Multi-Horizon 3D Position Prediction for IoT-Enabled UAVs: A Sensor-Enriched LSTM Benchmark in AirSim

1. Introduction

Unmanned aerial vehicles (UAVs) increasingly operate as mobile sensing, computation, and communication nodes within Internet of Things (IoT) ecosystems. Their mobility enables adaptive coverage, rapid deployment, and access to remote or hazardous environments, but it also creates strict requirements for localization, motion anticipation, and timely decision making [1,2,3,4,5]. Industry assessments likewise reflect the broadening commercial role of UAV platforms across sensing and monitoring applications [6]. A reliable short-horizon position predictor can provide an anticipatory state estimate for collision monitoring, route maintenance, link-quality forecasting, handover preparation, and control continuity.

UAV motion prediction is more difficult than road-constrained vehicle prediction. A multirotor can translate and rotate in three dimensions, respond rapidly to control inputs, and experience wind, sensor noise, and actuator disturbances. Surveys of future-location prediction and motion-risk assessment emphasize the importance of matching the predictor to the motion constraints and uncertainty structure of the platform [7,8]. Wind-rejection studies further show that disturbances can alter both state evolution and controller response [9,10]. Kinematic models and Kalman-filter variants remain attractive because they are interpretable and efficient, but their accuracy depends on process-model fidelity, covariance tuning, and noise assumptions [11,12,13,14]. Data-driven sequence models instead learn temporal relations directly from historical telemetry, potentially capturing residual dynamics that are difficult to specify analytically.

Long short-term memory (LSTM) networks are widely used for sequential prediction because gated memory mitigates vanishing gradients and preserves relevant temporal information [15]. Gated recurrent units provide a related encoder–decoder mechanism with fewer gates [16,17]. UAV studies have used recurrent networks to forecast ADS-B trajectories, predict local positions, and exploit velocity-enriched states [18,19,20]. However, the literature also includes technically different tasks such as full trajectory generation, obstacle-motion forecasting, disturbance estimation, closed-loop navigation, action generation, and spoofing classification [21,22,23,24,25,26,27]. These tasks use distinct targets, forecast horizons, inputs, and evaluation units and are therefore treated separately in this benchmark.

This work formulates UAV position forecasting as a flight-wise, multi-horizon, three-dimensional benchmark. A 2 s history predicts the complete next 1 s trajectory, the dataset channels and duration statistics are reported consistently, and analytical, filtering, recurrent, convolutional, and attention-based baselines are evaluated under the same protocol.

Figure 1 summarizes the motivation and scope of the benchmark. It links the role of IoT-enabled UAVs and the need for near-future prediction to the challenges of free-flight motion, the sensor-enriched input representation, the comparator families, and the edge-oriented evaluation criteria.

The research question is: Does adding gravity-resolved acceleration and orientation history to a compact LSTM improve flight-wise, multi-horizon 3D UAV position prediction relative to simpler kinematic predictors and matched neural sequence models, while satisfying edge-latency constraints? Four hypotheses are evaluated:

• H1—feature value: LSTM-PVAQ yields lower per-flight 1 s 3D RMSE than LSTM-PV under the same split and training protocol.
• H2—model value: LSTM-PVAQ outperforms persistence, constant-velocity, constant-acceleration, and EKF baselines.
• H3—comparative value: any advantage over GRU, TCN, and Transformer baselines remains after paired flight-level uncertainty analysis.
• H4—deployability: median batch-1 inference latency remains below the 20 ms model-update interval on the evaluated edge platform.

The contributions are:

• a direct multi-output formulation that predicts the complete next 1 s 3D trajectory at 50 Hz from 2 s of history;
• a consistent coordinate-frame and gravity-resolution procedure that distinguishes raw specific force from navigation-frame acceleration;
• a controlled feature ablation from position-only through position–velocity–acceleration–quaternion inputs;
• a matched benchmark spanning analytical, filtering, recurrent, convolutional, and attention-based models;
• a flight-level statistical protocol with hierarchical bootstrap intervals and paired comparisons; and
• an edge-oriented IoT evaluation combining accuracy, model size, latency, and memory measurements.

The remainder of this paper is organized as follows. Section 2 reviews the related work and defines the boundaries between position prediction and adjacent UAV learning tasks. Section 3 describes the AirSim dataset and preprocessing pipeline. Section 4 presents the multi-horizon 3D formulation and LSTM architecture. Section 5 details the benchmark models and training protocol. Section 6 and Section 7 define the statistical and edge-oriented evaluation procedures, respectively. Section 8 reports the experimental results, Section 9 discusses their implications and limitations, and Section 10 concludes the paper.

2. Related Work and Task Boundaries

2.1. Traditional and Learned UAV State Prediction

Traditional UAV prediction uses kinematic and dynamic models, Kalman filters, Gaussian processes, graph-based methods, and aerodynamic models [21]. Constant-velocity and constant-acceleration predictors are strong short-horizon baselines for smooth trajectories. Extended and unscented Kalman filters incorporate uncertainty and recursive state correction, but performance depends on the appropriateness of the model and noise assumptions [12,13]. Learned residuals and covariance adaptation can improve filters, although they introduce additional stability and calibration questions [14].

Zhang et al. combined ADS-B position histories with a recurrent LSTM for two-step 3D UAV trajectory prediction [18]. VECTOR enriched a GRU with velocity to improve real-time 3D forecasting under maneuvers and wind [20]. Jia et al. addressed a different problem: generation of complete 5–25 s trajectories from sparse waypoints using segmented LSTMs and real Crazyflie data [22]. These studies support recurrent modeling but also show that prediction horizon, output representation, and data source strongly influence model rankings.

2.2. Cross-Domain Foundations for Trajectory Prediction

Trajectory forecasting developed through location mining, trajectory-pattern discovery, and road-network clustering. Significant-location and pattern-mining methods predict future movement from recurring GPS traces, while road-network methods identify repeated spatial structures across users and routes [28,29,30,31]. More recent work uses geographically clustered deep estimators, convolutional models for pedestrian motion, recurrent models for vehicle trajectories, and vehicle tracks extracted from UAV imagery [32,33,34,35]. Interaction-aware graph-attention and Transformer models extend these ideas to multi-agent dependencies and social constraints [36,37,38]. These studies provide important methodological foundations, but their ground-motion assumptions and evaluation horizons do not directly represent free-flight UAV dynamics.

2.3. Alternative Neural Sequence Models

GRUs reduce the number of gates relative to LSTMs and often provide favorable accuracy–latency trade-offs [16,17,20]. Temporal convolutional networks (TCNs) use causal dilated convolutions and residual blocks to model long receptive fields with parallel computation [39]. Transformers use self-attention to capture long-range dependencies but can require more memory and computation, particularly for long input sequences [40]. Cross-domain benchmarking also indicates that recurrent and attention-based rankings depend on sequence length, noise, and the underlying data regime [41]. Accordingly, the benchmark uses the same history, target, features, training split, search budget, and direct multi-output objective for each architecture.

2.4. Adjacent but Non-Equivalent UAV Tasks

R-YOLO integrates object detection and recurrent forecasting to predict external obstacle motion near vertiports [23]; its target is not the ego-UAV state. Shankar et al. estimate wind from onboard telemetry and use the estimate in semi-autonomous control [24]; this is disturbance estimation. Layered-RQN learns collision-avoidance and target-acquisition actions in a dynamic environment [42]; this is closed-loop navigation. Dhiman et al. predict short-term PAV displacements and intervene using depth thresholds [25]; the system is evaluated by navigation success and collision rate. UAV-VLA predicts language-conditioned action chunks [26], while Sarode and Naresh classify GPS–IMU spoofing states [27]. These distinctions prevent invalid cross-task metric comparisons.

Table 1. Task boundaries within the supporting UAV/UAM literature.

Work	Task	Output	Relevance to this study
Zhang et al. [18]	Ego-UAV trajectory prediction	Two future 3D points	Recurrent prediction from ADS-B position histories
Nacar et al. [20]	Ego-UAV trajectory prediction	Future 3D positions	Demonstrates the value of velocity-enriched recurrent input
Jia et al. [22]	Complete trajectory generation	5–25 s spatiotemporal path	Longer-horizon generation from sparse waypoints
Ywet et al. [23]	Obstacle forecasting	Future external-object tracks	Integrates detection and prediction, but not ego-state forecasting
Shankar et al. [24]	Disturbance estimation/control	Wind estimate and control aid	Motivates use of inertial and attitude evidence
Guo et al. [42]	Navigation policy learning	Discrete motion action	Closed-loop DRL, not supervised position prediction
Dhiman et al. [25]	PAV navigation/control	3D displacement and maneuver	Evaluates mission success and collision outcomes
Gu [26]	Semantic action generation	Velocity action chunks/tokens	Multimodal transformer for language-conditioned navigation
Sarode and Naresh [27]	Security classification	Five attack/normal classes	Temporal classification, not motion forecasting
This study	Ego-UAV multi-horizon prediction	50 future 3D displacements	Controlled sensor ablation and edge benchmark

Table 1. Task boundaries within the supporting UAV/UAM literature.

Work	Task	Output	Relevance to this study
Zhang et al. [18]	Ego-UAV trajectory prediction	Two future 3D points	Recurrent prediction from ADS-B position histories
Nacar et al. [20]	Ego-UAV trajectory prediction	Future 3D positions	Demonstrates the value of velocity-enriched recurrent input
Jia et al. [22]	Complete trajectory generation	5–25 s spatiotemporal path	Longer-horizon generation from sparse waypoints
Ywet et al. [23]	Obstacle forecasting	Future external-object tracks	Integrates detection and prediction, but not ego-state forecasting
Shankar et al. [24]	Disturbance estimation/control	Wind estimate and control aid	Motivates use of inertial and attitude evidence
Guo et al. [42]	Navigation policy learning	Discrete motion action	Closed-loop DRL, not supervised position prediction
Dhiman et al. [25]	PAV navigation/control	3D displacement and maneuver	Evaluates mission success and collision outcomes
Gu [26]	Semantic action generation	Velocity action chunks/tokens	Multimodal transformer for language-conditioned navigation
Sarode and Naresh [27]	Security classification	Five attack/normal classes	Temporal classification, not motion forecasting
This study	Ego-UAV multi-horizon prediction	50 future 3D displacements	Controlled sensor ablation and edge benchmark

Figure 2 summarizes the task distinctions used throughout the manuscript. The central predictor estimates the ego-UAV’s future position sequence and supplies predictive state information to downstream planning, navigation, and control modules.

3. Dataset and Preprocessing

3.1. AirSim Flight Corpus

The dataset contains 3100 AirSim flight sequences over a mountainous environment. Raw logging was reported at 1 kHz, with a nominal speed near 3 m/s and independently varied horizontal wind components in $[-7,7]$ m/s. The dataset includes 20 scalar channels: global latitude, longitude, and altitude; local Cartesian position; linear velocity; acceleration or specific force; quaternion orientation; barometric pressure; and three-axis magnetic field. The primary PVAQ predictor uses 13 channels: local position, velocity, gravity-resolved acceleration, and quaternion orientation.

The analyzed corpus totals 136.83 h across 3100 flights, corresponding to a mean duration of 158.90 s per flight. All duration statistics are computed from the same post-cleaning flight manifest.

Table 2. Channel manifest for the AirSim dataset.

Group	Scalar channels	Count	Primary use
Global position	latitude, longitude, altitude	3	Raw geodetic metadata
Local position	$x,y,z$	3	Predictor history and target
Linear velocity	$v_x,v_y,v_z$	3	Predictor history
Acceleration/specific force	$a_x,a_y,a_z$	3	Predictor after frame conversion and gravity resolution
Orientation quaternion	$q_w,q_x,q_y,q_z$	4	Predictor after unit normalization and sign continuity
Barometer	pressure	1	Not used in the primary predictor
Magnetometer	$m_x,m_y,m_z$	3	Not used in the primary predictor
Total		20	13 predictors and 7 excluded raw channels

Table 2. Channel manifest for the AirSim dataset.

Group	Scalar channels	Count	Primary use
Global position	latitude, longitude, altitude	3	Raw geodetic metadata
Local position	$x,y,z$	3	Predictor history and target
Linear velocity	$v_x,v_y,v_z$	3	Predictor history
Acceleration/specific force	$a_x,a_y,a_z$	3	Predictor after frame conversion and gravity resolution
Orientation quaternion	$q_w,q_x,q_y,q_z$	4	Predictor after unit normalization and sign continuity
Barometer	pressure	1	Not used in the primary predictor
Magnetometer	$m_x,m_y,m_z$	3	Not used in the primary predictor
Total		20	13 predictors and 7 excluded raw channels

Figure 3. Distribution of UAV velocity magnitudes across the 3100 AirSim flights. The concentration near 3 m/s reflects the nominal operating speed and the smooth-flight character of the dataset.

Figure 3. Distribution of UAV velocity magnitudes across the 3100 AirSim flights. The concentration near 3 m/s reflects the nominal operating speed and the smooth-flight character of the dataset.

3.2. Acceleration and Coordinate-Frame Processing

The mean acceleration magnitude near 9.81 m/s² indicates that the simulated IMU signal includes gravity. The acceleration channels are transformed to the navigation frame and gravity-resolved as

$${\mathit{a}}_t^n=\mathit{R}\left({\mathit{q}}_t\right){\mathit{f}}_t^b+{\mathit{g}}^n,$$

(1)

where ${\mathit{f}}_t^b$ is body-frame specific force, $\mathit{R}\left({\mathit{q}}_t\right)$ rotates body to navigation coordinates, and ${\mathit{g}}^n$ is the gravity vector. Quaternion sequences are normalized and made sign-continuous by flipping ${\mathit{q}}_t$ when ${\mathit{q}}_t^{\top }{\mathit{q}}_{t-1}<0$.

3.3. Sampling, Flight-Wise Splitting, and Normalization

The raw 1 kHz signals are low-pass filtered before decimation to 50 Hz. A 20 Hz low-pass filter is applied before decimation, and the same filter configuration is used independently within every flight. Flights are assigned to 2170 training, 465 validation, and 465 test trajectories before normalization, window generation, or hyperparameter tuning. Feature normalization is fitted only on training flights and applied unchanged to validation and test data. Windows never cross flight boundaries and advance by 10 samples (0.2 s), reducing near-duplicate examples.

Figure 4. Flight-wise dataset preparation and preprocessing pipeline. Flight identifiers are partitioned before filtering, normalization, and window construction. The 1 kHz signals are filtered and resampled to 50 Hz, and training-set normalization statistics are applied unchanged to validation and test flights.

Figure 4. Flight-wise dataset preparation and preprocessing pipeline. Flight identifiers are partitioned before filtering, normalization, and window construction. The 1 kHz signals are filtered and resampled to 50 Hz, and training-set normalization statistics are applied unchanged to validation and test flights.

Table 3. Preprocessing and window-construction protocol.

Stage	Setting	Purpose
Native logging	1000 Hz	High-resolution source telemetry
Low-pass filter	20 Hz cutoff	Anti-aliasing before decimation
Model rate	50 Hz	20 ms update interval
Input history	2.0 s (100 steps)	Captures short-term motion trends
Forecast	1.0 s (50 positions)	Direct multi-output 3D trajectory
Reported horizons	0.1, 0.5, 1.0 s	Correspond to 5, 25, and 50 output steps
Window stride	10 samples (0.2 s)	Reduces redundant overlap within each flight
Split	2170/465/465 flights	Flight-disjoint 70/15/15 partition
Normalization	Training statistics only	Consistent scaling across all partitions

Table 3. Preprocessing and window-construction protocol.

Stage	Setting	Purpose
Native logging	1000 Hz	High-resolution source telemetry
Low-pass filter	20 Hz cutoff	Anti-aliasing before decimation
Model rate	50 Hz	20 ms update interval
Input history	2.0 s (100 steps)	Captures short-term motion trends
Forecast	1.0 s (50 positions)	Direct multi-output 3D trajectory
Reported horizons	0.1, 0.5, 1.0 s	Correspond to 5, 25, and 50 output steps
Window stride	10 samples (0.2 s)	Reduces redundant overlap within each flight
Split	2170/465/465 flights	Flight-disjoint 70/15/15 partition
Normalization	Training statistics only	Consistent scaling across all partitions

4. Multi-Horizon 3D Formulation

Let ${\mathit{p}}_t,{\mathit{v}}_t,{\mathit{a}}_t\in {\mathbb{R}}^3$ denote local position, velocity, and gravity-resolved acceleration, and let ${\mathit{q}}_t\in {\mathbb{R}}^4$ denote the unit quaternion. Historical positions are expressed relative to the final observed position:

$${\mathit{s}}_k=[({\mathit{p}}_k-{\mathit{p}}_t),{\mathit{v}}_k,{\mathit{a}}_k,{\mathit{q}}_k]\in {\mathbb{R}}^{13},k=t-T+1,\dots ,t.$$

(2)

The input and target are

$$\begin{array}{cc}\hfill {\mathit{X}}_t& =[{\mathit{s}}_{t-T+1},\dots ,{\mathit{s}}_t]\in {\mathbb{R}}^{T\times F},T=100,\hfill \end{array}$$

(3)

$$\begin{array}{cc}\hfill {\mathit{Y}}_t& =[{\mathit{p}}_{t+1}-{\mathit{p}}_t,\dots ,{\mathit{p}}_{t+H}-{\mathit{p}}_t]\in {\mathbb{R}}^{H\times 3},H=50.\hfill \end{array}$$

(4)

The decoder predicts 150 displacement values and reshapes them into 50 future three-dimensional positions, yielding a direct and operationally meaningful multi-horizon forecast.

An LSTM updates its gates and memory as

$$\begin{array}{cc}\hfill {\mathit{f}}_t& =\sigma ({\mathit{W}}_f[{\mathit{h}}_{t-1},{\mathit{x}}_t]+{\mathit{b}}_f),\hfill \end{array}$$

(5)

$$\begin{array}{cc}\hfill {\mathit{i}}_t& =\sigma ({\mathit{W}}_i[{\mathit{h}}_{t-1},{\mathit{x}}_t]+{\mathit{b}}_i),\hfill \end{array}$$

(6)

$$\begin{array}{cc}\hfill {\mathit{o}}_t& =\sigma ({\mathit{W}}_o[{\mathit{h}}_{t-1},{\mathit{x}}_t]+{\mathit{b}}_o),\hfill \end{array}$$

(7)

$$\begin{array}{cc}\hfill {\tilde{\mathit{c}}}_t& =tanh({\mathit{W}}_c[{\mathit{h}}_{t-1},{\mathit{x}}_t]+{\mathit{b}}_c),\hfill \end{array}$$

(8)

$$\begin{array}{cc}\hfill {\mathit{c}}_t& ={\mathit{f}}_t\odot {\mathit{c}}_{t-1}+{\mathit{i}}_t\odot {\tilde{\mathit{c}}}_t,\hfill \end{array}$$

(9)

$$\begin{array}{cc}\hfill {\mathit{h}}_t& ={\mathit{o}}_t\odot tanh\left({\mathit{c}}_t\right).\hfill \end{array}$$

(10)

The final representation passes through an explicit dropout layer and a linear decoder $128\to 150$. Regularization is applied explicitly after the encoded representation and before the decoder. Figure 5 summarizes the complete input-to-forecast data flow and the evaluated 0.1, 0.5, and 1.0 s horizons.

Table 4. Compact LSTM configurations.

Component	Setting	Implementation details
Input	$100\times F$	$F=6$ for LSTM-PV; $F=13$ for LSTM-PVAQ
Encoder	One-layer LSTM, hidden size 128	Final hidden state
Regularization	Explicit dropout $p=0.20$	Applied after the encoder
Decoder	Linear $128\to 150$	Reshaped to $50\times 3$ displacements
Loss	Mean squared 3D displacement	Normalized training and metric-space evaluation
Optimizer	Adam, initial ${10}^{-3}$	Selected using validation ADE
Early stopping	Patience 15, maximum 200 epochs	Validation ADE criterion
Seeds	Five fixed seeds	Repeated training runs

Table 4. Compact LSTM configurations.

Component	Setting	Implementation details
Input	$100\times F$	$F=6$ for LSTM-PV; $F=13$ for LSTM-PVAQ
Encoder	One-layer LSTM, hidden size 128	Final hidden state
Regularization	Explicit dropout $p=0.20$	Applied after the encoder
Decoder	Linear $128\to 150$	Reshaped to $50\times 3$ displacements
Loss	Mean squared 3D displacement	Normalized training and metric-space evaluation
Optimizer	Adam, initial ${10}^{-3}$	Selected using validation ADE
Early stopping	Patience 15, maximum 200 epochs	Validation ADE criterion
Seeds	Five fixed seeds	Repeated training runs

5. Benchmark Models and Training Fairness

The benchmark includes models that test distinct explanations for performance: no learned dynamics, simple kinematics, recursive filtering, gated recurrence, temporal convolution, and self-attention.

Table 5. Benchmark models and their scientific roles.

Model	Implementation	Input	Scientific role
Persistence	${\widehat{\mathit{p}}}_{t+h}={\mathit{p}}_t$	Position	Persistence reference
Constant velocity	Analytical	Position and velocity	Smooth-flight analytical baseline
Constant acceleration	Analytical	Position, velocity, acceleration	Analytical acceleration baseline
EKF-CA	Nine-state recursive filter	Matched kinematic observations	Classical estimator/predictor
LSTM-PV	One-layer, 128 hidden units	Position and velocity (6)	Reduced-feature recurrent ablation
LSTM-PVAQ	One-layer, 128 hidden units	Position, velocity, acceleration, quaternion (13)	Sensor-enriched predictor
GRU-PVAQ	One-layer, matched budget	Same 13 features	Lower-gate-count recurrent comparison
TCN-PVAQ	Causal dilated residual blocks	Same 13 features	Parallel temporal model with long receptive field
Transformer-PVAQ	Compact encoder	Same 13 features and positional encoding	Attention-based comparison

Table 5. Benchmark models and their scientific roles.

Model	Implementation	Input	Scientific role
Persistence	${\widehat{\mathit{p}}}_{t+h}={\mathit{p}}_t$	Position	Persistence reference
Constant velocity	Analytical	Position and velocity	Smooth-flight analytical baseline
Constant acceleration	Analytical	Position, velocity, acceleration	Analytical acceleration baseline
EKF-CA	Nine-state recursive filter	Matched kinematic observations	Classical estimator/predictor
LSTM-PV	One-layer, 128 hidden units	Position and velocity (6)	Reduced-feature recurrent ablation
LSTM-PVAQ	One-layer, 128 hidden units	Position, velocity, acceleration, quaternion (13)	Sensor-enriched predictor
GRU-PVAQ	One-layer, matched budget	Same 13 features	Lower-gate-count recurrent comparison
TCN-PVAQ	Causal dilated residual blocks	Same 13 features	Parallel temporal model with long receptive field
Transformer-PVAQ	Compact encoder	Same 13 features and positional encoding	Attention-based comparison

All models use the identical flight split, filtered 50 Hz signals, 2 s history, 1 s target, stride, normalization, and test windows. Learned models predict all 50 future positions directly. Neural parameter budgets are matched as closely as practical, and exact counts are reported. Each model receives the same validation-search budget and seed set. Physics baselines use the same sensor-derived kinematic inputs available to the learned models.

5.1. Training Diagnostics

Sensitivity analyses examined input-window length, batch size, convergence, and the distribution of held-out prediction errors. Figure 6 summarizes these optimization diagnostics and supports the selected training configuration.

6. Evaluation and Statistical Analysis

For test window i at horizon h, the Euclidean error is

$$e_{i,h}={∥{\mathit{p}}_{i,t+h}-{\widehat{\mathit{p}}}_{i,t+h}∥}_2.$$

(11)

Horizon-specific 3D RMSE, average displacement error (ADE), and final displacement error (FDE) are

$$\begin{array}{cc}\hfill {RMSE}_h& =\sqrt{{\displaystyle \frac{1}{N}}{\sum }_{i=1}^N{e}_{i,h}^2},\hfill \end{array}$$

(12)

$$\begin{array}{cc}\hfill ADE& ={\displaystyle \frac{1}{H}}{\displaystyle \sum _{h=1}^H}{∥{\mathit{p}}_{t+h}-{\widehat{\mathit{p}}}_{t+h}∥}_2,\hfill \end{array}$$

(13)

$$\begin{array}{cc}\hfill FDE& ={∥{\mathit{p}}_{t+H}-{\widehat{\mathit{p}}}_{t+H}∥}_2.\hfill \end{array}$$

(14)

All metrics are inverse-transformed and reported in meters. Axis-specific RMSE accompanies the aggregate metric to characterize horizontal and vertical prediction performance.

To preserve the flight as the independent evaluation unit, window-level metrics are averaged within each held-out flight and summarized across the 465 flight-level values. Each learned model is trained with five fixed seeds. Paired hierarchical bootstrap intervals resample test-flight identifiers and training seeds. The primary comparison is LSTM-PVAQ versus LSTM-PV at 1 s, while secondary comparisons with GRU, TCN, Transformer, and EKF use Holm-adjusted significance levels. Absolute differences, relative changes, and confidence intervals are reported together.

7. Edge-Oriented IoT Evaluation

Batch-1 inference was benchmarked on a Raspberry Pi 5 CPU using one thread, FP32 precision, and a $100\times F$ input history. The protocol used 100 untimed warm-up runs followed by 1000 timed inferences. Trainable parameter count, median latency, and peak resident memory were recorded for each learned model. Comparing median latency with the 20 ms sampling interval establishes the computational feasibility of edge-resident prediction within the model-update cycle.

8. Results

8.1. Multi-Horizon Three-Dimensional Accuracy

Table 6 reports flight-level 3D RMSE at the three forecast horizons. Persistence degraded rapidly as the horizon increased, reaching 2.963 m at 1 s. The analytical and filtering baselines substantially reduced this error, but all learned sequence models achieved lower 1 s RMSE than EKF-CA. LSTM-PVAQ produced the lowest error at every horizon: 0.043 m at 0.1 s, 0.168 m at 0.5 s, and 0.371 m at 1.0 s. TCN-PVAQ was the strongest alternative at 1 s with 0.409 m, followed by GRU-PVAQ with 0.427 m. Figure 7 visualizes the complete baseline family on a logarithmic RMSE scale and shows that the LSTM-PVAQ advantage persists across all three forecast horizons.

8.2. Trajectory-Level Accuracy and Edge Efficiency

The one-second trajectory-level metrics in Table 7 show the same ordering. LSTM-PVAQ achieved the lowest ADE (0.216 m) and FDE (0.339 m). TCN-PVAQ ranked second on both trajectory metrics and was the fastest learned model, with a median latency of 0.54 ms. LSTM-PVAQ required 92.6 K parameters, 14.2 MB peak RAM, and 0.88 ms median latency. All learned models remained far below the 20 ms update interval, while the compact Transformer was the slowest and largest learned model.

Figure 8. One-second trajectory-level average displacement error (ADE) and final displacement error (FDE) for the learned models. Lower is better.

Figure 8. One-second trajectory-level average displacement error (ADE) and final displacement error (FDE) for the learned models. Lower is better.

Figure 9. Accuracy–latency trade-off among learned predictors. The horizontal axis shows median batch-1 edge inference latency, the vertical axis shows 1 s three-dimensional RMSE, and marker area is proportional to trainable parameter count. All median latencies are below the 20 ms sampling interval, and the lower-left region represents the most favorable accuracy–latency trade-off.

Figure 9. Accuracy–latency trade-off among learned predictors. The horizontal axis shows median batch-1 edge inference latency, the vertical axis shows 1 s three-dimensional RMSE, and marker area is proportional to trainable parameter count. All median latencies are below the 20 ms sampling interval, and the lower-left region represents the most favorable accuracy–latency trade-off.

8.3. Feature Ablation

Table 8 isolates the contribution of each sensor group within the LSTM. Position-only input produced 0.612 m RMSE at 1 s. Adding velocity reduced error by 22.5%. Raw gravity-bearing acceleration produced a further 7.6% reduction, while gravity resolution improved the corresponding acceleration model by 8.9%. Quaternion orientation reduced RMSE by another 7.0%, yielding the full LSTM-PVAQ result of 0.371 m. Figure 10 summarizes the confidence intervals, incremental gains, and representative trajectory distributions.

8.4. Paired Flight-Level Comparisons

The paired analysis in Table 9 confirms that the LSTM-PVAQ advantage was consistent across held-out flights. Its 1 s RMSE was 0.103 m lower than LSTM-PV, 0.056 m lower than GRU-PVAQ, 0.038 m lower than TCN-PVAQ, 0.075 m lower than Transformer-PVAQ, and 0.126 m lower than EKF-CA. All intervals remained below zero after pairing, and the Holm-adjusted values were below 0.001.

Figure 11. Paired flight-level differences in 1 s three-dimensional RMSE between LSTM-PVAQ and LSTM-PV, GRU-PVAQ, TCN-PVAQ, Transformer-PVAQ, and EKF-CA. Error bars show 95% confidence intervals; negative differences favor LSTM-PVAQ, and the vertical zero line marks parity.

Figure 11. Paired flight-level differences in 1 s three-dimensional RMSE between LSTM-PVAQ and LSTM-PV, GRU-PVAQ, TCN-PVAQ, Transformer-PVAQ, and EKF-CA. Error bars show 95% confidence intervals; negative differences favor LSTM-PVAQ, and the vertical zero line marks parity.

9. Discussion

9.1. Interpretation of the Predictive Gains

The results support the primary feature hypothesis. Relative to LSTM-PV, the full LSTM-PVAQ reduced 1 s RMSE by 21.7%, and the sequential ablation attributed improvement to both gravity-resolved acceleration and quaternion orientation. The advantage increased with forecast horizon, which is consistent with the added channels becoming more informative as simple positional persistence and constant-velocity assumptions lose accuracy. The strong performance of constant-velocity and EKF-CA baselines at short horizons is expected because the dataset is dominated by smooth flight near 3 m/s.

The matched architecture comparison shows that LSTM-PVAQ also outperformed GRU, TCN, and Transformer variants receiving the same PVAQ input under the evaluated AirSim protocol and parameter budgets.

9.2. Accuracy Versus Deployability

LSTM-PVAQ provided the best accuracy, but TCN-PVAQ offered the strongest speed–accuracy compromise: its 1 s RMSE was only 0.038 m higher while its median latency was 0.54 ms rather than 0.88 ms. GRU-PVAQ used the fewest parameters and least peak RAM among the learned PVAQ models, while the compact Transformer was both slower and less accurate in this protocol. All learned models completed inference within a small fraction of the 20 ms update interval, supporting edge execution for the evaluated batch-1 workload. The results support LSTM-PVAQ for accuracy-oriented deployment and TCN-PVAQ for latency-oriented deployment.

9.3. Limitations and Future Work

The evaluation is based on AirSim flights from one mountainous environment, with trajectories concentrated near a nominal speed of 3 m/s. Performance on physical UAVs, aggressive turns, vertical maneuvers, payload changes, turbulence, and different vehicle platforms remains to be established. Model rankings may also vary with sensor-noise conditions, preprocessing choices, and architecture budgets.

The edge comparison reports median model-inference latency on one platform; preprocessing cost, tail latency, and energy consumption remain outside the present scope. Future evaluation will include physical UAV logs, multiple environments and maneuver regimes, sensor degradation, and closed-loop control or networking experiments.

10. Conclusions

This study reformulated UAV position prediction as a flight-wise, multi-horizon 3D benchmark and evaluated a compact sensor-enriched LSTM against analytical, filtering, recurrent, convolutional, and attention-based alternatives. Using 2 s histories to predict the complete next 1 s trajectory, LSTM-PVAQ achieved RMSE values of 0.043, 0.168, and 0.371 m at 0.1, 0.5, and 1.0 s. Its one-second RMSE was 21.7% lower than LSTM-PV and 9.3% lower than TCN-PVAQ, the strongest alternative learned model. The ablation showed that velocity, gravity-resolved acceleration, and quaternion orientation each contributed to the final accuracy.

The model required 92.6 K parameters and a median of 0.88 ms per batch-1 inference on a Raspberry Pi 5 CPU, demonstrating compatibility with the 20 ms update interval. TCN-PVAQ remained a competitive deployment option because it reduced median latency to 0.54 ms with a modest accuracy penalty. Within the evaluated AirSim conditions, the results establish a strong accuracy–efficiency profile for sensor-enriched multi-horizon prediction. Future work will extend the evaluation to physical UAV logs, aggressive three-dimensional maneuvers, unseen environments, sensor faults, and closed-loop networking or control outcomes.