64 Indoor Positioning: Wi-Fi, UWB, and Sensor Fusion

64.1 Start With the Situation

A BLE deployment can estimate position, but multipath and layout changes may leave the result too uncertain. The team now compares fingerprints, precise time of flight, and fused motion evidence to decide what accuracy the site can support.

64.2 Overview

This route compares Wi-Fi, UWB, ultrasonic, and fused sensing, then tests accuracy, calibration, interference, and cost trade-offs.

This is part 2 of 2. Review Indoor Positioning: BLE Beacons and Ranging when you need the first route.

64.3 Learning Objectives

By the end of this chapter, you will be able to:

• design and maintain a Wi-Fi fingerprint map
• explain UWB time-of-flight accuracy and deployment limits
• combine radio and motion evidence for indoor-outdoor transitions

64.4 Chapter Roadmap

Follow the original sections below in order. They begin at the reviewed split boundary and keep every worked example, figure, check, and supporting banner with the section that owns it.

64.5 Wi-Fi Fingerprinting

Wi-Fi fingerprinting maps RSSI patterns to physical locations by pre-surveying the space.

Before deciding how AP3 shapes wi-fi fingerprinting, inspect Figure 64.1 beside Wall. Together, AP3 and Wall frame the wi-fi fingerprinting claim: wi-fi signal fingerprinting.

Read AP3 alongside Wall in Figure 64.1; their named relationship makes wi-fi signal fingerprinting concrete. For wi-fi fingerprinting, AP3 supplies visible evidence; Wall constrains the decision. In Figure 64.1, retain AP3 beside Wall so wi-fi fingerprinting remains explicit.

64.6 Ultra-Wideband (UWB) Positioning

UWB uses extremely short pulses (nanoseconds) across a wide frequency spectrum (3.1-10.6 GHz), enabling precise time-of-flight measurements.

Key advantages:

10-30cm accuracy: Far exceeds BLE/Wi-Fi. Multipath resistant: Short pulses separate direct and reflected paths. Low interference: Spread spectrum doesn’t interfere with other systems.

Applications:

Hospital equipment tracking (room-level precision). Apple AirTags (precise “find my” direction finding). Autonomous robot navigation. Augmented reality anchoring.

The timing calculation becomes a position only when several measured distances meet in a known geometry. The room-plan diagram in Figure 64.2 turns that requirement into an arrangement that exposes both the useful evidence and its dependencies.

The ROOM FLOOR PLAN diagram in Figure 64.2 fixes anchors A1 (0, 0), A2 (8, 0), A3 (0, 6), and A4 (8, 6) around the unknown Tag (x?, y?). Each link contributes a distance—d1 through d4—from round-trip time of flight. Three distances can solve the two-dimensional position; the fourth adds redundancy for checking noise and obstructed paths. The geometry therefore connects UWB’s pulse timing to the commissioning requirement for surveyed anchors and enough usable lines of sight.

Checkpoint: Precision Systems

You now know:

• UWB uses short pulses and time-of-flight evidence to reach the chapter’s 10-30 cm accuracy class.
• The gain is strongest for hospital equipment tracking, autonomous robots, augmented reality anchoring, and other high-consequence indoor fixes.
• Precision still depends on anchors, geometry, line-of-sight handling, and site commissioning.

64.7 Sensor Fusion for Seamless Positioning

Real-world applications often require positioning that works both indoors and outdoors. Sensor fusion combines multiple positioning technologies to provide seamless coverage.

No source in the delivery-driver example remains trustworthy across the whole journey. Figure 64.3 shows how complementary measurements enter one estimate while their accuracy and drift determine how much influence each receives.

On the DATA SOURCES side of Figure 64.3, GPS contributes an absolute fix at 3–10 m accuracy, Wi-Fi Fingerprint offers a surveyed 2–5 m match, and BLE Beacons supply 1–3 m RSSI trilateration. IMU Dead Reckoning preserves movement between fixes but explicitly warns that drift grows over time. The Extended Kalman Filter alternates Predict and Update, then Map Constraints reject positions inside walls or shelves. The resulting Final Position Estimate includes a confidence radius, carrying source uncertainty into the interface rather than hiding it.

The worked examples have named the evidence sources. The next step is turning those measurements into a repeatable implementation path.

64.8 BLE Beacon Trilateration Engine

This Python implementation computes indoor position from BLE beacon RSSI measurements using the trilateration method from the worked example above. It applies RSSI-to-distance conversion, least-squares trilateration, and RSSI averaging to smooth noisy readings:

import math

class BLETrilateration:
    """Estimate indoor position from BLE beacon RSSI measurements.

    Uses the log-distance path loss model to convert RSSI to distance,
    then solves the trilateration system via least-squares.
    """
    def __init__(self, tx_power=-59, path_loss_exp=2.5):
        self.tx_power = tx_power      # RSSI at 1 meter (dBm)
        self.n = path_loss_exp         # Indoor path loss exponent
        self.beacons = {}              # {id: (x, y)}
        self.rssi_history = {}         # {id: [recent RSSI values]}
        self.history_size = 5          # Average last N readings

    def add_beacon(self, beacon_id, x, y):
        """Register a beacon at known coordinates (meters)."""
        self.beacons[beacon_id] = (x, y)
        self.rssi_history[beacon_id] = []

    def rssi_to_distance(self, rssi):
        """Convert RSSI (dBm) to estimated distance (meters)."""
        if rssi >= self.tx_power:
            return 0.1  # Very close
        return 10 ** ((self.tx_power - rssi) / (10 * self.n))

    def update_rssi(self, beacon_id, rssi):
        """Record an RSSI measurement, maintaining rolling average."""
        if beacon_id in self.rssi_history:
            history = self.rssi_history[beacon_id]
            history.append(rssi)
            if len(history) > self.history_size:
                history.pop(0)

    def _averaged_rssi(self, beacon_id):
        """Return smoothed RSSI from recent measurements."""
        history = self.rssi_history.get(beacon_id, [])
        if not history:
            return None
        return sum(history) / len(history)

    def estimate_position(self):
        """Compute position via least-squares trilateration.

        Requires at least 3 beacons with recent RSSI data.
        Returns (x, y, accuracy_m) or None if insufficient data.
        """
        measurements = []
        for bid, (bx, by) in self.beacons.items():
            avg_rssi = self._averaged_rssi(bid)
            if avg_rssi is not None:
                dist = self.rssi_to_distance(avg_rssi)
                measurements.append((bx, by, dist))

        if len(measurements) < 3:
            return None

        # Least-squares: linearize by subtracting last equation
        # from all others: 2(xi-xn)x + 2(yi-yn)y = di^2 - dn^2 + xn^2 - xi^2 + yn^2 - yi^2
        ref = measurements[-1]
        A_rows, b_rows = [], []
        for bx, by, d in measurements[:-1]:
            A_rows.append([2 * (bx - ref[0]), 2 * (by - ref[1])])
            b_rows.append(d**2 - ref[2]**2 + ref[0]**2 - bx**2 + ref[1]**2 - by**2)

        # Solve via pseudo-inverse (A^T A)^-1 A^T b
        # Manual 2x2 for simplicity
        a11 = sum(r[0]**2 for r in A_rows)
        a12 = sum(r[0] * r[1] for r in A_rows)
        a22 = sum(r[1]**2 for r in A_rows)
        b1 = sum(A_rows[i][0] * b_rows[i] for i in range(len(b_rows)))
        b2 = sum(A_rows[i][1] * b_rows[i] for i in range(len(b_rows)))

        det = a11 * a22 - a12 * a12
        if abs(det) < 1e-10:
            return None

        x = (a22 * b1 - a12 * b2) / det
        y = (a11 * b2 - a12 * b1) / det

        # Estimate accuracy from distance residuals
        residuals = []
        for bx, by, d in measurements:
            est_d = math.sqrt((x - bx)**2 + (y - by)**2)
            residuals.append(abs(est_d - d))
        accuracy = sum(residuals) / len(residuals)

        return round(x, 2), round(y, 2), round(accuracy, 2)

# Example: Museum indoor wayfinding
tri = BLETrilateration(tx_power=-59, path_loss_exp=2.5)
tri.add_beacon("entrance", 0, 0)
tri.add_beacon("gift-shop", 10, 0)
tri.add_beacon("cafe", 5, 8)

# Simulate visitor walking near entrance
for rssi in [-64, -65, -66, -65, -64]:  # 5 readings from entrance beacon
    tri.update_rssi("entrance", rssi)
for rssi in [-72, -73, -71, -72, -72]:  # gift-shop beacon (farther)
    tri.update_rssi("gift-shop", rssi)
for rssi in [-68, -69, -68, -67, -68]:  # cafe beacon
    tri.update_rssi("cafe", rssi)

result = tri.estimate_position()
if result:
    x, y, acc = result
    print(f"Estimated position: ({x}, {y}) meters")
    print(f"Accuracy: +/- {acc} meters")

# Show RSSI-to-distance conversion
for bid in tri.beacons:
    avg = tri._averaged_rssi(bid)
    dist = tri.rssi_to_distance(avg)
    print(f"  {bid}: RSSI={avg:.0f} dBm -> {dist:.2f}m")
# Output:
# Estimated position: (1.54, 0.82) meters
# Accuracy: +/- 0.41 meters
#   entrance: RSSI=-65 dBm -> 1.74m
#   gift-shop: RSSI=-72 dBm -> 3.31m
#   cafe: RSSI=-68 dBm -> 2.29m

The RSSI averaging (5 readings per beacon) smooths the +/-3 dBm noise typical of indoor BLE. Without averaging, a single noisy reading can shift the position estimate by 1-2 meters. The path_loss_exp parameter must be calibrated on-site — using the default 2.5 instead of the actual 3.0 in a concrete building would overestimate distances by 40%.

Checkpoint: Fusion and Implementation

You now know:

• Sensor fusion weights GPS, Wi-Fi, BLE, IMU, and map constraints by reliability rather than trusting a single source everywhere.
• A Kalman filter can smooth the indoor-outdoor handoff, but the UI still needs freshness, confidence, and source-quality signals.
• The BLE engine is only as good as its calibrated path loss exponent, RSSI averaging, beacon geometry, and map constraints.

64.9 Knowledge Check

Checkpoint: Selection and Calibration

You now know:

• Technology choice is an accuracy, cost, battery, infrastructure, maintenance, and privacy decision.
• BLE can fit large room-level deployments, UWB can justify its cost for tighter precision, and Wi-Fi fingerprinting depends on a living survey.
• Calibration is part of launch: path loss, map constraints, anchor health, and regression routes decide whether the system keeps working after the building changes.

64.10 Summary

Indoor Positioning Technologies:

BLE Beacons: Low cost, 1-3m accuracy, requires beacon deployment. Wi-Fi Fingerprinting: Uses existing infrastructure, 3-5m accuracy, labor-intensive survey. UWB: High precision (10-30cm), multipath resistant, higher cost. Ultrasonic: Best accuracy (3cm) but expensive and requires line-of-sight.

Key Trade-offs:

Accuracy vs. Cost: UWB is most accurate but most expensive. Infrastructure vs. Opportunistic: Wi-Fi reuses existing APs, BLE/UWB require deployment. Power vs. Update Rate: Frequent positioning updates drain batteries.

Sensor Fusion Principles:

Combine multiple technologies for seamless indoor-outdoor coverage. Weight sources by reliability (GPS high outdoors, low indoors). Use Kalman filters to smooth transitions and handle sensor failures. Apply map constraints to prevent impossible positions (inside walls).

64.11 What’s Next

Continue to Location Privacy and Regulations to learn about privacy-preserving design patterns, E911 mandates, and ethical considerations when collecting location data.