Further elaboration on acoustic-assisted indoor pedestrian dead reckoning—The extended implementation details and new evaluations

Abstract

Indoor pedestrian dead reckoning (PDR) using smartphone inertial sensors suffers from accumulated errors, so researchers use various indoor landmarks for correction. This study proposes acoustic sensing—using a smartphone's speaker and microphone to detect doors and walls—as a new ubiquitous landmark requiring no extra hardware or environment-specific training data. We present a neural-network-based acoustic event detector for door-passing and wall-proximity events with wall-distance estimation, and a particle-filter trajectory algorithm that uses these landmarks and map matching to correct inertial drift for offline trajectory reconstruction. Compared to the conference version, this paper adds implementation details, further experiments, and a thorough discussion of the method's limitations. Consistent with the conference version, results show that under relatively ideal conditions and a strict grasping posture, the method substantially outperforms the NeuralPDR baseline. However, the expanded evaluation shows that landmark recognition degrades sharply when grasping posture changes or obstacles/noise are present, that trajectory error grows exponentially at low landmark recall, and that the method's real-time processing, power, and memory demands remain impractical.

1 Introduction

1.1 Background

Wearable computing researchers use smartphone IMU–based indoor offline trajectory reconstruction systems, such as pedestrian dead reckoning (PDR), for GPS-free trajectory prediction. Pure IMU PDR has two main issues: gyroscope drift that accumulates large errors, and no way to determine the initial position/orientation, so auxiliary cues are required. To correct drift or obtain initials, researchers exploit indoor “landmarks:” Bluetooth low energy (BLE) beacons detected by the phone's Bluetooth for absolute coordinates (Taniuchi and Maekawa, 2015); magnetic signatures from infrastructure (e.g., elevators) via built-in magnetometers (Kim et al., 2019; Lee and Han, 2017); and location-specific human activity recognition (e.g., stair climbing, door opening) from phone or smartwatch IMUs (Abdelnasser et al., 2015; Gu et al., 2020; Hardegger et al., 2012; Grzonka et al., 2012).

1.2 Goal and approaches

Inspired by door-opening landmarks from wrist-worn devices (Hardegger et al., 2012; Grzonka et al., 2012), we treat ubiquitous doors and walls as dense indoor landmarks and identify them via active sound sensing¹ using off-the-shelf smartphone speakers/microphones. Compared with motion-based detection (which needs wrist motion), sound can detect passing through doors even if already opened, and can also detect wall-related events that motion methods miss. This article uses the events of passing through a door and passing by a wall as landmarks to correct the trajectory. Figure 1 illustrates our conception, where Figures 1a, b show passing through a door could produce short ToF, transient signals and large Doppler due to proximity and relative motion; while Figure 1c shows that approaching a wall will yield increasing echo amplitude as distance decreases, pronounced Doppler, and roughly constant ToF when moving parallel to the wall. Based on the above conjecture, we conducted an observational experiment and designed a particle filtering framework that can perceive landmarks through acoustic sensing without the need for infrastructure deployment. As with the conference version, this paper focuses on achieving relatively accurate offline trajectory reconstruction by leveraging high computing power and repeated iterative calculations.

Figure 1

Wang et al. (2025).

1.2.1 Challenges

During our experiment, the following challenges were discovered.

• Soft-constraint landmarks with unknown locations: The wall landmarks do not have absolute coordinates (Yonetani et al., 2024) (we call the wall a “fuzzy landmark”). There is no precedent for using them for particle filtering correction. We need to design a new particle filtering correction scheme.

• Inevitable erroneous landmarks & unknown initial state: Due to the obstruction of indoor objects and non-line-of-sight (NLoS) issues, there may be errors in identifying landmarks (i.e., false positive landmarks). Moreover, we do not assume the known initial position, which poses difficulties for the design of the particle filter.

1.2.2 Approaches

We propose a PDR pipeline that uses acoustic door and wall landmarks to correct inertial errors.

• Segmented particle-filter fusion: split the acoustic-event stream at detected doors; for each segment, run map-matching particle filtering on the segment's IMU data with candidate start/end positions from known door coordinates. Forward/backward tracking yields map-consistent sub-trajectories and unknown initials; short segment estimates reduce drift. Reconstruct the full path by merging sub-trajectories and discarding geometrically inconsistent segments.

• Soft-constrained particle filtering with wall landmarks: treat walls as ambiguous, soft constraints—use acoustically estimated distance and movement direction to bias particle weights and disambiguate positions without treating walls as absolute anchors.

1.3 Contributions

(i) The first indoor PDR aided by acoustic door and wall landmarks, with empirical characterization and detection methods; (ii) A particle-filter PDR pipeline that integrates both landmark types above to improve localization accuracy.

Compared to the original version (Wang et al., 2025), this article details the generation process of acoustic image sequences, the neural network structure, the working process of particle filtering, and the detailed process of erroneous landmark elimination. We conducted a deeper analysis of the original dataset at a low recall rate of D landmarks and additionally evaluated its running speed, power consumption, and memory usage on different devices. Furthermore, we also expanded the dataset to test the performance of landmark recognition under different users, different holding postures, and obstacle conditions. We have also revisited certain inaccurate descriptions in the conference version, such as the misnaming of the recognition metric IoU and the description of wall-penetration artifacts in the NeuralPDR baseline. In the conference version, NeuralPDR's “passing through walls” behavior was attributed to particle depletion; however, this characterization is inaccurate, as NeuralPDR does not employ particle filtering. These corrections do not alter any previously reported results; they serve solely to rectify the descriptions.

2 Related work

2.1 Pedestrian dead reckoning

IMU-based PDR derives motion from accelerometer step detection and stride models, with heading from gyroscope integration but subject to drift (Mezentsev et al., 2005; Huang et al., 2010; Scarlett, 2007; Abyarjoo et al., 2015; Ladetto and Merminod, 2002; Bian et al., 2025a). End-to-end deep models (LSTM, CNN) learn displacement and heading directly from raw inertial streams (Chen et al., 2018; Yoshida et al., 2019; Chen et al., 2020; Younas et al., 2021). Landmark-assisted schemes reduce drift by detecting seed landmarks (elevators, stairs) or organic cues (Wi-Fi/BLE, magnetic anomalies, visible-light, indoor GPS) (Abdelnasser et al., 2015; Gu et al., 2020; Guo et al., 2017b; Chen et al., 2015; Zhuang et al., 2016; Kim et al., 2019; Lee and Han, 2017; Kuo et al., 2014; Juneja and Vashisth, 2017; Zhou and Maekawa, 2023; Bian et al., 2021, 2025b); activity-based methods (e.g., ActionSLAM) exist but suffer high ambiguity (Hardegger et al., 2012; Zhou et al., 2015). We treat acoustic door/wall cues as complementary, low-cost landmarks.

2.2 Active acoustic imaging

Active probing (often frequency modulation continuous wave, FMCW) provides joint range and velocity estimates and is interference-resilient. Pulse compression enhances range resolution but handles instantaneous motion poorly (Dissanayake et al., 2023); array beamforming improves angular focus but smartphone mic layouts limit performance (Shen et al., 2020). (Inverse) Synthetic-aperture sonar (SAS/ISAS) approaches yield high resolution via motion but require precise trajectories or fixed setups (Yan et al., 2024; Wang et al., 2022). Range–Doppler processing separates time-of-flight and Doppler to detect fine displacements with modest hardware needs (Thayaparan et al., 2008), making it suitable for our smartphone deployment.

3 Acoustic imaging

Verifying the conjecture in the Introduction is the cornerstone of this article. Before experiments, we design acoustic imaging to obtain four-dimensional acoustic data.

3.1 Method overview

As Figure 1d shows, acoustic imaging has two steps: (i) form an echo matrix by digital dechirp, and (ii) produce an RD-map sequence by applying range-Doppler processing (RDP) to submatrices extracted with a sliding window. The echo matrix encodes frequency/phase differences between transmitted and reflected FMCW pulses, i.e., time of flight (ToF) and Doppler.

3.2 Signal design

We use FMCW swept from 15,000 Hz to 21,000 Hz to avoid common domestic noise. A single pulse is

The FMCW repeats with a pulse repetition interval (PRI) of 0.025 s and a pulse width (PW) of T_pw = 0.02 s (pulse repetition frequency, PRF = 1/PRI).

3.3 Digital dechirp

Dechirp separates phase/frequency differences within each PRI. Hardware dechirp uses a mixer whose inputs are the received signal s_r (one-PRI segment) and a reference s_ref (the transmitted FMCW). Consumer devices lack direct access to s_ref, so we recover it in software.

3.3.1 Construct reference signal

We model the reference signal as the non-linear frequency-modulated continuous wave (NLFM-CW) modulated by a nonlinear window W_ref caused by speaker/mic distortion:

where n denotes samples (nT_s). We recover W_ref by fitting a cubic spline on the collected spectral amplitude over 15–21 kHz; the complex exponential matches the cosine carrier phase.

3.3.2 Digital mixer

Compute an analytic received signal z_r via the Hilbert transform and form the IF (Hadamard product with the conjugate reference):

then low-pass filter s_IF to obtain the baseband dechirp output s_b.

3.4 Range-Doppler processing

3.4.1 Echo matrix

Each PRI yields a dechirped vector s_b (length n). Concatenate m successive s_b vectors to form an n×m echo matrix (Figure 1d).

3.4.2 Range-Doppler processing with sliding window

Apply FFT (sampling rate = PRF) across each row of the echo matrix to get an RD map. To produce a temporal RD sequence, extract submatrices with a sliding window of 50 PRIs along the m-axis and apply RDP to each submatrix, producing the RD-map time series used by the landmark detector.

3.5 Observation

Using the method in Section 3, we recorded acoustic data while walking indoors and converted it to a sequence of RD maps. Figure 2 shows representative frames. The vertical axis is range (distance to reflecting surfaces), and the horizontal axis is Doppler (an indicator of motion intensity). We set the displayed Doppler range to [−25, 25], slightly beyond the nominal Nyquist band (±PRF/2 = [−20, 20]) to visualize strong motions.

Figure 2

Wang et al. 2025).

3.5.1 No landmark (N)

Figure 2 (1) shows no nearby landmark: a persistent horizontal line at ≈1.3 m is a ground reflection, which exhibits small Doppler due to phone movement during steps.

3.5.2 Door (D)

Figure 2 (2, 3) show door-passage frames: transient features in the 0.25–1.0 m band appear and vanish rapidly, matching the short-duration nature of passing a door frame.

3.5.3 Wall (AW/PW)

Figure 2 (4, 5) (approaching wall, AW) display a bright oblique line whose range decreases, and Doppler changes as the user nears the wall (larger echo amplitude than the door). Figure 2 (6) (parallel to wall, PW) shows the diagonal feature collapsing into a short horizontal line at ≈0.35 m, indicating steady parallel walking at that lateral distance; small Doppler variations arise from gait-induced distance fluctuations (see Supplementary video for continuous RD sequences).

4 Acoustic-assisted indoor PDR system

4.1 System overview

We assume a user holds a smartphone that records accelerometer and gyroscope data and captures reflections of FMCW pulses emitted by the device speaker. We also assume the floorplan for the target level is available, including door coordinates/orientations and walls represented as line segments.

The system has four modules (Figure 3): the Acoustic Imaging Module (Section 3) produces a time series of RD maps; the Acoustic Landmark Detector converts RD maps into a landmark sequence and a wall-side distance sequence; the Neural PDR module (following state-of-the-art practice (Zhou and Maekawa, 2023)) predicts per-step displacement and heading deviation from inertial time-series; these outputs form a “prediction sequence” consumed by the Trajectory Estimation Module, a particle-filter with false-landmark rejection that produces the final trajectory.

Figure 3

Wang et al. 2025).

To increase particle-filter robustness, we apply “segmented-matching particle filtering”: split the prediction sequence at detected door landmarks, run map-matching particle filtering (forward/backward) on each short segment to produce candidate sub-trajectories, and merge them by geometric consistency using door locations. This mitigates long-sequence failures where all particles collide with walls and are pruned.

4.2 Acoustic landmark detector

The LRCN-based classification (Donahue et al., 2015) task is split into three separately trained networks, because the three prediction tasks differ substantially. Describing it in the conference version as using one LRCN classifier is confusing and inaccurate; this is corrected here. The D event has a clear duration prior: a complete D event typically lasts about 1–1.5 s (see Supplementary material). By contrast, the durations of N, AW, and PW are not fixed and are better handled with frame-wise outputs. The distance-regression task is also different from classification, so it is trained separately as well. All three networks share the same input format: a consecutive image window with per-frame resolution 60 × 50 and 3 input channels. The final frame-level output sequence is merged via an evidence-based approach to produce an event sequence in which segment boundaries exhibit slight overlaps.

4.2.1 Wall classification network

This network learns three semantic labels: N, AW, and PW. The original D label is merged into N. As shown in Figure 4, the model consists of convolutional blocks, a BiLSTM, temporal attention, and a frame-wise classification head. Its forward pass outputs three logits, one for each of N, AW, and PW; each is converted independently by a sigmoid into a per-frame confidence.

Figure 4

Each class is supervised by its own binary cross-entropy term; summing the three gives . With the PW false-positive weight at 4.0, the total loss is

Here, suppresses the probability that non-PW frames are misclassified as PW. Class weights are estimated from label frequencies in the training set, so that background and rare classes are treated differently during optimization.

During sample construction, after the window length is randomly selected, the center position will also be randomly perturbed. The forward pass outputs per-frame class confidences rather than hard labels.

4.2.2 D classification network

This network performs binary classification and outputs per-frame probabilities for D vs. non-D, as shown in Figure 4. A spatial attention block is inserted after the convolutional backbone. The model then uses a BiLSTM to capture temporal dependencies and keeps both a frame-wise classifier and a window-level classifier. The window-level head constrains whether a fixed-length window contains D.

Training samples are fixed-length windows of 70 frames. For each D segment, a positive window is first constructed near the segment center, with a center offset of at most 10 frames; the frame-level labels inside the positive window are determined by its overlap with the original D segment. Negative windows are sampled from background regions that do not overlap D. Each batch is then balanced by sampling so that positive and negative windows are approximately equal, which reduces the impact of class imbalance.

The total loss has two terms:

where is an asymmetric frame-wise BCE loss and is a window-level auxiliary BCE loss. The frame-wise term directly supervises whether each frame belongs to D, while the window-level term constrains whether the whole fixed-length window contains D, providing a higher-level existence constraint beyond frame boundary learning. False positives in negative samples are additionally penalized with weight 2.0.

The forward pass first produces frame-wise logits and their sigmoid probabilities; it also outputs window-level logits and corresponding sigmoid probabilities. These soft probabilities are used together with hard labels during training: hard labels provide supervision, while soft probabilities provide a differentiable response and later serve as input to frame-wise post-processing.

4.2.3 PW distance regression network

The last one in Figure 4 shows this network, which does not predict categories; instead, it regresses the distance value for PW frames. Its architecture consists of a lightweight convolutional backbone, a BiLSTM, temporal attention, and a regression head. The regression head concatenates the current frame features, global context, and context from the preceding AW segment, and outputs a scalar distance.

During training, the window length is randomly sampled within a certain range. Windows containing PW are preferred. If an AW segment precedes PW, the window includes at least 50 frames of context before the left boundary. The regression loss is computed only on PW frames, using Smooth L1 loss:

Here, Ω_PW denotes the set of PW frames.

4.2.4 Candidate Segment Extraction

Each of the four channels'—D, N, AW, and PW—training involves some form of class reweighting (D's balanced sampling, the wall network's label-frequency class weights, PW's added false-positive penalty), which shifts each raw logit by a known, closed-form amount; calibration therefore subtracts an analytically computed bias b_c and then using temperature scaling (Guo et al., 2017a) supplies the fitted parameter T_c, on full-sequence, unwindowed validation inference: .

For each channel c, frames with (default 0.47–0.78) seed an initial set of candidate fragments, refined by the rules below. Let π_c be the prior probability of class c from training-set label frequencies, and define the frame-wise log-likelihood ratio

Because π_D is small, a moderate already yields a large ℓ_{D, t}, while a common class such as N needs a higher raw confidence for the same evidential weight.

Two same-class fragments separated by a gap are merged iff the gap length does not exceed W_e = ⌈ϕL_class⌉ (with L_class the neighboring fragment's length and ϕ is the window proportion) and the gap's average LLR satisfies (from −0.4 to 0 depends on certain task). A fragment survives iff its accumulated evidence satisfies S_c(frag)≥τ_evid (default 3); otherwise it is reset to background.

4.2.5 Cross-Channel Segment Merging

Candidate segments from all four channels are pooled and sorted by start time, and each pair of temporally adjacent or intersecting segments A = [a_s, a_e] (channel c_A) and B = [b_s, b_e] (channel c_B), with a_s<b_s, is resolved according to how they overlap. A non-overlapping pair (b_s≥a_e) is left unchanged, and an overlap narrow enough that min(a_e, b_e)−max(a_s, b_s) ≤ Δ_max(A, B): = min(β_cA, β_cB)min(L_A, L_B)—with per-class ratios β_D = 0.23, β_PW = 0.11, β_N = β_AW = 0.28—is simply kept.

A wider overlap (b_e>a_e, beyond Δ_max(A, B)) is resolved from where the region-average evidence favors one side, since a frame-level crossing point is unstable under oscillating confidence. With overlap width L_ov, midpoint t_mid, and average LLRs over the overlap, the split point is

and a width-Δ_max overlap is kept centered at t^*, with the remaining frames assigned to whichever side's ℓ_{c, t} is locally higher.

When one segment lies entirely within the other (b_e ≤ a_e), we compare and over B's span: if B's is clearly higher, A is carved into two flanking fragments and B is kept independently; otherwise B is discarded and A is left intact. The D and N conflict is not resolved by directly comparing and , since the wall network's N class was trained on true D frames. With taken from each channel's retained curve over the disputed span, a merge-stage threshold τ^merge (default 0.63 to 0.81), and : resolve as D if and ; resolve as the dominant wall class if ; apply the split above to ℓ_{D, t} and ℓ_{N, t} if (default 0.22), , and M_W ≤ τ_low; otherwise resolve as N. Conflicts not involving both D and N use the rules above directly.

Any fragment produced or reassigned by the rules above—including a region resolved to the dominant wall class—must still satisfy S_c(frag)≥τ_evid. And note that the parameters mentioned above are based on heuristic design and require fine-tuning according to the specific application.

4.3 Sub-sequence segmentation

As shown in Figure 3, the inputs to the trajectory estimation module are four-dimensional prediction sequences, which are segmented into sub-sequences using door landmarks (the center of D event) as separators. After that, we apply the particle filter to each prediction sub-sequence.

4.4 Trajectory estimation module with particle filter

The Trajectory Estimation Module fuses Neural PDR and acoustic-landmark outputs in a particle filter (Gustafsson et al., 2002) for map-matching (Santo et al., 2017; Ohara et al., 2015). Each particle holds position , orientation , and weight . Acoustic landmarks (e.g., door or wall side) modulate particle weights to correct accumulated inertial error. Initial particles for a sub-sequence are seeded at door coordinates with orientation normal to the door; forward (and, for first segments, backward) tracking then runs the particle filter.

The filter iterates three steps: sampling (propagate particles with the Neural PDR displacement and heading plus Gaussian noise), weight calculation (score particles against landmarks and the floorplan), and resampling (select according to weights).

4.4.1 Sampling

We use a linear motion model: sample particles at time t from each particle at t−1 by applying predicted displacement and directional deviation from the Neural PDR and adding Gaussian noise.

4.4.2 Weight calculation

Figure 5a outlines the flow. Basic drift-based weights are combined with landmark-specific weights when an acoustic event is detected (D, First PW, and Subsequent PW). First PW finds the best trajectory match to the wall side; Subsequent PW adjusts orientation and lateral position relative to the wall. We use the following components.

Figure 5

4.4.2.1 Drift weight calculator

According to (Zhou and Maekawa 2023), basic weights w_d and w_o are inversely proportional to the Gaussian noises added to the displacement and directional deviation in the sampling process, respectively, indicating that a particle with a greater noise has a smaller weight.

4.4.2.2 Distance/door weight calculator

We upweight particles whose sampled distance to the closest landmark l matches the acoustically estimated distance ; the distance weight is:

where denotes the estimated distance between the user and the landmark predicted by the acoustic landmark detector, and σ_l is a hyperparameter of the normal distribution . Notably, when the detected landmark is a door, i.e., when passing through a door, the estimated distance is set to zero. In the first condition of the equation, the weight of the landmark step is directly reduced to zero if the sampled distance exceeds 3σ_l, to strictly limit the candidate trajectory. In the second and third conditions, we assign a heavy weight close to 1 when the estimated distance aligns with the sampled distance.

4.4.2.3 Orientation weight calculator

We upweight particles whose orientation θ_i aligns with the closest wall orientation (two possible wall-facing directions are considered); the orientation weight is:

where θ_i represents the orientation of particle . Unlike distance weights, determining orientation weights requires evaluating two possible orientations of the wall: or . The closest orientation of the particle will be selected.

4.4.2.4 Parallel orientation corrector

For subsequent PW steps, the closest wall's orientation directly corrects particle alignment by setting .

4.4.2.5 Normal distance corrector

For lateral correction, particles choose the nearer of the two candidate positions normal to the wall.

4.4.2.6 Collision filter

Particles that collide with walls receive zero weight via the coefficient α_w.

4.4.2.7 Weight combination

Combine components by multiplication:

where w_d and w_o, calculated by “Drift Weight Calculator,” represent Gaussian noise added to the displacement and directional deviation in the sampling process, respectively. Specifically, when the landmark is the subsequent PW, w_o is set to 1.

4.4.3 Resampling

We combine two resampling strategies: ordered resampling (keeps top trajectories by cumulative recent weight) and random resampling (injects variability). Both exclude zero-weight particles.

4.4.3.1 Ordered resampler

Used for D or First PW steps; cumulative weight over the recent N_c steps is:

and the top N_r trajectories by are selected.

4.4.3.2 Random resampler

Used for N or Subsequent PW steps; selects N_r trajectories randomly among nonzero-weighted endpoints to increase flexibility.

Figure 5b shows an example: First PW triggers ordered resampling over N_c steps to prune inconsistent trajectories; subsequent PW uses random resampling (only parallel-direction displacement is randomized) to diversify lateral corrections and avoid collapse. A later D event then prunes particles far from the closest door. It should be noted that the aforementioned particle filtering procedure is merely an empirical, heuristic method and has not undergone rigorous derivation.

4.5 Sub-trajectory merging

Sub-trajectories may fail during the particle filtering process (with weights dropping to zero); consequently, it is necessary to retry multiple times—changing the random seed—to test the feasibility of the initial landmark at the same time. Since our system prioritizes minimizing trajectory error regardless of computational cost, we continue execution even after obtaining candidate sub-trajectories in an attempt to find the one with the highest weight. If the process succeeds through retries, the sub-trajectory with the highest weight among the multiple attempts is selected as the sub-trajectory originating from that landmark. This means that after several attempts, the retry mechanism will automatically select the sub-trajectory that best conforms to the inertia data and the consistency of the map, which is beneficial for reducing errors.

Each prediction sub-sequence may yield multiple candidate sub-trajectories (and some may be produced under wrong landmarks); stitching these candidates into a global trajectory requires resolving matches and removing erroneous landmarks. We first introduce concise definitions used below:

• Match: a pair of sub-trajectories from two adjacent sub-sequences is a match if the earlier segment's end D landmark aligns in both position and direction with the later segment's start D landmark.

• Unique match: exactly one matching pair exists between the candidate sets of two adjacent sub-sequences.

• Unique candidate sub-trajectory: a sub-sequence that has a single candidate sub-trajectory.

• Correct Trajectory: a sub-trajectory whose start/end door positions and directions agree with ground truth.

• Match table: a table that lists, for each prediction sub-sequence S_n, its candidate sub-trajectories S_nT_k and the matching pairs M_n between S_n and S_n+1 (Figure 6, left).

• Merge sub-trajectories: when two adjacent sub-trajectories match, merge them into a new (unique) sub-trajectory and update the match table by removing the M column between their sub-sequences.

Figure 6

Using these notions we propose a recursive merging procedure driven by “Local Correct sub-Trajectories” (LCTs). The algorithm merges sub-trajectories in order of reliability (most reliable first) and treats endpoints of any LCT as known correct door positions/directions, which fixes the connecting endpoints of adjacent sub-sequences. If two sub-sequences between LCTs cannot provide candidate sub-trajectories whose endpoints match those known connectors, we infer one or more false-positive landmarks inside those sub-sequences, remove those suspect landmarks (i.e., keep only landmarks belonging to the surrounding LCTs), merge the sub-sequences, and re-run particle filtering on the merged segment. Figure 6 illustrates LCT cases and the merge workflow. Finally, we assume longer surviving sub-trajectories are more reliable (a particle that endures map-matching longer indicates greater consistency), so the merge order and trust decisions favor longer candidates. It should be noted that this is merely a heuristic method and has not undergone rigorous theoretical derivation.

5 Evaluation

The experimental assessment reported here relies on two distinct datasets and complementary analysis procedures. The first dataset, which we refer to as the “comprehensive evaluation” dataset, is used to derive broad, quantitative performance measurements that characterize the end-to-end behavior of the proposed pipeline across diverse deployment scenarios. To obtain more accurate quantitative metrics for trajectory correction, some tests provided more comprehensive assessments compared to the spot checks used in the conference version. The number of trajectory retries was also reduced to obtain new comparative results. The second dataset, designated the “robustness-evaluation” dataset, is constructed explicitly to interrogate the performance of the acoustic-landmark recognition stage under a variety of extreme interference and occlusion conditions. Note that the robustness-evaluation experiment constitutes an extension beyond the experiments presented in the original manuscript (Wang et al., 2025).

5.1 Comprehensive evaluation dataset

We curated a wide-ranging dataset consisting of recordings from nine heterogeneous indoor venues situated in multiple countries (see Table 1). The chosen venues include offices, laboratories, meeting rooms, shopping malls, hospitals, and busy lobbies; these places also incorporate office-like settings to provide adequate environmental landmarks. A portion of these environments supplied the training data (summarized in Table 2). To prevent data leakage and to provide a stringent estimate of generalization, we adopted a leave-one-environment-out cross-validation protocol: any device–environment pair appearing in the landmark training partition is strictly excluded from the corresponding test partition.

Training collections were recorded using two handset models (Samsung S20 Ultra and S21 Ultra), while two additional models (OPPO Find X3 and Xiaomi 10 Ultra) were withheld for testing in order to evaluate cross-device generalization (see Table 3). Inertial measurements were sampled at conventional rates (accelerometer at 100 Hz and gyroscope at 50 Hz), and ARCore served as the source of ground-truth positional references. Due to environmental differences and variations in inertial sensor models, separate inertial training and ground truth calibration are required for each combination of environment and device. Table 1 enumerates the geometric dimensions of each venue.

5.1.1 Evaluation methodology

In this paper, event detection is evaluated using the intersection over ground truth (IoGT) without a one-to-one matching constraint, defined as IoGT = |P∩G|/|G|, where P and G denote the predicted and ground-truth event intervals, respectively (this quantity was referred to as IoU in the conference version (Wang et al., 2025); we adopt the more precise IoGT terminology here, as our pipeline only requires predicted segments to cover the true event window). A predicted segment is counted as a correct detection when its IoGT meets or exceeds the threshold τ; throughout our experiments we set τ = 0.5. From these matches we compute the conventional retrieval metrics—precision, recall and F1-score. Using this protocol, we report recognition metrics for four classes of output events, encompassing both preliminary spot checks and comprehensive testing; for related FMCW-based wall-distance estimation performance, please see SAMS (Pradhan et al., 2018).

To place our method in context and to evaluate component contributions, we synthesize trajectories from IMU integrations and then apply the proposed correction filter. The evaluated systems and ablations are:

• Neural PDR: the competitive neural PDR baseline evaluated under the same protocol as the conference version, assuming a known initial location and omitting particle-filter-based map matching (Zhou and Maekawa, 2023). This article did not select other sensor-assisted PDR methods as a baseline because of the limitations of the experimental conditions.

• Proposed: the complete acoustic-assisted indoor PDR pipeline introduced in this work, which operates without an initial-position prior.

• W/o door: an ablation in which door landmarks are removed (the first detected door event is preserved but treated as unknown).

• W/o wall: an ablation excluding PW landmarks, used to assess how wall-derived cues affect filter corrections.

• W/o erroneous landmark elimination: an ablation that disables the erroneous-landmark filtering stage; MAE is nevertheless reported even when discontinuous trajectories result. Note that this elimination method essentially eliminates discontinuous sub-trajectories; discontinuous sub-trajectories can arise even in the absence of erroneous landmarks.

The trajectory evaluation metric employs the widely used Mean Absolute Error (MAE)—defined as the average Euclidean distance (meter) between points on the densified trajectory and their nearest points on the ground truth—to quantitatively assess the shape and offset distance of the reconstructed trajectory.

5.1.2 Results

5.1.2.1 Performance of acoustic event detection

Since a qualitative assessment of the model's effectiveness in the new environment-device combinations is required first, we need to begin by spot-checking the test set using the LOEO-CV method. Here, we viewed the F1 scores for each device-environment combination using the same sampled result as in the conference version, as shown in Figure 7a. In the non-training set environment, the recognition effect of landmark events was slightly worse, indicating that environmental differences can lead to a decline in recognition performance. Under most evaluation conditions, detection of D and PW events achieved high precision; instances where precision fell below 90% were relatively rare. These results indicate that acoustic events associated with D and PW generate distinct, class-discriminative features that the classifier can reliably utilize.

Figure 7

Wang et al. 2025).

After verifying the feasibility of the model, we conducted a relatively comprehensive test. The confusion matrix in Figure 7b reveals that low-confidence predictions increase the count of false positives (FP) labeled as N and AW. Many FNs originating from ground-truth D, AW, and PW events are classified as N, reflecting conservative, low-confidence outputs. Although the door and wall-related events were trained separately, there is still a possibility of confusion during the segment merging process, resulting in the D events still being confused with the wall-related events. A handful of D events being misassigned to AW, because when approaching the door, one also gets close to the walls on both sides, which causes the features to be obscured.

Although landmark-related events are not easily misidentified as other events, recall tends to be lower due to pragmatic deployment challenges that reduce classifier confidence-examples include occlusions that create non-line-of-sight (NLoS) conditions and various ambient noise sources. Because our recognition logic is designed conservatively and favors avoiding false positives, recall is treated as a secondary objective under this comprehensive dataset. Figure 7c breaks down the principal contributors to a part of false negatives (FN): the “noise interference” category primarily captures low SNR episodes; structural heterogeneity (for example, wide-open mall entrances) degrades D recall; a large amount of queued pedestrians substantially impair D detection confidence while exerting a smaller influence on PW detection (a human body presents a much weaker acoustic reflector than a wall); and PW detections are more likely to fail in regions where wall surfaces are heavily occluded or cluttered.

5.1.2.2 Performance of trajectory prediction

Figure 8 places the estimated traces from the four methods, with/out error elimination methods, alongside ARCore ground truth. The Neural PDR baseline (Figure 8a) exhibits cumulative drift over extended traversals and, this deviation is amplified under the setting that allows passing through walls. The W/o door ablation (Figure 8b) often fails to anchor corridor exits correctly, producing large endpoint errors in the absence of door-derived constraints. The W/o wall variant (Figure 8c) does not benefit from wall-side corrections and consequently shows systematic deviation from actual wall proximities. In contrast, the complete Proposed pipeline (Figure 8d), by fusing both door and wall landmarks, effectively bounds drift and yields trajectories that closely follow the ground truth.

Figure 8

Wang et al. 2025).

Figures 8e, f demonstrate why removing spurious landmarks matters. In the central region of Figure 8e, an erroneously detected door causes a trajectory to split into multiple fragments that are incorrectly matched to door locations during initialization. These fragments are identified as anomalous because they cannot be reconciled with the majority of other sub-trajectories; after excising landmarks associated with these fragments and reapplying particle filtering, the sub-trajectories are merged back into a single coherent trajectory.

To reduce the statistical uncertainty associated with the sampled evaluation used in the conference version, this journal version performs a more comprehensive evaluation, resulting in updated quantitative metrics while preserving the same qualitative conclusions again. In addition, the retry threshold has also been lowered from 30–60 to 10–20, to align with considerations regarding actual operational efficiency, meaning that trajectories with poorer geometric matching may also be accepted. Figure 9a presents the MAE comparison. Among them, removing door landmarks substantially increases the MAE compared with proposed method and produces more outliers, highlighting the weak geometric constraints provided by individual door events. However, sub-trajectory failure retry mechanism and map-matching constraints can still keep most trajectory errors within around 10 meters; for instance, many corridors are less than 3 meters wide, which limits significant trajectory drift. Excluding wall features results in a moderate increase in MAE, demonstrating the complementary contribution of PW information. Disabling erroneous landmark elimination causes both the MAE and variance to increase considerably, where both the magnitude and frequency of long-tail errors increase. By jointly exploiting door landmarks, wall features, and erroneous landmark filtering, the proposed framework achieves the lowest MAE (0.77 m) in these comprehensive environments while effectively suppressing outliers. Compared to the previous results, fewer retries significantly increase the number of outliers, thereby raising the overall average error. Compared with the Neural PDR baseline, the proposed method reduces the MAE by 79.90% and the standard deviation by 76.19%, demonstrating substantially improved localization accuracy and robustness.

Figure 9

The results of the significance test are shown in Figure 9b. Compared to the baseline method NeuralPDR, all methods—with the exception of “W/o door”—achieved r values greater than 0.5, indicating their overall effectiveness. The “W/o door” method showed relatively limited overall improvement; this is primarily because, although it shares similar initial conditions as NeuralPDR, it relies solely on walls for correction. The extent of improvement for the other two methods was also smaller than that of the method proposed in this paper. The aforementioned new evaluation results once again strongly support the conclusions of the conference paper.

The results above indicate that door landmarks are significant, whereas wall landmarks serve a supplementary role. Consequently, we further conducted end-to-end experiments on subsets to demonstrate the extent of error variation for door landmarks at different recall rates, as shown in Figure 10. The fitted curve reveals a general downward trend in error as the recall rate increases; as the recall rate decreases, the rate of error growth accelerates. These findings suggest that a prolonged absence of landmarks exacerbates trajectory drift. Therefore, improving the recall rate remains a critical issue that must be addressed for this method.

Figure 10

In order to further explore the impact of the absence of D landmarks on the overall trajectory prediction, we conducted additional tests on all trajectories where the number of D landmarks in the ground truth was equal to or greater than 8. We attempted to conduct trajectory prediction by randomly masking the D landmark. The methods of masking are divided into two types. One is “consecutive”, which means continuous masking of landmarks, that is, all the masked landmarks are in a sequential order. For example, when 6 landmarks are consecutively masked by 4, only the 1st and 6th landmarks are retained, while the consecutive landmarks in between are all masked. The other is “spaced,” which means intermittent masking, that is, the masked landmarks are as non-sequential as possible.

Table 4 shows the error distribution of each step under different recall in this landmark shielding experiment. The statistical method involves counting all the trajectory points. As the recall rate decreases, the error significantly increases. However, when the recall rate is above 25%, the average error can still be controlled within 10 meters. At all recall rates, continuous low landmark absence shows higher error than intermittent absence. When the recall rate is below 25%, continuous absence of the D landmarks will result in an error of approximately 30 meters. This indicates that the method proposed in this article still has room for improvement even at a low recall rate.

5.1.2.3 Computational performance and energy consumption evaluation

Most computations in our experiments were executed on multiple servers. Each server was equipped with an AMD EPYC 7313P processor and 512 GB of memory, running Ubuntu 22.04, and a Leadtek NVIDIA RTX A6000 48 GB GPU was used for model training and inference. In addition, to evaluate runtime and power consumption, we prepared one extra PC and two smartphones. The PC was a MacBook Pro (M1 Pro, 10-core chip, 32 GB memory) running macOS 14.1. The two phones were a OnePlus 13 (Qualcomm Snapdragon 8 Elite, 24 GB memory) running ColorOS 15.0, and a Xiaomi 10 Ultra device also used during data collection (Qualcomm Snapdragon 865, 16 GB memory) running MIUI 13.0.

We evaluated computational performance on the acoustic RD map sequence processing pipeline, including dechirping and RD processing, as well as the particle filter. We also measured storage overhead and energy consumption. The particle filter had already been parallelized using multithreading to maximize processor utilization. However, because Python includes a global interpreter lock and therefore cannot achieve true multi-core execution, we refactored the implementation into a multiprocessing version and used queue-based communication to enable concurrent multi-core processing. Since a complete test run takes a long time, we sampled subsets for rough, non-rigorous testing, aiming to gauge the order-of-magnitude relationships. It should be noted that these results are not absolute or strictly precise due to factors such as thermal throttling, power supply capacity, process latency and scheduling, and differences in underlying platform implementation; the primary objective is to verify real-time performance and the scale of memory footprint. Unless otherwise specified, “time” in this section refers to the time spent by the device in calculation, not the time in the data.

The energy consumption of the four phones during the data collection stage is shown in Table 5. And the timeout of transmission is shown in Figure 11, where the timeout rates of all four devices can all be kept below 10%.

Figure 11

The processing speed results for the four devices are shown in Table 6.

The battery consumption of the processing pipeline on the three battery-powered devices is shown in Table 7. Here, the time values indicate the runtime duration. It should be noted that the battery health of these devices is unknown, and there are other power-consuming processes and components; therefore, this result does not represent the precise power consumption level.

In the RD processing scenario, computers can be slower than smartphones, primarily due to differences in underlying implementation—for instance, Python is inherently less efficient at runtime than Java, and its idealized multi-process processing performs less effectively than true multi-threading. In contrast, the single-threaded dechirp operation allows the computer to demonstrate a certain speed advantage. However, when running the particle filter, the server achieved the best performance. Overall, while the acoustic processing performance allows for real-time operation, the particle filter is also much slower than the real-time threshold. This is a clear limitation of the proposed method. In other words, the method can only be run offline and cannot support real-time processing. Moreover, the logic of our method itself prevents real-time execution, mainly because the neural network contains a bidirectional LSTM, which requires future information as input, and because both sequence segmentation and sub-trajectory stitching also require non-real-time processing.

In the memory usage test (as shown in Figure 11), we recorded the memory usage of the two devices on subsets. We haven't yet found a way to measure memory usage on Android smartphones.

For dechirp and particle filtering, there is sufficient memory capacity. However, for the RDP step, generating the image sequence will consume a large amount of memory. On a 32 GB MacBook, a swap phenomenon occurred, indicating that in some cases 32 GB of memory might struggle to handle this kind of issue.

These results indicate that our method is not yet suitable for computation on mobile platforms, and noticeable heating was observed during testing. Therefore, when previously using smartphones to perform RDP computations, the memory occupied by some of the completed calculation data needed to be cleared. We also measured the size of the generated intermediate data, including the necessary CSV files and the TIFF images. The data volume is shown in Table 8, and a trajectory RD map sequence of about 5 min occupied approximately 16 GB. As of now, mainstream entry-level smartphones (e.g., the iPhone 17) typically provide 256 GB of storage. This is sufficient for caching RD map sequences, but storage pressure remains a concern.

5.2 Robustness evaluation of acoustic perception evaluation

In this additional dataset, we hope to conduct further tests on the robustness and generalization ability of acoustic landmark detection. Unlike the previous naturalistic obstacle exposure, where obstacles appear only incidentally and at varying, uncontrolled distances, this dataset deliberately intensifies such interference to probe boundary conditions.

5.2.1 Dataset and evaluation methodology

We collect data at Env. A and a new environment Env. J using S20U and S21U to conduct targeted, close-proximity stress tests. We have hypothesized several possible indoor obstacles that could have caused the low precision, so our experimental objects included 5 types of obstacles: single pedestrian (P), curtains (C), bar chairs (BC), tables (T) and whiteboards (W). The pedestrian volunteer and the tester holding a smartphone walked toward each other and passed by each other. In the other 4 tests, the tester walked while holding a smartphone to collect a series of RD map sequences without including landmark events; it simulated more extreme scenarios by approaching and deliberately moving in close proximity to these specially positioned obstacles. Among them, most obstacles were arranged in a high-density layout to increase the testing stress. Therefore, the ground truth of the above data was all N events. We introduced an additional 3 volunteers (V2, V3, and V4) in environment J to conduct the generalization test for the door event under different users (experiment U).

Our statistical method was based on duration with a maximum overlap rate of zero. That is, the proportion of the recognition duration of each category to the total duration. The dataset is shown in the Table 9.

To test the impact of different holding postures on the recognition effect, we selected 5 typical postures and displayed them in Figure 12. For the lateral grip test, in cases Figures 12a, b, respectively, there are samples where around half of the speakers face the wall and the other half face away from the wall. The training and testing datasets are presented in Tables 10, 11, respectively.

Figure 12

5.2.2 Result

5.2.2.1 Impact of obstacles

Table 12 shows the recognition result from the obstacle experiments. When the experimenter holding the smartphone was walking toward another volunteer, the classifier overwhelmingly assigns those instances to the N event, with only a very small proportion being labeled as AW event; this result indicates that human bodies exert only a minor and mostly benign influence on acoustic-landmark detection.

For objects such as curtains and bar chairs, the irregular and non-planar geometry of their reflecting surfaces prevents the acoustic wavefront from forming a coherent, focused reflection and promotes diffuse scattering (i.e., a diffuse-reflection phenomenon); consequently, the acoustic signatures produced by these irregular reflectors are markedly different from the characteristic patterns shown in Figure 2 (6). Therefore, it is difficult for the neural network to identify and label such events as PW events in this case. However, a small number of frames were still labeled as PW events, indicating that the proposed recognition method cannot completely avoid false detections when encountering obstacles.

Moreover, because the AW class inherently involves a short “approach” phase prior to the reflectors, AW instances are subject to a lower rate of precision: in these two experiments, on the order of approximately 35%–40% N event duration produces false identifications of AW events. This phenomenon precisely indicates that we did not take AW events as one of the factors to consider in our trajectory correction experiment.

In the latter two experiments, the false detection rates for event D and event PW increased, with the rate for event PW exceeding 30% in both cases. This is because the specular reflection characteristics of these dense obstacles produced distinct features on the RD map, thereby interfering with the neural network's decision-making. The experimental setup incorporates a wider variety of table arrangements; for instance, tables positioned against walls can cause secondary echoes in the acoustic signals, resulting in RD map patterns that closely resemble those of D events, while multiple whiteboards can also form shapes similar to door frames. The above results indicate that walking in close proximity to densely distributed obstacles may also reduce precision. However, for typical indoor environments, no known statistical reports have quantitatively characterized obstacle-related factors, such as density, spatial arrangement, and occurrence frequency. These findings therefore identify an additional potential factor affecting precision that has not been previously reported. This once again reflects the issue mentioned in the Introduction: a decline in recognition capability is inevitable in complex indoor environments.

Table 13 shows the generalization ability of door event recognition across different users, with an average recall of around 55%, which is lower than the single-user results shown in Figure 7. This indicates that, on the one hand, the method may have learned features specific to individual users; on the other hand, it indicates difficulties in generalizing across multiple users. The fundamental reason for this difference lies in the variations among users regarding factors such as height and walking speed.

5.2.2.2 Impact of postures

The recognition effects of the holding postures are shown in the Figure 13. When using a lateral grip, if the speaker is facing the wall, a distinct echo can be detected. However, if it is facing away from the wall, it is difficult to receive the echo, showing weak features. These situations result in a relatively low overall recall rate of PW when lateral grip (as shown in Figures 12a, b). Meanwhile, although D events have their own features, their dynamic features are similar to those of wall-related events and have a very short duration. When sideways grip with the screen facing laterally and the speaker facing forward, the situation is consistent with the default setting (screen facing upwards, microphone, and speakers all facing forward), resulting in a clear diagonal line appearing in the confusion matrix. However, the recall rates for the D and PW events are still lower than the default setting, which is due to the limited amount of training data. When holding the device facing the screen or with an arm swing, due to the presence of close-range echo noise (from the human body and the ground), the key features are masked, resulting in recall rates for D and PW both being below 20%. Furthermore, we trained the model by combining the data with different holding postures with the original training data, and obtained new prediction results, which are shown in Figure 14. The recall rate and F1 score of this result are much lower than those of the original result. This indicates that the model can only be trained for a single grip posture, and it is hard to conduct mixed training for multiple grip postures.

Figure 13

Figure 14

The above results indicate that the method discussed in this article is not applicable to all grip postures. This is mainly because the RD map sequence of events shows different features under different grip postures. Furthermore, certain holding postures can cause severe noise interference in the RD map, thereby reducing the performance of the discrimination. Therefore, the holding posture remains one of the conditions that restricts its wide application.

6 Discussion

6.1 Limitations

The approach presented here presupposes that an up-to-date floor map is available, and therefore, the manual effort required to annotate doors and walls may be non-negligible in very large or dynamically changing environments. Additionally, acoustic landmark sensing is inherently susceptible to non-line-of-sight conditions and occlusions: high precision is attainable under favorable acoustic propagation, but unfavorable acoustic propagation conditions can lead to poor recognition performance. At a low recall rate, the error of the trajectory will be significantly

increased. Especially when consecutive D landmarks are missing, the trajectory error becomes so large that the method effectively fails. The proposed method cannot perform real-time navigation. Besides inherent limitations in the method's logic (i.e., the retry mechanism of segmented particle filtering), the computational speed cannot match the data throughput. The system consumes a significant amount of power, making it unsuitable for battery-powered devices. It also experiences substantial memory pressure during RDP; therefore, a machine with at least 32 GB of RAM is recommended. Furthermore, the data processing requires substantial storage space to meet the storage needs of the image sequences, because the RDP can generate data at more than 40 MB/s (data time). Additionally, this method is quite sensitive to the holding posture. We strongly recommend using devices where the microphone and speaker are on the same side, and try to position the acoustic sensor near the chest and facing forward. Otherwise, the recall rate and accuracy will significantly decrease. The generalization ability across different users also needs to be improved.

6.2 Applications

Acoustic landmarks could be a viable complement to PDR systems that otherwise rely on infrastructure or auxiliary data sources (e.g., retail purchase logs) (Yonetani et al., 2024). We additionally propose a morphology and spatiotemporal-consistency-based false-landmark exclusion mechanism that prioritizes precision and is suitable for incorporation into other landmark-correction frameworks.

6.3 Future work

There are more acoustic events available for exploration as landmarks. Beyond the door and wall categories analyzed in this study, other discrete indoor landmarks—for instance, additional acoustically salient door-related signatures discussed in prior work (Dissanayake et al., 2018)—could be exploited. A key direction for future research is raising recall without compromising precision, for example, by applying targeted signal-enhancement techniques, exploiting multi-sensor fusion, or leveraging semi-supervised learning methods that make use of audio data. Furthermore, in the stress testing using the second dataset, the quantitative assessment of the frequency and typical distances of high-density obstacles appearing at close range in real-world scenarios remains an unresolved direction.

7 Conclusion

We have introduced an acoustic-assisted PDR calibration pipeline alongside an erroneous-landmark elimination algorithm, and we have demonstrated through experiments across a range of indoor environments that these components can provide significant correction capabilities for trajectories calculated directly from inertial sensors when conducting single-person tests and maintaining a strict holding posture. When there are many obstacles present, the landmark recognition effect will be poor, leading to a sharp increase in trajectory error. This method has a low deployment cost, yet it relies on highly idealized environmental conditions and substantial computational overhead with retry mechanism. Consequently, its practical deployment remains challenging, especially when adapted to real-time navigation systems. Although the method has many limitations, the use of acoustic perception to achieve low-cost and infrastructure-free acoustic landmarks still holds potential prospects.

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