridors of buildings. In addition to the above-mentioned single method, in order to obtain good indoor drone localization effects, many scholars have adopted a fusion approach, such as multiple sensor fusion [35], UWB fused with IMU [36], vision fused with IMU [37], and UWB fused with vision [38]. However, the use of visual signals in complex indoor environments is severely limited, and UWB nodes require additional financial costs for indoor deployment. Widely deployed Wi-Fi networks in indoor environments can communicate with most UAVs in the 2.4 GHz and 5 GHz bands [39], and the RSS values that are not affected by NLoS are extremely easy to obtain, which lays the foundation for the research in this paper.

Recent advancements also provide valuable insights into alternative approaches. For example, Batra et al. proposed a millimeter-wave-based indoor SAR sensing system assisted by chipless tags, which demonstrated effective self-localization capabilities for indoor environments [40]. Similarly, Xu et al. introduced a cooperative localization method for micro-UAV swarms using visible light communication (VLC), which achieves high-precision positioning but is constrained by line-of-sight (LoS) limitations in complex indoor spaces [41]. Onishi et al. further explored 3D drone tracking using reflected light from floor surfaces, offering a unique approach to non-line-of-sight positioning but facing challenges with signal reflection variability [42]. Despite the promising results of these techniques, Wi-Fi fingerprinting is selected in this paper due to its robustness in handling multipath effects and non-line-of-sight conditions, which are common in complex indoor environments. While millimeter-wave and VLC-based methods offer high accuracy, they often require additional infrastructure or depend on favorable lighting or reflection conditions, which may not always be practical for drone navigation. In contrast, Wi-Fi fingerprinting utilizes the existing wireless infrastructure and allows for reliable positioning in 3D indoor spaces without the need for new hardware. Moreover, fingerprinting methods have been shown to adapt well to environmental changes, ensuring consistent performance across various scenarios, making them well suited for drone positioning tasks in dynamic indoor environments.

Although fingerprint localization based on RSS values can achieve higher localization accuracy, the offline fingerprint signal collection work during the fingerprint acquisition phase is time-consuming and labor-intensive. The areas to be located are often large indoor environments, such as sports stadiums, airports, and shopping malls, which pose greater challenges to fingerprint collection. In these scenarios, often only coarse-grained fingerprints can be obtained, such as an interval of several meters between two RPs, which poses a potential risk to subsequent localization accuracy. To illustrate this issue, an intuitive perception of different RP densities in the same simulated indoor environment is presented in Figure 2. In a spacious indoor environment, specifically a gymnasium, we divided a region of 71 m in length and 17 m in width into 353 × 84 small cubes. Each cube has a side length of 20 cm. Within this region, six APs were uniformly distributed. As a result, a total of 177,912 fingerprints were collected for the initial fingerprint database, as shown in Figure 2a. The fingerprint data volumes of 1/200, 1/500, and 1/1000 of the initial fingerprint database were compared, as shown in Figure 2b, 2c, and 2d, respectively. It can be observed that with an increase in the number of fingerprints, the fingerprint database becomes increasingly fine-grained, providing a more refined selection for matching localization. The time and labor costs required to achieve this with each field measurement are not negligible, especially for the localization of the UAV in indoor 3D space.

Given the aforementioned rationales, leveraging Wi-Fi RSS fingerprints for indoor UAV positioning appears viable. Moreover, within the three-dimensional indoor setting, this study employs the WGAN technique to enhance the comprehensive RSS fingerprint database. To achieve the most optimal localization outcome, the IMU system of the UAV is enlisted for auxiliary support and integration throughout the localization process in this paper.

2.2. WGAN in Data Imputation

Data augmentation is a technique that increases the diversity of the training set through various methods without the need to manually collect new data. In many machine learning tasks, especially vision and speech recognition tasks, data augmentation has proven to be an effective way to improve the generalization ability of the model. For the task of fingerprint indoor localization, WGAN can be used for data enhancement to increase the fine granularity of the data. Considering the indoor localization process based on fingerprints, WGAN can play the role of corresponding data imputation in the phases shown in

Table 1. WGAN tasks at different phases used to complete the data imputation.

Phase	Task	Function
Training	Train WGAN using existing data	WGAN’s generator learns the statistical distribution of simulated data.
Generate new sample	Create new data sample	The new samples are created based on the learned data distribution, helping to fill in the uncovered data space areas.
Increase diversity	Import generator via different noise vectors	Generate a variety of new samples, enrich the diversity of data, and help the model learn a wider range of features and patterns.
Avoid overfitting	Use data augmentation	Prevent model overfitting and improve model training effect.
Improve accuracy	Training model	Data generated through WGAN improve model accuracy.

.

In the context of indoor localization, a possible problem is that the collected RSS data may not be sufficient to cover all possible orientations and locations in the environment, such as a certain crowd sensing signal. WGAN can be trained based on these existing fingerprint data and then learn to generate more fingerprints. These generated fingerprints are statistically similar to the real data, but different in specific values, and can be used to fill in the uncollected data in the dataset.

3. UAV Indoor Localization System

A 3D localization algorithm system designed for indoor UAV navigation is introduced in this section that combines fingerprinting techniques and IMU-assisted tracking. Section 3.1 outlines the process of spatially partitioning the indoor environment into 3D reference RCs and building a fingerprint database based on RSS measurements. Section 3.2 then describes how the IMU assists the localization process by optimizing the initial position estimate obtained through fingerprint matching. Together, these components form a robust framework for real-time, accurate indoor UAV localization in complex scenarios.

3.1. Three-Dimensional Spatial Fingerprint Division

Before presenting the proposed algorithm, it is necessary to establish the mathematical model for 3D indoor localization based on RSS fingerprints. A physical location in the real world, such as an interior space within a building, is partitioned into n1 × n2 rectangles with the presence of M effective Wi-Fi APs. In the three-dimensional spatial environment where indoor UAV operates, the vertical direction encompasses n3 layers of grid points, thus dividing the entire airspace into N = n1 × n2 × n3 cuboids, referred to as reference cuboids (RCs) in the fingerprint database, as shown in Figure 3. Let $r_n=\left(x_n,y_n,z_n\right)$ be the 3D position coordinates of $R{C}_n$ and $R=(r_1,r_2,\dots ,r_N)$ be a 3-by-N matrix indicating the positions of all RCs. In each RC, the fingerprint vector can be expressed as

$$F_n={\left[f_{n,1},f_{n,2},\dots ,f_{n,m},\dots ,f_{n,M}\right]}^T,$$

(1)

where $f_{n,m}$ denotes the RSS value measured from $A{P}_m$ in $R{C}_n$. In the proposed fingerprint-based location system, the primary aim is to generate a target location estimate $r_T=\left(x_T,y_T,z_T\right)$ by utilizing the stored RCs within the radio map.

3.2. IMU-Assisted UAV Localization System

Assuming that the position of the UAV at time k is $p_k=\left(x_k,y_k,z_k\right)$, k = 1, 2, …, K, the time interval between two adjacent points on the UAV trajectory is $\mathsf{\Delta }{t}_i$, i = 1, 2, …, K − 1. The drone user can obtain the mean velocity of $v_i=\left(v_{x,i},v_{y,i},v_{z,i}\right)$ at $\mathsf{\Delta }{t}_i$ according to the data measured by the IMU carried on the UAV. In the specific scenario shown in Figure 4, the numerical expression in the three directions of $v_i$ is

$$\left\{\begin{array}{c}{v}_{x,i}={\displaystyle \frac{v_{x,k}+v_{x,k+1}}{2}}\\ v_{y,i}={\displaystyle \frac{v_{y,k}+v_{y,k+1}}{2}}\\ v_{z,i}={\displaystyle \frac{v_{z,k}+v_{z,k+1}}{2}}\end{array}\right..$$

(2)

In view of the above analysis, a two-step strategy is adopted in the localization process in this paper. In the online phase, the UAV first uses the fingerprint matching algorithm to compare with RCs in PFM to complete the preliminary localization. Then, the preliminary positioning result is modified to obtain the final localization result according to the time $\mathsf{\Delta }{t}_i$ spent on the fingerprint matching and the flight inertia $v_i$ of the UAV during this period.

In our proposed method, the initial position of the UAV is obtained using a fingerprint-based localization system, which is essential for overcoming the limitation of inertial sensors, which provide only relative motion information and do not offer absolute positioning. The fingerprint-based method utilizes RSS from multiple Wi-Fi APs deployed within the indoor environment.

4. The Role of the WGAN Algorithm in Offline and Online Phases

The method of using WGAN and PFM to enhance 3D localization is introduced in detail in this section. How to use WGAN to enhance the fingerprint database is discussed in Section 4.1, and the application of the WGAN-IM method in online localization is described in Section 4.2. Together, these techniques significantly improve the localization accuracy and robustness, providing an effective solution for real-time UAV localization in complex indoor environments.

4.1. Enhanced Fingerprint Database with WGAN

GAN suffers from difficulties in training, the loss of the generator and the discriminator being unable to indicate the training process, and the lack of diversity of generated samples [43]. Many researchers have tried to solve it, but the results are not satisfactory, and WGAN succeeds in the following breakthrough points. To completely solve the problem of GAN training instability, it is no longer necessary to carefully balance the training degree of generator and discriminator [44]. During the training process, there is finally a value such as cross-entropy and accuracy to indicate the training process. The smaller the value, the better the GAN training is and the higher the data quality generated by the generator. It settles the problem of the collapse mode to ensure the diversity of the generated samples. All of these benefits do not require elaborate network architecture, but can be achieved with the simplest multi-layer fully connected network [45,46]. Due to its superior predictive ability, the WGAN model is no longer limited to image processing, but continues to display its potential in various signal processing and data generation fields [47,48,49].

The flow chart of the WGAN algorithm in the fingerprint database upgrade process proposed in this paper is shown in Figure 5. The initial coarse-grained fingerprint database $R_I$ is composed of RSS signals collected at key locations, and these signals can be collected in advance by measuring UAV or obtained by crowd-sensing equipment. The main objects of initialization are generator G and discriminator D in WGAN, and their weights are determined according to the indoor environment. The generator G receives random noise r and generates new RSS fingerprint data $F_g$ with the goal of mimicking realistic and finely changing fingerprint data so that it approximates the distribution of real fingerprint data. The discriminator D evaluates the similarity of the real data from $F_n$ to the generated data from $F_g$ via the Wasserstein distance and provides feedback on the generative ability of G.

Wasserstein distance is a core concept in WGAN and is used to measure the difference between the generated data distribution and the real data distribution. This measure is mathematically formalized by optimal transport theory. Wasserstein distance, also known as Earth Mover’s distance, can be intuitively understood as the amount of work required to move one pile of soil, that is, the generated data distribution, to another pile of soil, that is, the real data distribution. If both piles of soil are exactly the same shape, no work is required. If the shapes are different, the amount of work required to move the soil to complete the shape matching is the Wasserstein distance. The Wasserstein distance in WGAN, in the system proposed in this paper, is defined as follows:

$$W\left({\mathcal{P}}_n,{\mathcal{P}}_g\right)={\inf }_{\gamma \in {\displaystyle \prod \left({\mathcal{P}}_n,{\mathcal{P}}_g\right)}}{\mathbb{E}}_{\left(F_n,F_g\right)\sim \gamma }\left[‖F_n-F_g‖\right],$$

(3)

where inf represents the lower bound, ${\mathcal{P}}_n$ is the real $F_n$ distribution in the 3-dimensional space, ${\mathcal{P}}_g$ is the $F_g$ distribution generated by the generator G, and ${\displaystyle \prod \left(P_r,P_g\right)}$ is the set of all possible joint distributions of $P_r$ and $P_g$ combined. For each possible joint distribution $\gamma$, a real reference cuboid fingerprint $F_n$ and a generated reference cuboid fingerprint $F_g$ from $\left(F_n,F_g\right)\sim \gamma$ are sampled, and then the distance can be obtained as the expected value ${\mathbb{E}}_{\left(F_n,F_g\right)\sim \gamma }\left[‖F_n-F_g‖\right]$ under the joint distribution $\gamma$. ${\mathbb{E}}_{\left(F_n,F_g\right)\sim \gamma }\left[‖F_n-F_g‖\right]$ can be understood as the consumption required to move ${\mathcal{P}}_n$ to position ${\mathcal{P}}_g$ under the path planning $\gamma$, and $W\left({\mathcal{P}}_r,{\mathcal{P}}_g\right)$ is the minimum consumption under the optimal path planning.

The goal of the discriminator is to maximize the following objective function,

$$L_D={\mathbb{E}}_{F_n\sim {\mathcal{P}}_n}\left[D\left(F_n\right)\right]-{\mathbb{E}}_{F_g\sim {\mathcal{P}}_g}\left[D\left(F_g\right)\right],$$

(4)

which is approximately the negative value of the Wasserstein distance. The discriminator D attempts to assign higher scores to samples $F_n$ from the true distribution and lower scores to samples $F_g$ generated by the generator. The optimization of this function enables the discriminator D to differentiate between samples drawn from distributions $P_r$ and $P_g$, thereby assessing the disparity between these two distributions.

After optimizing the discriminator D to effectively estimate the Wasserstein distance between two distributions, the generator G attempts to minimize the loss function reflecting this distance:

$$L_G=-{\mathbb{E}}_{F_g\sim {\mathcal{P}}_g}\left[D\left(F_g\right)\right].$$

(5)

This implies that the objective of G is to produce data that D is inclined to believe are similar to real samples to the greatest extent possible. In this manner, G receives feedback on how to adjust its generation strategy to better mimic the distribution of real data. The outcome of this iterative process is that G progressively enhances the quality of generated data, while the feedback provided by D based on the Wasserstein distance continuously steers G toward the right direction for improvement, ultimately enabling G to generate data almost indistinguishable from the distribution of real fingerprints.

Equations (4) and (5) are referred to as the loss functions of the discriminator D and the generator G, respectively, with their weights updated using the gradient descent method. Each step of this process updates the parameters of G and D according to the gradient of the loss function to minimize the loss function. In Equation (4), ${\mathbb{E}}_{F_n\sim {\mathcal{P}}_n}\left[D\left(F_n\right)\right]$ is the expected evaluation of the real fingerprint data $F_n$, and ${\mathbb{E}}_{F_g\sim {\mathcal{P}}_g}\left[D\left(F_g\right)\right]$ is the expected evaluation of the fingerprint data $F_g$ generated by the generator. The gradient descent method is used to maximize this loss function, and its update rule is

$${\theta }_D\leftarrow {\theta }_D+{\alpha }_D{\nabla }_{{\theta }_D}{L}_D,$$

(6)

where ${\theta }_D$ represents the parameter of the discriminator D, ${\alpha }_D$ is the learning rate, and ${\nabla }_{{\theta }_D}{L}_D$ is the gradient of the loss function $L_D$ with respect to ${\theta }_D$. Equation (5) represents the loss function of generator G. The parameters of the generator are updated using the method of gradient rise, which is equivalent to minimizing the negative loss function. The update rule is as follows:

$${\theta }_G\leftarrow {\theta }_G-{\alpha }_G{\nabla }_{{\theta }_G}{L}_G,$$

(7)

where ${\theta }_G$ represents the parameter of the generator G, ${\alpha }_G$ is the learning rate, and ${\nabla }_{{\theta }_G}{L}_G$ is the gradient of the loss function $L_G$ with respect to ${\theta }_G$.

In WGAN, the 1-Lipschitz constraint is to ensure that the discriminator D function is a 1-Lipschitz function, which is one of the key conditions for the stability of the algorithm [50]. Gradient penalty (GP) is utilized in this paper to enhance the training stability and model quality, and it is implemented through the following loss function,

$$L_{GP}=\lambda {\left({‖{\nabla }_{F_{n\sim g}}D\left(F_{n\sim g}\right)‖}_2-1\right)}^2,$$

(8)

where $F_{n\sim g}$ is the data interpolated from the real fingerprint and the generated fingerprint data, ${\nabla }_{F_{n\sim g}}$ represents the gradient to $F_{n\sim g}$, $D\left(F_{n\sim g}\right)$ is the judgment output of the discriminator for $F_{n\sim g}$, and $\lambda$(10) is the weight coefficient of the gradient penalty; its value varies in different indoor environments.

After completing the aforementioned steps, G and D are trained in an alternating fashion until they reach a predetermined number of iterations. The fingerprint data $F_g$ generated by the generator G is as close as possible to the real data $F_n$, and the corresponding fingerprint databases $R_g$ and $R_I$ are combined to form a fine-grained fingerprint database R.

4.2. Application of WGAN-IM in Online Localization Phase

Since WGAN-IM has already played an important role in other digital signal processing and image processing, significant progress has been made [51,52,53]. In this paper, WGAN-IM aims to invert the given target fingerprint information back to the latent space of the pre-trained WGAN model. The generator can then faithfully reconstruct similar fingerprint groups to the offline-stage synthetic fingerprint database based on the inverse code. WGAN-IM makes the controllable directions found in the latent space of existing trained WGANs suitable for editing real fingerprint data without any supervision or expensive optimization. As shown in Figure 6, after inputting the real fingerprint flip into the latent space, the position information of the fingerprint’s attribute by changing its code along a specific direction can be edited. Different from the generation process using generator G in the offline phase, WGAN-IM maps the target’s fingerprint to the latent space and obtains the target noise $\tilde{r}$. The regeneration fingerprint ${\tilde{F}}_g$ is obtained by ${\tilde{F}}_g=G\left(\tilde{r}\right)$. The parameters $v_i=\left(v_{x,i}, v_{y,i}, v_{z,i}\right)$ of the UAV in three-dimensional space were previously derived through measurements from the IMU unit, allowing the PFM to be obtained using the following equation:

$$\left\{\begin{array}{c}{\tilde{F}}_{g,x}=G\left(\tilde{r}+v_{x,i}\right)\\ {\tilde{F}}_{g,y}=G\left(\tilde{r}+v_{y,i}\right)\\ {\tilde{F}}_{g,z}=G\left(\tilde{r}+v_{z,i}\right)\end{array}\right..$$

(9)

A sustained localization continuity can be obtained using PFM to maintain accurate positioning when Wi-Fi signals are temporarily lost or disrupted, thereby minimizing the duration and extent of connectivity interruptions.

The offline fingerprint database is built by collecting the RSS at known locations and establishing a mapping between positions and RSS readings. When a set of RSS fingerprints is obtained during online localization, the closest matching record from the offline database needs to be identified. For each RSS dataset generated by the WGAN-IM algorithm for different directions $\left(v_{x,i}, v_{y,i}, v_{z,i}\right)$, the most matching RSS record in the offline database is found through a search algorithm such as K-Nearest Neighbors (KNN) [54], Support Vector Machine (SVM) [55], Convolutional Neural Network (CNN) [56], and Particle Filter (PF) [57].

The point fingerprint information of the target becomes plane fingerprint information after the above processing. Plane matching considers the entire object surface so it can obtain more comprehensive information and capture more of the geometric structure and surface shape of the object, making the matching result more detailed and accurate compared with point matching.

5. Simulation Design and Results Analysis

To facilitate a valid comparison among localization architectures, it is essential to propose a common framework that enables the evaluation and fair contrast of the performance of each architecture. Therefore, two common experimental scenarios are proposed for the subsequent analysis.

One is a small indoor scenario similar to the size of an office, home, or classroom. The scenario is referred to as Scenario 1, and it has been left vacant in order to test, on a purely theoretical basis, whether the design is effective for 3D localization of UAVs. Another scenario is a large indoor environment similar to a warehouse, stadium, or airport. In this simulation environment of Scenario 2, the real situation is simulated, and obstacles are placed indoors in the form of various objects. In this way, the localization effect of the proposed scheme on the UAV in real life can be reflected as much as possible.

5.1. Simulation of Scenario 1

5.1.1. Simulation Setup

The devised Scenario 1, shown in Figure 7, depicts a typical indoor environment with nothing in the room. The transmitter subsystem, which in fact is the Wi-Fi routers at the known positions in the room, generates the signals in people’s daily lives, that is, 2.4 GHz and 5 GHz. The performance of the localization system proposed in this paper is assessed by implementing a simulation in MATLAB (R2023b). In order to simulate an indoor environment as described above, the routers at the (x, y, z) coordinates are located to equal (0, 0, 3), (0, 5, 3), (5, 5, 3), and (5, 0, 3), where all the numbers are in the meter unit. The transmitting end of the wireless signal is simulated as a Wi-Fi signal, and its transmitting amplitude is −10 dBm.

There is no obstacle for the deployment of routers, thus constituting the scenes where wireless signals are in a line-of-sight (LoS) environment. To better observe how the WGAN and PFM operate in the offline and online phases, the process is divided into two simulations as described below.

In the first stage of the simulation, the performance of WGAN in the offline phase is primarily tested. Therefore, a relatively coarse indoor 3D initial fingerprint scenario is simulated. In this $5\times 5\times 3$ environment mentioned above, the sampling interval is defined as 1 m; that is, RC is $1\times 1\times 1$. Then, there are 75 initial fingerprint RCs of $R_I$ in the whole room. After upgrading the fingerprint database using the WGAN algorithm, the $R_I$ is replaced by $R_g$ consisting of 600 RCs, where this value is determined for ease of simulation. If the time cost is not taken into consideration, an increase in this number may be observed. In the simulations, the trajectory of UAV is generated randomly, ${\mathbf{V}}_i$ = 1 m/s, K = 20, and $\mathsf{\Delta }{t}_i$ = 0.5 s. In the 3D plot of Figure 8, 75 initial RCs and 600 RCs after upgrading using the WGAN algorithm are shown. All parameter details are shown in

Table 2. Main parameter settings for Scenario 1.

Parameter	Transmitter Frequency	Transmitting Amplitude	Router Coordinates	Simulation Environment	Sampling Interval	Initial Fingerprint RCs	Upgraded Fingerprint RCs	${\mathbf{V}}_{\mathit{i}}$	Number of Algorithms (K)	$\mathsf{\Delta }{\mathit{t}}_{\mathit{i}}$
Value	2.4 GHz, 5 GHz	−10 dBm	(0, 0, 3), (0, 5, 3), (5, 5, 3), (5, 0, 3)	5 × 5 × 3	1 m	75	600	1 m/s	20	0.5 s
Description	Signals generated by Wi-Fi routers	Wi-Fi signal amplitude	Positions in meters	Size of the indoor environment	RC is 1 × 1 × 1	Number of initial fingerprint RCs	Number of RCs after WGAN upgrade	UAV’s speed	Number of classic matching algorithms	Time interval for UAV trajectory

.

After the initial fingerprint database is formed and the fingerprint database is upgraded, the matching algorithm needs to be selected in the online phase to complete the location of the UAV. To evaluate the suitability of the WGAN algorithm for pairing protocols, this study employed four distinct algorithms, KNN, SVM, CF, and PF, for the systematic matching of the feature sets $R_I$ and $R_g$, thus facilitating a comprehensive comparison across various matching scenarios. The following specific configurations were made in this scenario for the four matching algorithms.

The K value is the most important parameter in the KNN algorithm, which represents the number of nearest neighbors that will be considered when making classification decisions. The K value is chosen as a typical value of 5, which strikes a balance between smoothing effects and sensitivity to outliers. Choosing a too-small K value may make the model sensitive to noise, while a too-large value could blur the classification boundaries, reducing precision. The method used to calculate the distance between the unknown UAV position and the known RC is the Euclidean distance, which is a common choice in indoor localization scenarios. In SVM matching, the kernel function type is selected as radial basis function; the penalty parameter is set to 1, which balances model complexity and accuracy, preventing overfitting while ensuring the model can generalize well; and the kernel function parameter is 0.1, which controls the influence of individual training samples, ensuring a balance between generalization and model sensitivity.

The convolution kernel size is set to 3 × 3; the pooling layer strategy is Max Pooling; the learning rate is set to 0.01, which ensures stable and gradual convergence during training; and the batch size is set to 32 when using the third matching algorithm CNN. In the PF matching process, the number of particles is set to 200, which strikes a balance between computational cost and accuracy and is evenly distributed. The state transfer function is set to uniform linear motion within $\mathsf{\Delta }{t}_i$. In order to simulate the uncertainty in the indoor environment, white noise is added to the state transfer process and a resampling strategy adopted. When the number of effective particles (Neff) drops to 50% of the total number of particles, resampling is triggered.

5.1.2. Analysis of Simulation Results

The localization strategy is to first calculate the time T from the target UAV transmitting the fingerprint to the server and the server completing the matching algorithm to obtain the position coordinates. Then, the displacement of the target UAV in three directions of 3D space is calculated according to Equation (2) as the final position estimation result and transmitted to the target UAV.

First, the coarse-grained initial fingerprint database is used to complete the simulation. The matching algorithm of the estimated trajectory is set according to the previous settings. KNN, SVM, CNN, and PF for matching are used in this simulation. The true track in the simulation is set to 8 m, and the UAV is positioned every 0.01 s. The estimation of true track in 1 time is not enough to illustrate the localization effect, so the 8 m trajectory was repeated 1000 times with different headings, and the average was then taken as the estimated result. The simulation result of a certain time is shown in Figure 9, showing the true track and estimated trajectory in 3D and plane view, respectively.

The same simulation experiment was conducted using the WGAN-processed fingerprint database with the same basic data configuration. There were 1000 random routes of the UAV, each with a length of 8 m positioned. The localization situation of one group is shown in Figure 10, where (a) shows the 3D view and (b) shows the localization effect of the plane view. The final mean localization error results are shown in Figure 11. The errors of the four matching localization algorithms were reduced by 33.85%, 23.76%, 35.79%, and 27.78%, respectively, using the fingerprint database processed by the WGAN algorithm.

The quality and consistency of the data were significantly improved by processing the initial fingerprint database using the WGAN algorithm, and the impact of noise and outliers was reduced. This provided more reliable input data for the subsequent localization algorithms, leading to substantial error reductions. Specifically, due to their different mechanisms and dependencies on data quality, the error reduction varied for each algorithm. KNN and CNN, which are more sensitive to data quality improvements, saw the greatest reductions, while SVM and PF also experienced significant improvements. In summary, WGAN demonstrated its powerful ability to enhance fingerprint database quality, thereby effectively boosting the overall performance of UAV Wi-Fi-based indoor localization systems.

5.2. Simulation of Scenario 2

In the online localization phase, the PFM generated by the WGAN-IM is used for matching and positioning. The performance of PFM was demonstrated and tested in Scenario 2.

5.2.1. Simulation Setup

Since the PFM algorithm primarily operates during the online phase, the data from the offline phase needed to be unified in order to evaluate its performance. Therefore, in this verification, the fingerprint database processed by WGAN was uniformly used. Regarding the selection of the test site, modifications were made compared with Scenario 1, primarily involving an expansion of the indoor area and the addition of obstacles.

In simulation scenario 2, the performance of the PFM algorithm was also verified through 1000 tests conducted. Figure 12 shows the entire indoor environment of the UAV flight. The UAV needs to fly a certain distance around the obstacles to perform a localization accuracy test of the PFM algorithm. It should be noted that the sizes and positions of the obstacles are random, so this is just a specific arrangement for one time. In the rest of the simulation settings, the position and size of obstacles change, yet the indoor size of 50 × 30 × 6 is fixed.

Figure 3 shows the spatial segmentation method. There are a total of 9000 RCs in this UAV flight scenario after WGAN expansion; that is, the number of RCs in $R_g$ is 9000, and each RC is a cube with a side length of 1 m. The number of obstacles is fixed at 15, but the length of their edges within 5 m is random. Regarding the flight parameter settings of the UAV, this simulation scenario is the same as Scenario 1. Specifically, the trajectory of the UAV is generated randomly, $V_i$ = 1 m/s, K = 20, and $\mathsf{\Delta }{t}_i$ = 0.5 s. The fingerprint data are plotted into a 3D display graph using MATLAB, where the x-axis coordinate represents RCs, and there are 9000 in total; the y-axis coordinate represents APs, and there are 15 in total; and the z-axis coordinate represents the RSS value (dBm) received by the UAV at the corresponding position. The Wi-Fi transmitting amplitude is set to −10 dBm. Figure 13 shows the final fingerprint database, i.e., the output result of $R_g$. All parameter details in Scenario 2 are shown in

Table 3. Main parameter settings for Scenario 2.

Parameter	Transmitter Frequency	Transmitting Amplitude	Number of Tests	Simulation Environment	RC Size	$\mathbf{Number}\mathbf{of}\mathbf{RCs}\mathbf{in}{\mathbf{R}}_{\mathit{g}}$	Number of Obstacles	${\mathbf{V}}_{\mathit{i}}$	Number of Algorithms (K)	$\mathsf{\Delta }{\mathit{t}}_{\mathit{i}}$
Value	2.4 GHz, 5 GHz	−10 dBm	1000	50 × 30 × 6	1 m	9000	15	1 m/s	20	0.5 s
Description	Signals generated by Wi-Fi routers	Wi-Fi signal amplitude	Tests conducted to verify PFM algorithm performance	Size of the indoor environment	Each RC is a cube with a side length of 1 m	Total number of RCs after WGAN expansion	Fixed number of obstacles	UAV’s speed	Number of classic matching algorithms	Time interval for UAV trajectory

.

In the online matching phase, the four algorithms—KNN, SVM, CNN, and PF—are still selected for the analysis, and their related parameter settings are consistent with Section 5.1.1. Based on the PFM algorithm, in the process of locating the UAV, ${\tilde{F}}_{g,x}$, ${\tilde{F}}_{g,y}$, and ${\tilde{F}}_{g,z}$ are generated using its real-time fingerprint information, and then the above four algorithms are used for matching and positioning. The final localization result is the centroid position of the graph composed of the three localization points.

5.2.2. Results of Scenario 2

The effectiveness of the WGAN algorithm was demonstrated in the previous experiment. Therefore, in this experimental scenario, the fingerprint database processed by WGAN is directly utilized for localization testing. Initially, the single fingerprint information of the target UAV is used for localization, corresponding to its designated reference fingerprint. This represents a traditional indoor localization method, which is then compared with the PFM algorithm. It should be noted that 1000 localization tests were conducted, with the position and size of obstacles randomized within the specified range for each test. To enhance the clarity of the trajectory route, all obstacles are represented in the same color when presenting the localization results, distinguishing it from the previous localization scenario presentation.

The result of the localization trajectory is shown in Figure 14. The designated reference trajectory is set to 200 m, which is appropriate for this extensive localization scenario. The UAV needs to bypass obstacles, and the observation from the figure is that this designated trajectory cannot intersect with the obstacles. The above four algorithms are used to estimate the trajectory of localization. Since the estimated trajectory is virtual and only illustrates the distance from the designated trajectory, it may appear to pass through obstacles. Figure 13 shows only one scene from the 1000 localization tests, and the final localization result is the average value obtained after these tests.

To enhance the UAV’s performance in navigating complex indoor environments, the A-star path planning algorithm is integrated. The A-star algorithm is specifically designed to find the shortest path from a starting point to a destination while avoiding obstacles. In this case, it helps the UAV plot a course that bypasses obstacles within the simulated indoor environment. The A-star algorithm ensures that the UAV navigates around obstacles, as indicated by the fact that the real trajectory does not intersect with any obstacles. The results, shown in Figure 14, illustrate how the UAV successfully avoids obstacles. By zooming in locally, the gap between the red set true trajectory and the estimated trajectory can be observed more intuitively.

The single fingerprint of the UAV was expanded using the PFM algorithm under the same real trajectory, and the localization test was conducted again. The results are presented in Figure 15. It can be observed that the localization curve achieved by the four algorithms in Figure 15 is closer to the real trajectory compared with the localization trace curve in Figure 14. This can be observed in more detail by zooming in on the image. As for the detailed localization error values, the mean errors of KNN, SVM, CNN, and PF before and after localization using the PFM algorithm are, respectively, 1.89 m, 1.55 m, 1.48 m, 1.4 m and 1.38 m, 1.07 m, 1.1 m, 0.99 m, and their localization accuracy is improved by 27.0%, 30.1%, 25.7%, and 29.3%, respectively.

To test the robustness and environmental adaptability of the PFM algorithm in complex environments with varying signal strengths, the signal strength at the Wi-Fi transmitting end was reduced to −30 dBm, and experimental tests were subsequently conducted. The final localization results are shown in Figure 16 under this setting. It can be seen that without using PFM, the localization errors of the four algorithms have decreased significantly. The use of the PFM algorithm prevents this downward trend in localization accuracy.

After combining with the PFM algorithm, the four matching algorithms have significantly improved localization accuracy, environmental adaptability, and robustness, as shown in Table 2. The following explanations are required for the items in the table. The percentage reduction in localization error when the transmitted signal strength is decreased from −10 dBm to −30 dBm with the PFM algorithm quantifies how well each algorithm adapts to changes in environmental conditions. A numerical value representing the algorithm’s performance stability under signal noise changes could be derived from experiments or simulations where algorithms are subjected to controlled perturbations.

Table 4. The improved localization accuracy, environmental adaptability, and robustness of various algorithms when combined with the PFM algorithm, demonstrating the significant benefits of using PFM despite the increased computational complexity.

Algorithm	Localization Error (m, without PFM)	Localization Error (m, with PFM)	Computational Complexity (Time, Memory)	Environmental Adaptability (Error Reduction %)	Robustness (Performance under Perturbations)
KNN	2.11	1.41	12 ms,100 MB	2.2%	85%
SVM	1.76	1.1	21 ms, 200 MB	2.8%	90%
CNN	1.7	1.13	36 ms, 500 MB	2.7%	92%
PF	1.68	1.06	52 ms, 800 MB	7.1%	95%

illustrates the improvements in localization accuracy, environmental adaptability, and robustness of the various algorithms when combined with the PFM algorithm, highlighting the significant benefits despite the increased computational complexity. The data show that all algorithms experience a notable reduction in localization error with the introduction of PFM. For instance, the KNN algorithm’s localization error decreases from 2.11 m to 1.41 m, representing a reduction of approximately 33.2%. Similarly, the PF algorithm sees its error drop from 1.68 m to 1.06 m, a reduction of 37.5%, indicating the effectiveness of PFM in enhancing localization precision. However, this improvement comes at the cost of increased computational complexity; for example, KNN’s computation time rises from 12 milliseconds to 21 milliseconds, and memory usage increases from 100 MB to 800 MB.

The environmental adaptability is reflected in the error reduction percentages, with the PF algorithm achieving a 7.1% reduction compared with KNN’s 2.2%, showcasing PFM’s ability to better adapt to varying environmental conditions, particularly in complex indoor settings. Moreover, the robustness metric demonstrates enhanced performance under perturbations for all algorithms, with the PF algorithm achieving a robustness score of 95%, the highest among the tested methods. This comprehensive analysis highlights that while PFM increases computational demands, its substantial contributions to localization accuracy and robustness make it a valuable addition to indoor positioning systems.

6. Conclusions

In this study, the impact of the WGAN algorithm on a coarse-grained fingerprint database was first investigated, resulting in a significant improvement in the indoor localization accuracy of the UAV. The errors of the KNN, SVM, CNN, and PF matching localization algorithms were reduced by 33.85%, 23.76%, 35.79%, and 27.78%, respectively, using the fingerprint database processed by the WGAN algorithm. The application of the PFM algorithm, in combination with the four matching algorithms, was then explored for indoor UAV localization. The results indicate that integrating PFM with these algorithms significantly improves localization accuracy, environmental adaptability, and robustness. The increase in computational complexity is justified by the substantial gains in localization efficiency, and their localization accuracy is improved by 27.0%, 30.1%, 25.7%, and 29.3%, respectively. Furthermore, the PFM algorithm exhibits strong robustness to environmental changes, maintaining high localization accuracy even with reduced signal strength. The localization algorithm combined with the IMU proposed in this paper was utilized to assist in all the aforementioned localization processes. These findings validate the potential of the PFM algorithm in enhancing the performance of indoor UAV localization systems.