Hospital BLE Asset Tracker: RSSI Trilateration (2D)

Tag Motion

Drag the red tag or any grey beacon on the floor plan to reposition it by hand — the tag resumes wandering when you release it.

Tag speed 0.35 m/s

RSSI noise (σ) 2.0 dB

Path-loss exponent n 2.0

Active beacons 6

Localization

Position error

0.0 cm

Beacons in range

Est. position (x,y)

0.0, 0.0 m

Update rate

2.0 Hz

Accuracy vs. receivers & noise

Live Monte-Carlo sweeps (40 trials each) re-run every few seconds from the same trilateration solver used above, at the tag's current true position — confirming more active beacons and lower RSSI noise measurably shrink position error.

How it works

A BLE tag on a mobile infusion pump broadcasts an advertising packet a few times per second. Every fixed ceiling receiver ("beacon") that hears it measures the Received Signal Strength Indicator (RSSI) and converts it to an estimated distance using the log-distance path-loss model:

RSSI(d) = RSSI₀ − 10·n·log₁₀(d / d₀) + Xσ

d = d₀ · 10^((RSSI₀ − RSSI) / (10·n))

where RSSI₀ is the calibrated strength at reference distance d₀ = 1 m, n is the path-loss exponent (2.0 in free space, higher through walls and bodies), and Xσ is zero-mean Gaussian multipath/shadowing noise. Each beacon's distance estimate defines a circle of possible tag positions around it on the floor plan.

With three or more circles, the tag's true position is the point that best satisfies all of them simultaneously. This simulator solves that with linear least-squares multilateration: subtracting the equation for a reference beacon from every other beacon's equation cancels the quadratic |tag|² term, leaving a linear system A·x = b solved (via 2×2 normal equations) for the (x, y) floor-plan position that minimizes total squared residual — implemented from scratch, no external solver.

Tag speed — how fast the simulated pump wanders around the floor plan when not being dragged.
RSSI noise (σ) — the standard deviation of the shadowing/multipath error added to every reading; higher σ spreads the distance circles and inflates position error.
Path-loss exponent n — how fast signal decays with distance; higher n (more walls/obstruction) makes RSSI→distance conversion less linear and noisier.
Active beacons — beacons beyond ~9 m range or disabled here stop contributing; fewer beacons means a more poorly conditioned (or unsolvable, below 3) least-squares system and larger error, exactly as the accuracy charts show.

Real hospital RTLS (real-time locating systems) use exactly this pipeline — Bluetooth AoA/RSSI, Wi-Fi RTT, or UWB — to find infusion pumps, wheelchairs and portable monitors on a floor plan, the "resource tracking" layer of a connected hospital's medical IoT.

True tag position Estimated position Beacon (ceiling receiver)

Error vs. beacon count

Error vs. RSSI noise