Geomagnetic-based indoor positioning has been widely studied as an alternative to WiFi-based indoor positioning systems. However, the geomagnetic-based approach is challenging in practice due to its limited feature diversity and susceptibility to noise. Also, geomagnetic ground-truth locations are dificult to be obtained. This study aims to overcome the inherent limitation of magnetic data and discrepancies between testing conditions and real-world scenarios, where the ground-truths are unknown.
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Indoor positioning has received significant attention over the years due to the growth of the
location-based services market. Recent technological advances and demand from various
industries further accelerate research and development of indoor positioning solutions.
Particularly, modern smartphones with various types of sensors provide accessibility to ubiquitous
positioning systems[
While technologies such as Ultra-Wideband (UWB)[
The primary challenge encountered in geomagnetic-based indoor positioning is its inherent physical limitations. Unlike WiFi-based methods that leverage the number of access points as rich feature dimensions, geomagnetic-based approach relies solely on three-axis measurements[12]. This limited feature diversity challenges the accurate positioning process based on magnetic patterns[13]. Moreover, sensitivity of magnetometers necessitates adequate calibration. Magnetometers are prone to biases induced by common materials with soft- and hard-iron properties.[14] In other words, daily exposure to magnetic objects can distort the magnetic field of devices, resulting in sensor bias and adversely afecting the accuracy of the data acquisition.
Thus, calibration is conventionally necessary to mitigate biases and compensate for sensor distortions caused by external elements. However, calibrating for every usage in practical applications using smartphone sensors is not feasible, leading to discrepancies between real-world environments and controlled testing conditions, resulting in inaccurate indoor positioning[15].
This study aims to reduce the discrepancies generated from uncalibrated sensors and identify the representations of space-oriented features. Accordingly, we (1) extract spatio-temporal features from both magnetic patterns and trajectories with time-series similarity measures of latent space and (2) develop a position inference model that points to the target space with consideration of deep-embedded features.
Because magnetic patterns can be captured by a movement along the space, diferent walking speed and pattern generates diferent pattern. Also, noise and fluctuation of sensors generate diferent anomalies in the same area. Therefore, researches on geomagnetic indoor positioning systems involve feature extraction and pattern recognition to identify robust representation.[16, 13, 17].
Qu Wang et al.[16] proposed an indoor positioning system that combines the detection of magnetic loop closure with the calibration of pedestrian dead reckoning (PDR) trajectories using formerly collected magnetic patterns stored in a database. By detecting magnetic loop closure, when a person passes through a physical location previously visited, the system can identify known locations and utilize them to calibrate the PDR trajectory. The magnetic patterns stored in the database are reference points for accurate positioning. AMID(Accurate Magnetic Indoor Localization Using Deep Learning) system[13] is one of the earliest studies of geomagnetic-based indoor positioning using a deep neural network by converting magnetic patterns into images, which are then classified to enable precise indoor positioning.
Both studies focus on magnetic patterns for indoor positioning. They acknowledge magnetic patterns as reliable indicators of specific locations within indoor environments. Additionally, both studies employ a sliding window technique to extract magnetic patterns instead of relying solely on the absolute intensity of a reference point. By identifying magnetic pattern changes by implementing a sliding window approach, these studies aim to improve the performance and reliability of indoor positioning systems in real-time applications. However, when considering the practical application of magnetic patterns for indoor positioning, several challenges exist: • Indoor magnetic patterns change dynamically[18]. • Sensor calibration is frequently required to ensure accurate results[19].
• Data collection conditions are not constant, further complicating the positioning process.
As a result, it becomes essential to consider both temporal and spatial information, highlighting the need for more robust feature extraction methods. Asadi et al.[20] developed a model with deep-embedded learning using autoencoders to consider both spatial and temporal features of trajectory data. The model aims to minimize spatial, reconstruction, and clustering loss simultaneously, enabling the extraction of meaningful representations that capture the underlying patterns and relationships within the trajectory data. Vayer et al.[21] introduced DTW-GI (Dynamic Time Warping with Global Invariances) as an enhanced version of the traditional dynamic time warping technique[22]. DTW-GI incorporates additional considerations of axis discrepancies and rotation, making it suitable for comparing sequences that exhibit both temporal and spatial distortions. DTW-GI metrics, therefore, have found applications in trajectory analysis, human pose estimation, and other fields.
In this paper, we propose a DNN model of diferent parallel autoencoder structures with a fullyconnected network combined. Autoencoders are designed to build latent feature representations from magnetic and trajectory data. This feature extracting part reduces discrepancies between devices resulting from lack of calibration by adapting DTW-GI metrics. Then, the rest part of the model infers the current location from the latent features. The DTW-GI metric is also adapted for window size determination of input data features before the model development steps.
Experimental data was collected using magnetometers and inertial measurement units(IMU) on two diferent human-held smartphones, for two hours along the same tracks. Figure 1 shows the accessible corridors within the target building. The data acquisition process was carried out assuming typical daily indoor positioning conditions without sensor calibration. The magnetometer sample rate was set at 400Hz, while the IMU had a sample rate of 100Hz which is the default sampling rate of Android sensors. A lower sampling rate of 4 Hz was chosen to synchronize and integrate the magnetometer and IMU data. Data preprocessing step includes converting from the local reference frame to the global reference frame using game rotation vectors provided by the Android sensor system.
A magnetometer measures the 3-axis magnetic intensities at a specific location. However, pointreferenced magnetic intensities are insuficient for discerning distinct coordinates accurately. Sliding window technique is popularly used for enhancing time series data features. Sliding windows identify space-oriented indoor magnetic patterns making more feature dimensions. For instance, existing ferromagnetic objects within a particular spatial unit, such as the characteristic pattern associated with the presence of an elevator, can be treated as indicators or landmarks of specific locations. By converting sequential magnetic data into time series data representative of the target space, spatial features can be extracted from the magnetic field and efectively augment temporal information for indoor positioning purposes.
Magnetic sequence data presents identical patterns at the same position, but uncalibrated sensors lead to discrepancies between the axis by diferent devices, as shown in Figure 3. Also, the fluctuations or variations in magnetic patterns are so minor and subtle, making magneticbased indoor positioning challenging.
Therefore, we apply the DTW-GI (Dynamic Time Warping with Global Invariances) technique to measure temporal similarities or diferences between sequential data. Unlike conventional DTW, DTW-GI incorporates the consideration of both axis discrepancies and rotation, making it suitable for comparing sequences with temporal and spatial distortions, disregarding variations due to diferent devices, speeds, and noise levels. Furthermore, by warping the time axis, DTWGI enables optimal alignment between two sequences, allowing for non-linear and variablespeed alignments, thereby enhancing the accuracy and precision of similarity measurements, particularly for space and time-dependent sequences.
The key concept behind Dynamic Time Warping(DTW) is to find the best alignment by minimizing the cumulative distance between corresponding points in the sequences. It dynamically constructs a warping path connecting corresponding points in the sequences, allowing for local deformations in the time axis. The path is determined by considering the distances between y ∈ ℝ × with the feature dimension , the vanilla DTW is calculated as follows: points and neighbors to minimize the overall alignment cost. Given two time series x ∈ ℝ × (1) (2) (3) min ∈ (
x,y) (,)∈ DTW (x, y) = ∑ ( x , y ) = − log (
∑ ∈ ( x,y) − ∑(,)∈ ( x ,y )/ )
By considering axial rotation through manifold alignment, the DTW-GI algorithm becomes a powerful tool for capturing and analyzing spatio-temporal patterns, providing more accurate and robust results for various applications, including indoor positioning and trajectory mapping. The DTW-GI calculation is expressed as the cross-similarity matrix between samples from x and ( y), where ℱ stands for a family of functions, for a short-cut optimization function, and denotes the Frobenius inner product [21]:
DTW(x, y) = min
∑ ( x , y ) ∈ (
x,y) (,)∈ where ( x, y)is the set of all alignments, is a ground metric(mostly Euclidean distance), and is pairs of time series[22].
DTW
extends the vanilla DTW by a soft-min operator to let DTW diferentiable calculation. In case of = 0, DTW is equivalent to the DTW calculation[23].
DTW -GI(x, y) =min
min ⟨ , ( x, ( y))⟩ ∈ℱ ∈ (
x,y) ∈ℱ = min − log
∑ ∈ ( x,y) ⟨ ,( x, ( y))⟩/
To specify a trajectory within the global context, similarity scores are calculated for each of the three axes, measuring the extent of resemblance between corresponding locations in the sequences. Once the DTW-GI scores for each axis are obtained, their summation yields a comprehensive measure of total sequential similarity. This summation consolidates information from all three axes, providing a holistic assessment of the representative patterns in the data. Scatter plots facilitate the visualization of temporal correspondence, as depicted in Figure 3. Lighter points in the scatter plots indicate a higher likelihood of representing the same trajectory. The DTW-GI-based analysis revealed that a 10-second window was suficient for identifying spatial representatives from the magnetic data.
The Inertial Measurement Units (IMU) consist of accelerometers and gyroscopes, informing
the relative displacement and motion. By integrating data from these sensors, IMU can track
changes in position, velocity, and orientation, thereby facilitating the mapping of complete
trajectory or path within the indoor environment. The AI-IMU model[
As mentioned, the sliding window technique has been applied to enhance the magnetic pattern within the target space. Consequently, the resulting features inherently pertain to the trajectory rather than being point-referenced. Thus, aligning them along the corresponding trajectory is essential to represent and analyze the space-oriented magnetic features accurately. Furthermore, this alignment facilitates a comprehensive connection of the spatial feature of the magnetic patterns. By integrating data from accelerometers and gyroscopes, the IMU captures changes in position and computes the relative trajectory.
However, it is essential to acknowledge that the presence of integral error in the gyroscope readings can introduce drift and inaccuracies during the trajectory mapping process. Despite the identical nature of the tracks in real-world scenarios, the cumulative efects of integral error in the gyroscope can lead to deviations from the ground-truth paths in the estimated trajectories. Various techniques, such as pattern matching, feature extraction, or similarity measures, can achieve this track identification and alignment. In the next chapter, these spatio-temporal features are combined to develop a position inference model, and the trajectories with features will be aligned with the deep learning technique.
Autoencoders are unsupervised learning models that reconstruct input data by compressing it into a lower-dimensional representation, known as the latent space or bottleneck. The autoencoder architecture consists of an encoder, which maps the input data to the latent space, and a decoder, which reconstructs the data from the latent representation. By training the autoencoders to minimize the reconstruction error, it learns to extract the most representative features from the input data.
In this research, autoencoders were built to capture the spatio-temporal similarities present in both the magnetic sequences and trajectories. Consequently, two separate autoencoders were constructed to extract features from the magnetic patterns and trajectories, respectively, as shown in figure 5. For both magnetic sequence autoencoder and trajectory autoencoder, each model reconstructs its respective data with a fixed window size of 10 seconds and a 0.25-second interval. Each autoencoder in the proposed method consists of five layers, with the third layer as the bottleneck layer.
The sequential data undergo normalization within the sliding window in the trajectory encoder before feeding an autoencoder as input data. This approach focuses solely on the local trajectory and ensures blindness to the global context. Normalizing the trajectory into sliding windows narrows the analysis and feature extraction process to the local segment within each window. This localized approach allows for a detailed examination of the temporal dynamics within the time horizon, enabling accurate analysis and capturing of relevant spatio-temporal patterns. Furthermore, by being blind to the global context, the trajectory encoder can extract features and characteristics specific to the local trajectory by understanding the data in the context of the given time window.
Two autoencoders generate deep embeddings at the bottleneck layer. These deep embeddings, which represent the encoded features, are subsequently combined. The resulting concatenated features are then mapped onto the trajectory using a bias term to facilitate the inference of the current indoor position. This multimodal structure, therefore, consists of two autoencoders and one deep neural network minimizing the reconstruction losses ( 1, 2) and the prediction loss( ). Therefore the loss function for feature reconstruction is as follows where for magnetic, stands for trajectory: =1
=1 ∑ || − 1( )|2| + ∑ || − 2( )|2| (4)
This approach enables the incorporation of spatio-temporal similarities into the positioning process. The dataset was divided into a 2:1 ratio, with two-thirds of the data used for training and the remaining one-third for testing. The positioning model of the neural network structure was trained to identify and indicate the location along the relative trajectory.
We designed the model to pair inputs from two diferent datasets of magnetic sequences in the training phase to align the devices. The structure of the model is one single multimodal block combining autoencoders and fully connected layers. Two magnetic sequences and one trajectory are fed to train the representation for the same position, sharing the weights of the magnetic feature extractor. Soft DTW-GI scores of magnetic sequence in latent space are calculated as an additional metric to synchronize coinciding data.
The model is designed to predict the position from the magnetic patterns along the trajectory by minimizing sum of reconstruction losses and soft DTW-GI loss with the window size of 10 seconds, updating with 0.25-second intervals. The magnetic sequence autoencoder and the trajectory autoencoder demonstrated a reconstruction error of less than 3 percent, as shown in Table 1, indicating their efectiveness in capturing the underlying patterns and features. Additionally, the mapping accuracy reached 96 percent, highlighting the performance of the models to map the trajectories accurately.
A change point analysis extracted landmarks in the corner points to identify the specific location. The analysis method involves the computation of trajectory data derivatives within each window, enabling the identification of notable variations in the data. The corner points are selected when the sampled data exceeds a predefined threshold. Post-processing is necessary once corners are defined by the change point algorithms due to possibilities for misidentification caused by fluctuations in the trajectory. After the corner definition step, the proposed indoor positioning model maps one unified trajectory and achieves precise localization performance and accurate positioning by mapping each node at the corners in the target area.
To summarize, integrating multimodal learning for feature extraction and results from change point analysis make it possible to compute absolute indoor positioning coordinates, resulting in a comprehensive and accurate representation of the indoor space. This approach ensures reliable and precise indoor positioning.
This study presents a practical implementation with analysis of magnetic sequence data and IMU-oriented trajectories collected from smartphone sensors. The analysis leverages the DTWGI technique in conjunction with a sliding window approach to extract spatio-temporal features and identify space-oriented magnetic patterns. By measuring temporal similarities using DTWGI, similarity scores are computed for each axis and aggregated to provide an overall measure of sequential similarity. The findings demonstrate that a 10-second window is suficient for identifying spatial representatives from the data.
To capture the spatio-temporal similarities in magnetic sequences and trajectories, autoencoders, one type of unsupervised learning, are employed. These models compress the data into a lower-dimensional latent space and reconstruct it, focusing on minimizing reconstruction errors and extracting informative features. The trajectory encoder specifically operates within the sliding window, enabling a detailed analysis of temporal dynamics within each window while disregarding the global context. This localized approach facilitates the capture of intricate spatio-temporal patterns. Moreover, the trajectory encoder extracts features specific to the local trajectory, enhancing understanding and utilization within the given time window.
Supervised learning techniques using deep neural networks are then applied, using relative trajectories as target labels. The models are trained on labeled data to predict relative trajectories based on landmark nodes. This approach significantly improves the system’s performance to estimate positions and movements within the target building. In future studies, the integration of self-supervised learning methods with the DTW-GI technique is planned to map relative trajectories to precise positioning. This research contributes to developing efective and robust indoor positioning systems in real-world practical scenarios without sensor calibration, focusing on the representative pattern.
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