EB-Navigation: Energy-Based Routing

• EB-Navigation is a paradigm that prioritizes minimizing energy consumption over distance or time, applicable to both electric vehicles and wearable inertial systems.
• For EVs, it employs real-world energy models, polynomial regressions, and graph-based algorithms to enhance range with proven low error rates in energy estimation.
• For wearables, systems like PilotEar use sensor fusion and drift correction with in-ear IMUs to deliver improved personal navigation accuracy.

EB-Navigation, or Energy-Based Navigation, refers to a class of navigation systems that optimize a route or path with respect to energy consumption, rather than simply minimizing distance or time. The term spans domains from eco-routing for electric vehicles (EVs) to inertial navigation employing ear-worn sensors for personal navigation. This entry presents a comprehensive overview of EB-Navigation, focusing first on energy-optimal vehicular routing (Wu et al., 2020) and then on energy-aware inertial navigation using earables (Ahuja et al., 2021).

1. EB-Navigation for Electric Vehicles

EB-Navigation in the vehicular context is defined as the computation of a travel route for an electric vehicle that requires the least amount of energy for the trip, with the goal of extending EV range. Instead of classical shortest-path or least-time criteria, the system minimizes cumulative propulsion energy subject to the vehicle's current battery state and anticipated driving conditions (Wu et al., 2020).

1.1. Vehicle Energy Consumption Model

The instantaneous propulsion power required by an EV is modeled as:

$$P_{\rm inst}(v,a,\theta) = \frac{1}{\eta} \left[ \frac{1}{2}\rho C_d A v^3 + mgC_r v + mv a + mgv \sin\theta \right]$$

where $v$ is speed, $a$ is acceleration, $\theta$ is road grade, $\rho$ is air density, $C_d$ the drag coefficient, $A$ the frontal area, $m$ the vehicle mass, $g$ gravity, $C_r$ the rolling-resistance coefficient, and $v$0 the drivetrain efficiency. The energy consumption over interval $v$1 is:

$v$2

Real-world implementation for link-level energy estimation employs an "Energy Operational Parameter Set" (EOPS): a polynomial regression fit $v$3 over observed speed and grade data per road link $v$4, yielding per-link energy consumption $v$5 in Wh, where $v$6 is the link’s length.

1.2. Graph Representation and Cost Function

The road network is modeled as a directed graph $v$7, with edges corresponding to physical road segments. Each edge $v$8 is associated with a bespoke energy cost $v$9. The optimal path $a$0 from origin $a$1 to destination $a$2 is obtained by solving:

$a$3

where $a$4 is the available battery energy.

1.3. Real-Time Implementation

• Data Acquisition: OBD-II data (battery current $a$5, voltage $a$6), vehicle speed, and accessory loads are streamed at 20 Hz; GPS at 1 Hz. Data are aligned via resampling and cross-correlation.
• EOPS Updater: Every 5 minutes (or on demand), traffic speed data per link are ingested, updating $a$7 and the corresponding $a$8.
• Routing Engine: A standard Dijkstra algorithm with binary-heap priority queue and potential enhancements (A*-style heuristics for large networks or battery-range pruning) computes the least-energy path.

2. Empirical Validation and Quantitative Performance

The EB-Navigation system was validated on a 2013 Nissan LEAF, equipped with merged OBD and GPS instrumentation:

• Scale: >100 trips across 3,000+ miles, three urban/rural region pairs
• Sensor error: GPS vs OBD speed SMAPE < 1.7%
• Energy estimation: Link-level regression yields ~0.6% mean trip-level energy error; well within the ±10% target window.
• Simulation (6,048 virtual trips):
  • Relative energy penalty for shortest-distance: 5–25%
  • For shortest-time: 25–51% (versus EB-Navigation)
  • Least-energy paths increase distance by 11–22%, and time by up to 100–200%, revealing a tradeoff owing to EV efficiency at low speeds (10–20 mph).

3. System Architecture and Implementation Aspects

3.1. Modular Hierarchy

• Front-end (Vehicle): Sensor interfacing (CONSULT III + GPS), data fusion, map-matching, and user interface for route display and choice.
• Back-end (Server - DynaNet): Real-time and historical traffic data acquisition, EOPS computation, graph database maintenance, and routing engine.
• Communications: Secure wireless link synchronizes vehicle queries and server-side updates.

3.2. Algorithmic Workflow

The core route-finding procedure is as follows:

$\theta$5

A*-like potentials or battery-based pruning may be added to improve computational efficiency for large graphs.

4. Considerations, Limitations, and Future Directions in Vehicular EB-Navigation

• Elevation/Grade Data: System performance depends on accurate elevation and road grade extraction; GPS-based grade measurements are noisy and may necessitate high-definition mapping.
• Traffic Prediction: Short-term forecasts would support truly online link energy estimations, reducing reliance on stale average speeds.
• Multi-Objective Optimization: Pure energy minimization increases travel time. Incorporating multi-objective or weighted-sum objectives (energy vs time) would align routing better with user preferences.
• Vehicle Adaptation: EOPS functions must be re-calibrated for different EV models with varying mass, regenerative braking, and aerodynamic profiles.

5. EB-Navigation in Inertial Navigation Systems: The PilotEar Case

Extending the concept, "EB-Navigation" also refers to end-to-end inertial navigation using energy-aware (inertial sensor-based) hardware.

5.1. System Overview

PilotEar is an in-ear inertial navigation platform using IMUs (accelerometer, gyroscope, magnetometer) integrated into custom ear-worn devices (Ahuja et al., 2021). Core features include:

• Arduino Nano 33 BLE Sense MCU with 3D IMU sensors
• Optional two-node (dual ear) deployment delivering improved heading and stride estimation via particle filtering

5.2. State Estimation and Propagation

PilotEar internally models the full INS state:

$a$9

The continuous-time INS propagation is:

$\theta$0

where $\theta$1 are calibrated sensor measurements, $\theta$2 is the quaternion rotation, and $\theta$3 is gravity.

5.3. Sensor Fusion and Error Mitigation

• Vibration Damping: Head–neck biomechanics provide ~30% higher SNR on IMU data compared to wrist/waist, reducing the process noise in the system.
• Drift Correction: No foot-mounted ZUPT; gyro drift is controlled via complementary filtering with periodic magnetometer re-calibration using smartphone heading anchors.
• EKF Reference: No direct implementation in PilotEar, but state and measurement models are structurally compatible with a standard INS-EKF framework.

5.4. Calibration and Coordinate Frames

Accelerometer, gyroscope, and magnetometer calibration follows established static and dynamic routines, aligning sensor, body, and navigation frames. The $\theta$4 transformation is statically estimated for each user, with navigation output in Earth-fixed ENU coordinates.

6. Experimental Evaluation and Performance Metrics

6.1. Experimental Setup

• 6 subjects (3 male, 3 female), dual earable with iPhone 11 compass ground truth
• Indoor: 10 m corridor repeating loops
• Outdoor: ~750 m campus loop

6.2. Quantitative Results

Configuration	Drift (m/s)	Std Dev (m/s)
Left ear only	0.181	0.025
Right ear only	0.170	0.082
Dual earables (fused)	0.106	0.039

Typical single-ear drift is 0.15 m/s, dual-ear 0.11 m/s, matching or outperforming wrist (0.20–0.25 m/s) and waist (0.12–0.18 m/s) IMU deployments.

Magnetometer-only heading yields 15.1° mean error and 0.133 m/s drift; fusion with gyroscope marginally improves angular drift.

7. Broader Implications and Future Directions

• Vehicular EB-Navigation: Future improvements include integrating traffic prediction, grade map refinement, multi-objective optimization, and generalization to heterogeneous vehicle fleets.
• Wearable EB-Navigation: Ongoing directions are enhancement with zero-velocity/zero-angular-rate updates, multi-modal sensor fusion (e.g., IMUs + UWB or vision), real-time SLAM integration, and adaptation of stride models to individual users. Accessibility is a key application area, enabling audio-guided navigation for visually impaired users (Ahuja et al., 2021).

A plausible implication is that EB-Navigation, both in vehicular networks and wearable inertial sensing, allows for substantial reductions in energy overhead, as empirically demonstrated—up to 51% for EV trips over conventional route planning (Wu et al., 2020) and ~0.1–0.15 m/s drift in earable personal navigation (Ahuja et al., 2021). These approaches contrast sharply with legacy navigation systems optimized solely for distance or elapsed time. Limitations remain in sensor calibration reliance, environmental noise sensitivity, and the need for tailored calibration when generalizing to new platforms or user populations.