With people nowadays spending an increasing amount of time indoors, smartphone-based indoor positioning technology holds significant practical value. However, existing Pedestrian Dead Reckoning (PDR) algorithms typically require smartphones to maintain specific attitudes, severely limiting their practicality. Attitude changes afect both heading estimation accuracy and step detection performance, leading to positioning errors. Current research addressing attitude constraints primarily focuses on optimizing individual modules rather than providing comprehensive system solutions. This paper proposes a complete attitude-unconstrained smartphone PDR system integrated with Wi-Fi positioning technology. The system encompasses three core modules: (1) Step detection employing multi-sensor fusion technology with cross-sensor axis combinations; (2) Heading estimation adopting frequency-domain analysis to align the smartphone coordinate system with the actual walking direction through angle traversal and coordinate transformation; (3) Step length estimation using an enhanced Weinberg model based on biomechanical characteristics, comprehensively considering height, acceleration variations, and step frequency factors. The PDR results are subsequently adjusted using an adaptive weighted fusion mechanism integrating Wi-Fi fingerprinting. The complete proposed tracking solution is demonstrated through real-world experiments with average positioning errors of 0.66m and 1.1m, for pocket and reading modes respectively.
Pedestrian localization and tracking have attracted considerable attention due to their importance in
search and rescue, emergency services, and location-based applications. With eight billion smartphones
predicted to be in use by 2028 [
The remainder of this paper is organized as follows: section 2 reviews related work; section 3 presents the proposed system architecture and methodology; section 4 describes the experimental setup and performance evaluation; section 5 concludes this work.
Pedestrian Dead Reckoning (PDR) systems have been extensively studied for indoor localization due to their independence from external infrastructure. However, smartphone carrying positions and device orientations significantly impact PDR performance, as diferent phone orientations introduce substantial challenges to accurate positioning [4]. The authors in [5], demonstrated that orientation changes can cause shifts in the acceleration signal dominant axis, leading to significant performance degradation in traditional single-axis detection methods. Research has shown that heading estimation modules are most sensitive to orientation changes, followed by step detection, while step length estimation exhibits relative robustness [6].
Various approaches have been proposed to improve step detection robustness against orientation variations. Traditional signal processing techniques include threshold detection, double threshold detection, and peak detection methods [7], [8]. Furthermore, the heading estimation represents the most challenging component for achieving orientation independence in PDR systems, primarily due to the misalignment between the smartphone device heading and the pedestrian walking direction. Traditional approaches assume a constant ofset angle between device and user heading, but when devices are placed in pockets or diferent positions, the ofset angle varies with body movement, causing this assumption to fail. In [9], the pocket placement problem was addressed by developing rotation matrix and principal component analysis methods that consider dynamic coordinate system changes, projecting acceleration signals into reference coordinate systems to extract the actual walking directions without being afected by device orientation. The step length estimation demonstrates better robustness to device orientation changes compared to other PDR components. The Weinberg model relies primarily on acceleration magnitude diferences and step frequency information, maintaining stable accuracy across diferent device placements [ 7]. Multi-pattern step detection algorithms have achieved high accuracy across diferent walking patterns using smartphone sensors [10].
The PDR systems inherently sufer from cumulative errors caused by sensor noise, bias drift in low-cost MEMS sensors, and the integration of inertial measurements over time, leading to positioning accuracy degradation during extended operation. To overcome cumulative errors, researchers have explored fusion methods combining PDR with other positioning technologies. Extended Kalman filterbased approaches fuse WiFi fingerprinting with PDR using adaptive measurement noise estimation [ 11]. Bluetooth technology and PDR fusion frameworks achieve meter-level positioning accuracy through intelligent parameter adaptation based on RSS measurements [12]. In addition, multi-modal systems combining Wi-Fi, Bluetooth, and PDR demonstrate superior localization performance using unscented Kalman filters [ 13]. Recent factor graph models with local attention mechanisms show enhanced interference resistance in multi-sensor fusion systems [14].
PDR is an infrastructure-free technology primarily used for navigation. It is essential to estimate pedestrian positions accurately over time without imposing predetermined limitations on smartphone placement. In order to obtain a reliable indoor positioning that can adjust to changes in posture, the integration of Wi-Fi fingerprinting with the suggested posture-unconstrained PDR localization method is required.
The step detection is based on the multi-sensor axes fusion method proposed in [15]. In particular, the following four sensors, i.e., accelerometer (A), linear accelerometer (L), gyroscope (G) and magnetometer (M) are combined in four diferent 3-sensor fusion groups: ALG, ALM, LGM, and MAG. By decomposing each sensor into its X, Y, Z axes components, each fusion group results in 9 diferent data-streams resulting in 84 possible combinations per group. The optimal combination is selected by calculating: fusion() = √︁12() + 22() + 32(), (1) where 1, 2, 3 are the three selected axis component measurements. Subsequently, adaptive threshold peak detection is performed based on the combined signal’s standard deviation.
The traditional PDR heading estimation requires fixed smartphone orientation, limiting practical applicability. Users frequently change device positions, i.e., handheld and pocket, causing misalignment between device heading and actual movement direction. The present work adopts the constraint-free heading estimation method proposed in [16], which utilizes the frequency domain characteristics of acceleration signals during human locomotion, and identifies the optimal coordinate system alignment. In particular, through coordinate system rotation transformation, the smartphone’s carrier coordinate system is realigned so that one axis aligns with the person’s actual forward direction. The following three steps are used to implement the algorithm:
1. Multi-axes Rotation Optimization: Follow the sequence to perform three-axes rotation traversal to identify the optimal smartphone coordinate system: • For ∈ [0∘ , 90∘ ]: Rotate around X-axis, identify step frequency maximum peak • For ∈ [0∘ , 90∘ ]: Apply , rotate around Y-axis, repeat analysis • For ∈ [0∘ , 90∘ ]: Apply , , rotate around Z-axis, calculate frequency ratio The binary search method used in the original paper may converge to a local optimal search value, therefore this paper adopts a grid search method for full-angle range exploration, ensuring finding the globally optimal solution that meets the optimization objective.
2. Coordinate Transformation and Filtering: Through the multi-axes rotation optimization in step 1, the system sequentially searches for angles that maximize step frequency characteristics along X, Y, and Z axes, ultimately obtaining the optimal rotation angle combination ( , , ). The determination of these three angles indicates finding the optimal coordinate system configuration that aligns one smartphone axis with the user’s actual walking direction. After rotation, a low-pass filter is applied to the forward direction, while band-pass filters are used for the lateral and vertical direction.
3. Geographic Projection and Heading Calculation: A direction cosine matrix is derived from Quaternion Extended Kalman Filter-based Attitude and Heading Reference System (QEKF-AHRS) attitude estimation using the rotated and filtered sensor data, i.e., accelerometer, gyroscope, and magnetometer, composed of Euler angles that describe the smartphone’s orientation relative to the Earth’s reference frame. This provides the transformation from the aligned body coordinate system to the geographic coordinate system, i.e., East-North-Up coordinate system.
The Weinberg model is a classical step length estimation method proposed by Weinberg et al. [7], that estimates pedestrian step length by establishing a nonlinear relationship between step length and the magnitude of vertical acceleration variations. This model has been widely adopted due to its simplicity, efectiveness, and thorough validation, along with its certain degree of robustness to device orientation changes, making it a fundamental model suitable for scenarios involving device attitude variations. The traditional Weinberg model establishes the relationship between step length and acceleration variations as follows: = ×
√4︀(max − min), where denotes the estimated step length, represents a calibration constant typically associated with pedestrian height, and max and min correspond to the maximum and minimum acceleration signal values respectively, within a single gait cycle. The present study deploys an enhanced Weinberg model that builds upon this fundamental approach by introducing a multi-factor adjustment mechanism to improve robustness to device attitude variations while maintaining computational eficiency. In particular, the framework initially establishes a foundation step length based on pedestrian height as follows:
Base_SL = × , where = 0.34 serves as the base calibration coeficient. Subsequently, the model incorporates a comprehensive multi-factor adjustment mechanism as follows: (2) (3) = Base_SL × accel × freq, where accel represents the acceleration adjustment factor, derived through normalization of acceleration diferentials estimated by: while represents the step frequency adjustment factor, set to 0.95 when step frequency is below 90% of the average step frequency, set to 1.05 when above 110%, and set to 1.0 otherwise. The efective gain = × × is determined through dynamic adjustment, with a gain range of approximately 0.27-0.41.
The system establishes a base step length based on height (0.34 × height), and estimates the acceleration adjustment factor through the normalization (0.85 + 0.3 × normalized diference), and obtains the ifnal step length by multiplying the base step length with the two adjustment factors. Finally, to ensure the rationality of the estimated step length, boundary constraints are implemented as follows: = √︃∑︁ × (RSSonline, − RSSfp,)2, (4) (5) (6) (7) (8) min_SL ≤ ≤ max_SL
The Wi-Fi fingerprinting module employs an adaptive Weighted k-NN (WKNN) algorithm that assigns weights based on the detection frequency of the Media Access Control (MAC) addresses across fingerprint sampling locations. The detection frequency is calculated as the ratio of sampling locations where each MAC address is detected to the total number of fingerprint sampling locations. Specifically, characteristic MAC addresses with detection frequencies below 20% are assigned 3.0 times weight due to their high location specificity, regional MAC addresses with frequencies between 20%-60% receive 1.5 times weight, while common MAC addresses with frequencies exceeding 60% are given 1.0 times weight. The weighted distance is estimated as follows:
where , represents the real-time signal strength of the -th WiFi access point, , denotes the pre-stored signal strength of the same access point in the fingerprint database, and is the adaptive weight assigned to each access point based on its spatial coverage rate. Based on distance distribution, characteristic MAC density, signal variance and matching quality, multi-strategy fusion dynamically determines the k-value (3 ≤ k ≤ 8). Final positioning adopts k-nearest neighbor weighted average, combining distance-based weights (1/d²) and matching quality weights.
Finally, the adaptive weighted fusion is applied, which is estimated as follows:
= · + (1 − ) · , where represents the fused position estimation, represents the PDR position estimation, represents the WiFi position estimation, and represents the adaptive fusion weighting coeficient. The weighting coeficient is dynamically determined based on the Euclidean distance = || − ||2 between PDR and WiFi position estimations, with values of 0.95, 0.75, 0.65, and 0.55 corresponding to distance ranges of >20m, 10-20m, 5-10m, and <5m respectively.
Experiments were conducted in a Z-shaped corridor at the Cyprus University of Technology, providing a representative indoor environment with consistent flooring, uniform lighting, and magnetic interference (a) Experimental site (b) Pocket Mode (c) Reading Mode from electronic devices. The test path consisted of three segments: 32 meters in the direction of 50∘ east of North, 11 meters in the direction of 320∘ west of north, and 11 meters in the direction of 50∘ east of north, totaling 54 meters with two significant directional changes to evaluate the performance of the attitude-unconstrained PDR system under dynamic conditions.
The data acquisition was performed by using a OnePlus 10 Pro smartphone equipped with integrated MEMS sensors, i.e., tri-axial accelerometer, gyroscope, and magnetometer. Sensor data were captured by utilizing the AndroSensor application at a sampling frequency of 100Hz. The experiments employed two smartphone carrying modes: pocket mode (device placed in trouser pocket) and reading mode (handheld with screen facing the user). The experimental site and the carrying modes are shown in Figures 2a, 2b and 2c respectively. Additionally, the experiments required prior collection of ofline Wi-Fi fingerprint data and establishment of a fingerprint database. Experiments were conducted with participants walking at normal speeds (approximately 1.2-1.5 m/s). The Wi-Fi fingerprint database was constructed approximately 10 hours prior to the online positioning experiments. Wi-Fi fingerprints were collected at 2-meter intervals along the trajectory, with 1-meter intervals near endpoints. Considering the temporal variations in signal strength, multiple 20-30 second stationary Received Signal Strength Indicator (RSSI) measurements were collected at each reference point during diferent time periods to establish the ofline database. Sensor data required for PDR and online Wi-Fi fingerprint data were collected to prepare for subsequent algorithm processing.
Figure 3a and Figure 3b demonstrate the step detection results. Step detection using the Accel_XAccel_Y-Lin_Acc_Z configuration correctly identified 92 steps in reading mode and 89 steps in pocket mode under the same configuration, both matching the actual step counts. The adaptive threshold efectively handled amplitude variations, with approximately 0.3 for reading mode and 0.6 for pocket mode, demonstrating excellent adaptability to non-stationary walking signals. Meanwhile, the detected peaks (red circles) were consistently distributed throughout the time series, showing robust stride recognition capability. Using the enhanced Weinberg model, Figure 4b shows step length variations in pocket mode ranged from 0.52-0.76 meters with an average of 0.65 meters, while as shown in Figure 4a, reading mode showed shorter step lengths of 0.48-0.67 meters with an average of 0.57 meters.
As shown in Figure 5a and Figure 5b, the heading estimation concluded in average errors of 22.74°in pocket mode and 16.91°in reading mode, with reading mode demonstrating better accuracy. Although the errors were somewhat larger than those in [16], possibly due to diferences in experimental environments, equipment, and optimal parameter selection, the method accurately captured the overall heading change trends, demonstrating the robustness of the approach.
The experiments employed Sequential Importance Resampling (SIR) particle filter [ 17] for comparison. The adaptive weighted fusion method achieved optimal performance in both modes of this experiment. As shown in Figure 6a and Figure 7a, in reading mode, adaptive weighted fusion achieved a mean error of 1.10m, median error of 0.84m, and 95th percentile error of 2.82m, while SIR particle filter achieved 1.52m, 1.55m, and 3.07m respectively. Pure attitude-unconstrained PDR exhibited errors of 2.51m, 2.43m, and 4.29m, while standalone WiFi positioning showed poor performance with 95th percentile error of 3.99m. 0.7 0.65 ) (hm0.6 t g n e tpL0.55 e S 0.5 0.45 360 315 )°270 l(e225 g n A180 g n iad135 e H90 45 0
Detected 92 Steps, Threshold = 0.308 ,Reading Mode
Detected 89 Steps, Threshold = 0.578 ,Pocket Mode 0.8 0.75 As illustrated in Figure 6b and Figure 7b, the pocket mode, adaptive weighted fusion demonstrated superior performance with mean error of 0.66m, median error of 0.61m, and 95th percentile error of 1.41m. SIR particle filter achieved 1.36m, 1.38m, and 2.51m respectively, while pure PDR exhibited 1.94m, 1.69m, and 3.86m. Standalone Wi-Fi positioning showed poor stability with 95th percentile error of 4.78m. Compared to pure PDR, adaptive weighted fusion achieved improvements of 56-66% in mean error, 48-65% in median error, and 24-63% in 95th percentile error across both modes.
In this paper we propose a comprehensive, attitude-unconstrained PDR system integrated with Wi-Fi ifngerprinting technology, aiming to decrease attitude dependencies among PDR components and eliminate the impact of attitude variations on positioning accuracy. Our preliminary experimental results indicate that the proposed attitude-unconstrained PDR system demonstrates good robustness and positioning accuracy across diferent carrying modes, with significantly enhanced performance when combined with WiFi fusion technology. In this setting, the adaptive weighted fusion method outperformed both pure PDR and SIR particle filter approaches in both pocket and reading modes, demonstrating the efectiveness and practicality of the integrated positioning system.
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