Sparse fingerprint enhancement method based on spectrum enhancement

Abstract

A sparse fingerprint enhancement framework based on spectrum enhancement comprises the following steps: 1) converting multi-dimensional RSSI data into a low-resolution fingerprint image; 2) converting the image to a frequency domain through fast Fourier transform; 3) designing a sparse fingerprint spectrum enhancement network, and adopting an encoder-decoder structure and combining an efficient channel attention mechanism to enhance key frequency domain features; 4) recovering the enhanced frequency spectrum to a spatial domain through inverse fast Fourier transform to obtain fingerprints with higher density and consistency; and 5) applying a composite loss function MSE-SSIM to balance the pixel precision and the space consistency. According to the method, the problem of structural information loss caused by sparse sampling is effectively relieved, the positioning error is remarkably reduced under different sparseness conditions, the fingerprint quality and the positioning stability are improved, the effectiveness of the attention module and the composite loss function is verified through an ablation experiment, and the method has high practical value and popularization significance.

Description

Technical Field

[0001] This invention belongs to the fields of indoor positioning and electronic information science, and in particular, fingerprint enhancement to obtain a dense fingerprint database. Background Technology

[0002] Wi-Fi fingerprint positioning has gained widespread attention due to its advantages such as high infrastructure coverage, low equipment cost, and good compatibility. The Received Signal Strength Indication (RSSI) value of Wi-Fi signals can directly reflect the spatial characteristics of the environment, thus making Wi-Fi fingerprint positioning highly practical. However, Wi-Fi signals are susceptible to environmental changes and noise interference, resulting in sparse and unstable fingerprint data, which limits the feature representation capabilities of the database. Compared to complex deep models that rely on massive amounts of data for training, improving the representation quality of sparse fingerprint data through effective data augmentation techniques is a more economical and feasible approach.

[0003] Machine learning research mainly introduces statistical prediction methods to generate virtual fingerprints. Sun W. et al. (Sun W., Xue M., Yu H., et al, Augmentation of Fingerprints for Indoor Wi-FiLocalization Based on Gaussian Process Regression [J]. IEEE Transactions on Vehicular Technology, 67(11): 10896-10905, 2018.) proved that Gaussian Process Regression (GPR) can generate dense radio maps, reducing the need for field measurements and providing spatial smoothing and uncertainty estimation. However, this method is sensitive to kernel selection and suffers from boundary effects and high computational costs. In practical systems, semi-crowdsourcing and efficient update designs have also been explored. Tao Y. et al. (Tao Y., Zhao L., AIPS: An Accurate Indoor Positioning System with Fingerprint Map Adaptation[J] IEEE Internet of Things Journal, 9(4): 3062-3073, 2022.) proposed AIPS, which uses K-means to classify access point (AP) types and uses GPR to update outdated fingerprints to maintain accuracy in dynamic environments. While these systems reduce maintenance workload, their performance depends on the reliability of auxiliary signals and stable clustering results. Deep learning techniques offer more advanced fingerprint enhancement capabilities. Junoh S. et al. (Junoh S. and Pyun J., Enhancing Indoor Localization with Semi-Crowdsourced Fingerprinting and GAN-Based Data Augmentation [J]. IEEE Internet Things Journal, 11(7): 11945–11959, 2024.) introduced AP selection based on Deep Q-Network and Generative Adversarial Network (GAN) enhancements to expand radio maps with minimal manual effort.Lan T. et al. (Lan T., Wang X., Chen Z., et al, Fingerprint Augment Based on Super-Resolution for WiFi Fingerprint Based Indoor Localization) [J]. IEEE Sensors Journal, 22(12): 12152–12162, 2022.) converted fingerprint data into an image representation and applied Enhanced Deep Super-Resolution (EDSR) to improve its resolution. Yang and Chen (Yang H. and Chen L., Improving Indoor Localization Through Data Augmentation of Visualized Multidimensional Fingerprints via Enhanced Generative Networks [J] IEEE Sensors Journal, 24(24): 42549-42560, 2024.) used ESRGAN to enhance image detail and diversity.

[0004] In summary, while existing data augmentation methods improve localization accuracy by expanding the training dataset, most focus on spatial modeling and synthesis. These methods learn spatial patterns and generate new fingerprints, ignoring the sparsity and non-uniform distribution of fingerprints. Many generative methods also rely on large labeled datasets, which have high training costs and limited adaptability to dynamic environments. In recent years, spectral augmentation has received increasing attention as a promising approach to address these problems. Its value lies in its ability to recover sparse signals and perform high-resolution reconstructions. In wireless sensing, improving the spectral structure of a signal can improve signal quality and enhance data reliability. This approach provides a valuable complement to spatial domain augmentation. Recent research in other wireless domains also reflects this shift. In radar sensing, Zheng R. et al. (Zheng R., Sun S., Liu H., et al, Model-Based Knowledge-Driven Learning Approach for Enhanced High-Resolution Automotive Radar Imaging [J]IEEE Transactions on Radar Systems, vol 3: 709-723, 2025.) described millimeter-wave radar super-resolution imaging as a one-dimensional spectral estimation task. They proposed a model-driven network, SR-SPECNet, which combines an iterative adaptive method within a deep learning framework. This sets a new benchmark for spectral enhancement and highlights the potential of spectral domain techniques under sparse measurements. In spectrum sharing systems, Jiao L. et al. (Jiao L., Ge Y., Zeng K. et al, LocationPrivacy and Spectrum Efficiency Enhancement in Spectrum Sharing Systems [J]IEEE Transactions on Cognitive Communications and Networking, 9(6): 1472-1488, 2023.) studied beamforming-based spectrum enhancement to balance primary user privacy and secondary user communication efficiency.In cognitive radio spectrum sensing, Su Z. et al. (Su Z., Teh KC, Xie Y., et al, SignalEnhancement Aided End-to-End Deep Learning Approach for Joint Denoising and Spectrum Sensing [J] IEEE Transactions on Vehicular Technology, 73(3): 4424-4428, 2024.) proposed a joint denoising and sensing framework. Their U-Net model uses self-attention blocks to emphasize subcarriers less affected by fading, thereby improving robustness in low signal-to-noise ratio environments. In underwater acoustic signal processing, Yao S. et al. (Yao S., Kuang Q., Liu Q., et al, Noise PSD Estimation Based on Time–Frequency Signal Presence Probability Sensing for Noncooperative UnderwaterAcoustic Pulse Signal Enhancement [J] IEEE Journal of Oceanic Engineering, 50(4): 3201-3217, 2025.) proposed a noise power spectral density estimation method based on time-frequency signal presence probability sensing, which enhances noncooperative pulse signals under strong interference.

[0005] The above analysis shows that although spectrum domain processing technology has made some progress, its application in the recovery and completion of sparse fingerprint data in Wi-Fi positioning is still rare. Existing research mainly focuses on modeling methods in the spatial or temporal domains, failing to fully explore the key features contained in the spectrum domain, thus limiting further improvements in fingerprint-based positioning accuracy. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention proposes a sparse fingerprint augmentation framework (SFAF). This method can dynamically recover the spatial details of fingerprints with varying degrees of sparseness, effectively improving the estimation accuracy of RSSI and the final localization performance in sparse sampling environments.

[0007] This invention is achieved through the following technical solutions.

[0008] A fingerprint data enhancement framework based on spectrum enhancement according to the present invention includes the following steps:

[0009] Step 1: The RSSI value after time-averaging filtering between the kth (0 < k ≤ K) access point and the reference point with spatial coordinates (i, j) is normalized. The RSSI data is standardized to the interval [0, 1] using the min-max normalization formula. After normalization, the coordinates of the reference point in physical space are mapped into the fingerprint image on the two-dimensional plane, and the position of each reference point corresponds to a pixel of the image. For a fixed access point k, the corresponding two-dimensional fingerprint image slice can be expressed as:

[0010]

[0011] The entire multi-dimensional fingerprint image is composed of K two-dimensional slices stacked together, forming a three-dimensional tensor m×n×K, that is , and the process of converting the fingerprint database into an image is as Figure 1 shown;

[0012] Step 2: Perform a two-dimensional fast Fourier transform (Fast Fourier Transform, FFT) on the multi-dimensional fingerprint image obtained in Step 1, express it in the form of a spectrum, and then perform a frequency shift centering operation to move the direct current component in the Fourier transform result from the corner of the array to the center position;

[0013] The spatial domain fingerprint image is composed of K two-dimensional slices stacked together. The spectrum fingerprint image slice can be expressed as:

[0014]

[0015] where represents the frequency domain coefficient of the spectrum fingerprint image at the position and the kth channel. Each slice corresponds to a complete spectrum image of an access point:

[0016]

[0017] The frequency domain transformation process is as Figure 2 shown;

[0018] Step 3: Taking the spectrum image in Step 2 as the input, a sparse fingerprint spectrum enhancement network (Sparse Fingerprint Spectrum Enhancement Network, SFSE-Net) based on the convolutional encoder-decoder structure is designed, which is specifically used to reconstruct and enhance the amplitude spectrum of the Wi-Fi signal, and obtain the enhanced spectrum fingerprint image .

[0019] The network structure is as follows:

[0020] (1) A symmetrical encoder-decoder architecture is adopted. The encoder extracts multi-scale features from the input spectrum by increasing the number of channels layer by layer, while the decoder gradually restores the spatial details of the spectrum, thereby achieving accurate reconstruction of the spectrum amplitude. (2) The network introduces an efficient channel attention (ECA) mechanism to strengthen the expression of key frequency components. Through lightweight convolution and non-linear activation operations, the importance of each channel in the feature representation is adaptively adjusted to improve the network's ability to distinguish different frequency channels. (3) The network introduces a skip connection structure to retain the original information in the input, enhance information flow, and alleviate the gradient vanishing problem.

[0021] In the training part of the network, a composite loss function MSE-SSIM based on mean squared error (MSE) and structural similarity index (SSIM) is adopted.

[0022] The composite loss function is constructed as follows:

[0023] (1) Calculate the pixel-level difference between the enhanced fingerprint and the real dense fingerprint by calculating the MSE loss:

[0024]

[0025] Where H and W represent the height and width of the fingerprint image, respectively. This is the network prediction value. The actual value;

[0026] (2) Introduction Measuring local texture similarity addresses the issue of MSE loss being insensitive to structural information.

[0027]

[0028] Among them, the stability constant , , The normalized pixel value range is [0,1] to prevent division by zero errors.

[0029] (3) The composite loss function is defined as:

[0030]

[0031] Among them, weight , This weight allocation ensures that the network maintains high-frequency details without overly smoothing fingerprint texture features;

[0032] Step 4: Combining the phase information of the original spectrum, the enhanced complex spectrum is mapped back to the spatial domain using the Inverse Fast Fourier Transform (IFFT) to reconstruct a higher-quality fingerprint image. The enhanced and reconstructed fingerprint image is represented as follows:

[0033]

[0034] in, Indicates the enhanced image pixels;

[0035] Step 5: After completing the inverse transformation reconstruction in Step 4, the obtained dense enhanced fingerprint database is directly applied to the localization task. The localization module estimates the target location based on the Weighted K-Nearest Neighbors (WKNN) strategy. The weight type and its parameters are automatically adjusted through Leave-One-Out Cross-Validation (LOOCV) grid search. Finally, the k nearest reference points are selected, and different weights are assigned according to the neighbor distance. The target location estimate is obtained by weighted averaging. The predicted target location can be expressed as:

[0036]

[0037] in, Let be the spatial coordinates of the i-th neighbor. Finally, by comparing with the real location... Euclidean distance calculation for positioning error :

[0038]

[0039] This invention provides a sparse fingerprint enhancement framework based on spectrum enhancement. First, a fingerprint image conversion module converts the acquired RSSI fingerprint database into low-resolution fingerprint images. Second, a frequency domain transformation module transforms the sparse data in the spatial domain to the frequency domain using a two-dimensional FFT. Next, a frequency domain enhancement module uses SFSE-Net to deeply enhance the amplitude spectrum. This network is based on an encoder-decoder structure, integrates an ECA channel attention mechanism, and is supplemented with skip connections to preserve original information. After enhancement, an inverse transform reconstruction module uses IFFT to restore the enhanced spectrum to fingerprint data in the spatial domain. Finally, a positioning estimation module uses the enhanced fingerprint database as input, significantly mitigating the positioning accuracy degradation caused by sparse signal sampling. This invention innovatively combines frequency domain signal processing with deep learning technology, providing a complete and efficient solution to the sparse fingerprint enhancement problem in Wi-Fi indoor positioning. Attached Figure Description

[0040] Figure 1 This is a flowchart of the fingerprint image conversion process in this invention.

[0041] Figure 2 This is a flowchart of the frequency domain transformation in this invention.

[0042] Figure 3 This is a comparison image of sparse fingerprint images and enhancement effects from the self-built dataset AP10 in this invention.

[0043] Figure 4 This is a comparison image of the sparse fingerprint image and the enhancement effect of the publicly disclosed dataset AP1 in this invention.

[0044] Figure 5 The bar chart shows the enhanced error test results under different module ablation conditions in this invention. Among them, (a) is the ablation of the ECA module; (b) is the ablation of the MSE-SSIM module; and (c) is the combined ablation of the ECA module and the MSE-SSIM module.

[0045] Figure 6 The bar chart shows the performance improvement under different ablation combinations and sparsity rates in this invention. Detailed Implementation

[0046] To verify the feasibility and effectiveness of the present invention, the present invention will be described in further detail below. The specific embodiments described herein are only for explaining the present invention and are not intended to limit the invention.

[0047] This invention uses a self-built dataset and the publicly available Wi-Fi RSSI indoor positioning dataset from IEEE Dataport for verification testing. The self-built dataset was collected in a 30m × 20m indoor office environment. The experimental scenario included multiple rooms, corridors, and office areas, with 10 Wi-Fi access points deployed in the environment. The dataset contains 150 Reference Points (RPs), uniformly or quasi-uniformly distributed within the experimental area, using a two-dimensional Cartesian coordinate system (X, Y) to identify spatial locations. Data was collected at 40 different time points, with each snapshot recording the RSSI measurements received from the 10 access points at all RPs. -100 dBm indicates that the location could not receive the signal from the corresponding AP. The benchmark open-access dataset was used in an office building corridor environment, consisting of a main corridor approximately 35m long and 2.5m wide, and two vertical branch corridors approximately 16.2m long. 27 Wi-Fi access points were deployed in this environment, evenly distributed along the corridor to provide comprehensive signal coverage. The dataset contains 250 reference points (RPs), each collecting 75 RSS samples over a 100-second sampling period. To ensure experimental consistency and balance computational efficiency with localization performance, we selected the RSSI measurements from the top 10 access points (APs) in the dataset. This configuration reduces model computational complexity and memory overhead while enabling the frequency domain augmentation algorithm to process Wi-Fi fingerprint data in real time.

[0048] This invention underwent all data processing and testing on a desktop computer equipped with an Intel Core i7-13700KF CPU and an NVIDIA RTX4080 GPU. All data preprocessing and spectrum enhancement operations were performed using Python 3.9, and a deep learning network was built using the PyTorch 2.7.1 framework for RSSI fingerprint enhancement and localization prediction.

[0049] The original Wi-Fi fingerprint data structure is a four-dimensional tensor (T×A×H×W), where T represents the number of time frames, A represents the number of access points (APs), and H×W is the spatial grid size. 20% of all coordinates are randomly selected as test points (TPs). For each RP, the minimum distance to all TPs is calculated, and only RPs with distances greater than a preset threshold are retained, ensuring complete spatial separation between RPs and TPs. The Min-Max normalization method is used to map RSSI values ​​to the [0,1] interval, and all subsequent operations use a unified normalization parameter to ensure global consistency in data processing. The training of the spectrum enhancement model is strictly limited to RP data. The time frames of the RPs are divided into training and validation sets in an 8:2 ratio. The RSSI vectors of the RPs are then reconstructed into a 2D spatial grid and normalized. During the training phase, a random sparsity strategy is used to simulate different degrees of signal loss, randomly discarding 10%-70% of the RSSI values ​​for each sample to construct a sparse input paired with a complete target. During the localization phase, a consistent preprocessing-driven approach is employed, constructing a completely consistent data preprocessing chain on both RPs and TPs to ensure the consistency of feature distribution. First, a missing value pushdown strategy is used, replacing missing RSSI values ​​with extreme values, allowing them to be naturally excluded during subsequent sorting. Next, Top-M strong signal filtering is performed, retaining the six APs with the highest signal intensity for each sample, and introducing a 12dBm signal intensity threshold to filter weak signals, preserving high-quality strong signal features for localization calculations. Finally, AP-by-AP standardization is implemented, calculating the mean and standard deviation of each AP on the preprocessed RPs data to form unified standardized statistical parameters. These same parameters are then applied to the TPs data, aligning the distributions of RPs and TPs in the feature space.

[0050] During training, we set the maximum number of training epochs to 100, the initial learning rate to 0.005, and dynamically adjusted it using a cosine annealing strategy. Considering the balance between memory usage of the spectral images and training stability, the batch size was set to 8. The Adam optimizer was used for training. The loss function adopted was the MSE-SSIM composite loss function, where the MSE weight coefficient was set to 1.0 and the SSIM weight coefficient was set to 0.1. An early stopping strategy was employed during training; training was stopped when the validation set loss did not improve for 10 consecutive epochs to prevent overfitting. The weights that performed best on the validation set were saved for subsequent augmentation tasks. In the following examples, unless otherwise specified, the implementation and testing conditions are consistent with those described above.

[0051] Example 1: Verification test of image enhancement quality and positioning performance.

[0052] To verify the effectiveness of the spectral image enhancement method designed in this invention, tests were conducted on a self-built dataset and a publicly available dataset.

[0053] In our self-built dataset, we selected AP10 as a representative access point for analysis and obtained its fingerprint images under different sparsity conditions for system comparison. For example... Figure 3 As shown, the complete fingerprint image constructed based on a 100% sampling rate is considered the ground truth (GT). This example demonstrates the original sparse fingerprint images acquired at sparsity rates of 10%, 30%, 50%, and 70% to reflect the information loss caused by different sampling densities. It is evident that the original sparse fingerprint suffers severe loss of structural information as the sampling rate decreases. However, after enhancement using the proposed SFAF method, the fingerprints at each sparsity rate show significant recovery in spatial patterns and details, closely approaching the GT. The test results on public datasets are consistent with the conclusions of our self-built dataset. Figure 4 As shown, the localization error of sparse sampling increases significantly with increasing sparsity, while the enhanced version is significantly better than sparse sampling at most sparsity rates, continuously bringing the localization performance closer to the baseline level. Compared to the original sparse fingerprint image, the localization performance is improved to a certain extent after enhancement by this invention. As shown in Table 1, the localization error of the self-built dataset is reduced to 3.443 m, 4.74 m, 6.29 m, and 8.87 m at sparsity rates of 10%, 30%, 50%, and 70%, respectively, representing a 28.16%–32.47% improvement in localization accuracy relative to the sparse fingerprint image. The performance improvement of the publicly available dataset is 16.14%, 27.47%, and 11.32% at sparsity rates of 30%, 50%, and 70%, respectively, further verifying the effectiveness and generalization ability of SFAF in open environments. These test results verify the effectiveness of the spectral image enhancement method designed in this invention.

[0054] Table 1. Performance of the proposed SFAF on self-built and public datasets at different sparsity rates.

[0055]

[0056] Example 2: Verification test of ablation of different modules.

[0057] Tests were conducted on a self-built dataset. Figure 5 The results show a comparison of enhancement errors under different ablation settings and three sparsity rates. Figure 5 (a) A comparison of the performance after introducing and removing the ECA module; Figure 5 (b) The differences between using only MSE and using the combined loss (MSE+SSIM) were analyzed; Figure 5(c) compares the performance of the complete model (including ECA+MSE+SSIM) with that of removing both. The tests show that, at all sparsity rates, introducing either ECA or SSIM can significantly reduce the augmentation error. Figure 6 The localization improvements compared to the complete model under different combinations are summarized. Test results show that removing ECA or MSE+SSIM both lead to performance degradation, and removing both simultaneously results in a negative improvement. This trend is consistent across all three sparsity rates, indicating that the two designs in this invention work synergistically to enhance the frequency domain and restore the spatial structure, jointly supporting the overall performance of SFAF. Table 2 lists the detailed results of each ablation combination on RMSE, MSE, PSNR, SSIM, and localization error. Test results show that the combination of the ECA mechanism and the composite loss significantly improves the reconstruction quality and localization accuracy of the fingerprint map. In particular, at sparsity rates of 10%, 30%, and 50%, the localization error of the complete model is reduced by 28.2%, 32.5%, and 29.3% respectively compared to the sparse baseline, verifying the superiority of SFAF in sparse fingerprint enhancement tasks.

[0058] Table 2 Ablation experiment results on the impact of ECA module and composite loss function on SFSE-Net performance

[0059]

[0060] Example 3: Comparative test of different enhancement methods.

[0061] In the test, the present invention was compared with traditional methods and deep learning-based enhancement methods. Table 3 shows the comparison results of localization errors of different methods on two types of datasets.

[0062] Table 3. Performance comparison of different models on two datasets based on different sparsity rates.

[0063]

[0064] The test results show that, on the self-built dataset, SFSE-Net achieved the lowest localization error of 3.44m with a sparsity of 10%, a 28.2% reduction compared to 4.79m with unrecovered sparsity. As the sparsity increased to 70%, SFSE-Net maintained its advantage with an error of 8.87m. On publicly available datasets, SFSE-Net also performed excellently, achieving an error of 4.71m with a 30% sparsity, demonstrating the consistent advantage of this invention across various sparsity levels.

Claims

1. A sparse fingerprint enhancement framework based on spectral enhancement, characterized in that, Includes the following steps: Step 1: Calculate the RSSI value between the k-th access point and the reference point with spatial coordinates (i,j) after time averaging and filtering. Normalization is performed using the minimum-maximum normalization formula to standardize the RSSI data to the interval [0,1]. After normalization, the coordinates of the reference points in physical space are mapped onto the fingerprint image on the two-dimensional plane, with each reference point's position corresponding to a pixel in the image. For a fixed access point k, its corresponding two-dimensional fingerprint image slice can be represented as: The entire multidimensional fingerprint image is composed of K superimposed two-dimensional slices, forming a three-dimensional tensor m×n×K, i.e. ; Step 2: Perform a two-dimensional Fourier transform on the fingerprint images obtained in Step 1, representing them in spectral form. Then, perform a frequency shift and centering operation to move the DC component in the Fourier transform result from the corner of the array to the center position. The spatial domain fingerprint image is composed of K superimposed two-dimensional slices, and the spectral fingerprint image slices are represented as follows: in, , The spectral fingerprint image represents the first... Frequency domain coefficients of the k-th channel; each slice corresponds to a complete spectrum image of an access point: ； Step 3: Using the spectral image from Step 2 as input, design a sparse fingerprint spectral enhancement network SFSE-Net based on a convolutional encoder-decoder structure to enhance the amplitude spectrum of Wi-Fi signals. Reconstruction and enhancement are performed to obtain the enhanced spectral fingerprint image. ; The SFSE-Net is a symmetric encoder-decoder structure, containing an efficient channel attention module and skip connections. During training, it employs a composite loss function consisting of MSE and SSIM. Wherein, weight λ MSE =1.0, λ SSIM =0.1; The MSE loss is: Where H and W represent the height and width of the fingerprint image, respectively. This is the network prediction value. The actual value; The SSIM loss is: Among them, the stability constant , , The corresponding normalized pixel value range is [0,1]. Step 4: Combining the phase information of the original spectrum, the enhanced complex spectrum is mapped back to the spatial domain to reconstruct a fingerprint image of higher quality; the enhanced and reconstructed fingerprint image is represented as: in, Indicates the enhanced image pixels; Step 5: After completing the inverse transformation reconstruction in Step 4, the obtained dense enhanced fingerprint database is directly applied to the localization task. The localization module estimates the target location based on the weighted nearest neighbor (WKNN) strategy. The weight type and its parameters are automatically adjusted through leave-one-out cross-validation (LOO) grid search. Finally, the k nearest reference points are selected, and different weights are assigned according to the neighbor distance. The target location estimate is obtained by weighted averaging, and the predicted target location is expressed as: in, Let i be the spatial coordinates of the i-th neighbor; finally, by comparing with the real location... Euclidean distance calculation for positioning error : 。

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