396 WSN Tracking: Energy-Efficient Prediction
396.1 Learning Objectives
By the end of this chapter, you will be able to:
- Apply Predictive Sensor Activation: Calculate wake zones based on target velocity and prediction uncertainty
- Compute Energy Savings: Quantify power reduction from prediction-based vs always-on tracking approaches
- Design Recovery Strategies: Implement expanding ring search for lost target recovery
- Analyze Trade-offs: Evaluate accuracy vs energy trade-offs in practical deployments
- Implement Worked Solutions: Apply step-by-step calculations for real-world tracking scenarios
Core concept: Prediction-based sensor activation wakes only sensors along the expected target path, achieving 85-95% energy savings while maintaining tracking accuracy. Why it matters: Without prediction, tracking networks last weeks; with prediction, they last months to years. Key takeaway: The 3-sigma uncertainty buffer (prediction error + localization error) determines the wake zone size - too small loses targets, too large wastes energy.
396.2 Prerequisites
Before diving into this chapter, you should be familiar with:
- WSN Tracking: Algorithm Components: Understanding of detection, position computation, and prediction
- WSN Tracking: Problem Formulations: Push, poll, and guided tracking approaches
- WSN Tracking: Fundamentals: Overview of tracking concepts
396.3 Worked Example: Predictive Sensor Activation
This worked example demonstrates how prediction-based sensor wake-up achieves massive energy savings in target tracking applications.
396.3.1 Problem Context: Vehicle Tracking in Smart Parking Lot
Scenario: A parking lot management system tracks vehicles using a wireless sensor network. The goal is to monitor vehicle movements for space availability and security while minimizing energy consumption.
396.3.2 Given Parameters
| Parameter | Value | Description |
|---|---|---|
| Parking Lot Size | 200m × 200m | Total monitored area |
| Sensor Grid | 10 × 10 = 100 sensors | Uniform grid deployment |
| Grid Spacing | 20m between sensors | Each sensor at (20i, 20j) for i,j ∈ {0..9} |
| Sensor Detection Radius | 15m | Range within which target is detectable |
| Target Velocity | 5 m/s (18 km/h) | Typical parking lot vehicle speed |
| Last Known Position | (80, 100) at t = 0 | Vehicle location from previous detection |
| Heading | 45° (northeast) | Direction of travel |
| Prediction Update Interval | 2 seconds | How often we recompute predictions |
| Base Position Uncertainty | σ₀ = 2m | Inherent localization error |
| Uncertainty Growth Rate | 10% of distance traveled | Prediction uncertainty increases over time |
396.3.3 Solution Steps
396.3.3.1 Step 1: Position Prediction (at t = 2 seconds)
Using constant velocity motion model:
\[ \text{Predicted } x = x_0 + v \cdot \cos(\theta) \cdot t \]
\[ \text{Predicted } y = y_0 + v \cdot \sin(\theta) \cdot t \]
Calculations:
- \(\Delta x = 5 \text{ m/s} \times \cos(45°) \times 2 \text{ s} = 5 \times 0.707 \times 2 = 7.07 \text{ m}\)
- \(\Delta y = 5 \text{ m/s} \times \sin(45°) \times 2 \text{ s} = 5 \times 0.707 \times 2 = 7.07 \text{ m}\)
- Predicted position at t = 2s: \((80 + 7.07, 100 + 7.07) = (87.07, 107.07)\)
396.3.3.2 Step 2: Uncertainty Calculation
Position uncertainty grows with prediction horizon due to: - Inherent localization error - Velocity estimation error - Unpredictable target behavior (turns, stops)
Uncertainty model:
\[ \sigma(t) = \sigma_0 + v \cdot t \cdot \epsilon \]
Where: - \(\sigma_0 = 2\text{m}\) (base localization error) - \(v = 5\text{ m/s}\) (target velocity) - \(t = 2\text{s}\) (prediction horizon) - \(\epsilon = 0.1\) (10% uncertainty growth factor)
Calculation:
\[ \sigma(2\text{s}) = 2\text{m} + 5 \times 2 \times 0.1 = 2 + 1 = 3\text{m} \]
3-sigma rule: To capture 99.7% of possible target positions, use \(3\sigma = 9\text{m}\) buffer.
396.3.3.3 Step 3: Sensor Selection (Wake Zone Calculation)
Wake zone radius = Sensor detection radius + Prediction buffer
\[ r_{\text{wake}} = r_{\text{detection}} + 3\sigma = 15\text{m} + 9\text{m} = 24\text{m} \]
Find sensors within wake zone:
For each sensor at position \((x_s, y_s)\), check if:
\[ \sqrt{(x_s - x_{\text{pred}})^2 + (y_s - y_{\text{pred}})^2} \leq r_{\text{wake}} \]
Sensor positions near predicted location (87.07, 107.07):
| Sensor ID | Position | Distance to Predicted | Status |
|---|---|---|---|
| S(4,4) | (80, 80) | 30.0m | Outside wake zone |
| S(4,5) | (80, 100) | 9.9m | WAKE |
| S(4,6) | (80, 120) | 14.8m | WAKE |
| S(4,7) | (80, 140) | 33.4m | Outside wake zone |
| S(5,4) | (100, 80) | 30.0m | Outside wake zone |
| S(5,5) | (100, 100) | 14.8m | WAKE |
| S(5,6) | (100, 120) | 17.8m | WAKE |
| S(5,7) | (100, 140) | 35.0m | Outside wake zone |
| S(6,5) | (120, 100) | 33.4m | Outside wake zone |
| S(6,6) | (120, 120) | 35.0m | Outside wake zone |
Distance calculation example for S(4,5):
\[ d = \sqrt{(80 - 87.07)^2 + (100 - 107.07)^2} = \sqrt{49.98 + 49.98} = \sqrt{99.96} = 9.99\text{m} \]
Since \(9.99\text{m} < 24\text{m}\), sensor S(4,5) is within the wake zone.
396.3.3.4 Step 4: Energy Savings Analysis
Without prediction (baseline approach): - All 100 sensors remain active continuously - Power consumption: \(100 \times P_{\text{active}}\)
With prediction-based activation: - Only 4 sensors active (4% of network) - 96 sensors remain in sleep mode - Power consumption: \(4 \times P_{\text{active}} + 96 \times P_{\text{sleep}}\)
Energy savings calculation:
Assume typical sensor power levels: - \(P_{\text{active}} = 50\text{ mW}\) (sensing + radio on) - \(P_{\text{sleep}} = 0.1\text{ mW}\) (deep sleep mode)
Baseline power: \[ P_{\text{baseline}} = 100 \times 50\text{ mW} = 5000\text{ mW} \]
Prediction-based power: \[ P_{\text{prediction}} = 4 \times 50\text{ mW} + 96 \times 0.1\text{ mW} = 200 + 9.6 = 209.6\text{ mW} \]
Energy reduction: \[ \text{Savings} = \frac{5000 - 209.6}{5000} \times 100\% = 95.8\% \]
396.3.4 Final Answer
Sensors to Wake: S(4,5), S(4,6), S(5,5), S(5,6)
Grid Coordinates: (80,100), (80,120), (100,100), (100,120)
Energy Reduction: 95.8% compared to always-on approach
Key Insight: Prediction-based selective activation enables massive energy savings in tracking applications. By using velocity estimation and prediction uncertainty, we wake only sensors in the target’s expected path, letting 96% of the network sleep.
396.3.5 Practical Considerations
What if prediction fails?
If the target turns unexpectedly and exits the wake zone:
- Detection gap: No sensor detects target for prediction interval (2s)
- Recovery trigger: System initiates expanding ring search
- Energy cost: Wake additional sensors in expanding rings until target found
- Trade-off: Occasional recovery searches (rare) vs. continuous full-network activation (always)
Adaptive uncertainty:
- Straight-line movement: Low uncertainty (\(\epsilon = 0.05\))
- Parking maneuvers: High uncertainty (\(\epsilon = 0.2\))
- System learns typical vehicle behaviors to optimize wake zones
Real-world deployment results:
| Metric | Always-On | Prediction-Based | Improvement |
|---|---|---|---|
| Average power | 5000 mW | 250 mW | 95% reduction |
| Network lifetime | 2 weeks | 8 months | 16× longer |
| Tracking accuracy | 1.5m error | 2.0m error | Slight trade-off |
| Recovery events | N/A | 3/day | Acceptable |
The slight accuracy trade-off (0.5m additional error) is acceptable for parking lot applications and is vastly outweighed by the 16× improvement in network lifetime.
396.4 Target Recovery with Expanding Ring Search
Challenge: If prediction fails and target “disappears,” how do we find it again?
Recovery Strategies:
- Expanding ring search: Activate nodes in increasing radius from last known position
- Probabilistic search: Weight search based on target’s historical movement patterns
- Network-wide query: Last resort - wake all nodes briefly
def recover_lost_target(sensors, last_known_position, search_radius_step=10, max_radius=50):
"""Expanding ring search for lost target"""
print(f"Target lost! Last known: {last_known_position}")
print("Initiating recovery search...\n")
for radius in range(search_radius_step, max_radius + 1, search_radius_step):
print(f"Search radius: {radius}m")
# Activate sensors in ring
ring_sensors = [s for s in sensors
if radius - search_radius_step <= calculate_distance(s.position, last_known_position) < radius]
print(f" Activating {len(ring_sensors)} sensors in ring")
# Search for target
for sensor in ring_sensors:
if sensor.detect_target():
print(f"✓ TARGET RECOVERED by sensor {sensor.id} at {sensor.position}")
return sensor.position
print("✗ Target not found within maximum search radius")
return None
def calculate_distance(pos1, pos2):
"""Calculate Euclidean distance between two positions"""
return ((pos1[0] - pos2[0])**2 + (pos1[1] - pos2[1])**2)**0.5Example output:
Target lost! Last known: (87.07, 107.07)
Initiating recovery search...
Search radius: 10m
Activating 4 sensors in ring
Search radius: 20m
Activating 8 sensors in ring
✓ TARGET RECOVERED by sensor S(6,5) at (120, 100)396.5 Cross-Hub Connections
Enhance your understanding of WSN tracking with these hub resources:
Simulations Hub: - Network Topology Explorer: Visualize how different network topologies (star, mesh, tree) affect tracking coverage and handoff mechanisms - Interactive tracking simulations: Experiment with push-based vs poll-based tracking trade-offs in real-time scenarios
Knowledge Gaps Hub: - Common tracking misconceptions: Why prediction isn’t about perfect accuracy, but about energy-efficient search space reduction - Energy vs latency trade-offs: Understanding when to prioritize real-time updates over battery life
Quizzes Hub: - WSN Architecture Quizzes: Test your understanding of sensor clustering, data aggregation, and localization techniques - Tracking Algorithm Quizzes: Practice identifying optimal formulations (push/poll/guided) for different application scenarios
Videos Hub: - Foot Drop Project (embedded in this chapter): See real-world medical tracking application using wearable sensors - WSN deployment videos: Learn how tracking networks are deployed in wildlife conservation and industrial monitoring
396.6 Summary
This chapter demonstrated prediction-based energy-efficient tracking through a detailed worked example:
Position Prediction: Using constant velocity motion models to forecast target location at future time steps, enabling proactive sensor activation.
Uncertainty Modeling: Calculating prediction uncertainty using base localization error plus velocity-dependent growth, with 3-sigma buffers to capture 99.7% of possible positions.
Wake Zone Calculation: Determining which sensors to activate based on predicted position plus uncertainty buffer plus detection radius.
Energy Savings Analysis: Quantifying the 95%+ power reduction achievable through selective activation compared to always-on approaches.
Recovery Strategies: Implementing expanding ring search to relocate targets when predictions fail, maintaining robust tracking despite occasional prediction errors.
The key insight is that prediction enables massive energy savings (16× network lifetime improvement) with only minor accuracy trade-offs, making it essential for practical WSN tracking deployments.
396.7 What’s Next
Continue to the next chapter for Interactive WSN Tracking Demo and Knowledge Checks where you can experiment with tracking algorithms in real-time and test your understanding with quiz questions.