BLE Beacon EKF Position Tracker

Radio Environment

Path-loss exponent n 2.5

RSSI noise σ (dB) 3.0

Filter motion trust q 0.60

Phone walk speed 1.0×

Live Beacons

EKF Position Estimate

Position error

0.00 m

Running RMSE

0.00 m

Filter uncertainty σ

0.00 m

Active beacons

True (x, y)

0.0, 0.0

Estimated (x, y)

0.0, 0.0

How it works

Each fixed BLE beacon broadcasts at a known reference power. The phone inverts the log-distance path-loss model to turn its measured signal strength into an estimated range:

RSSI(d) = TxPower − 10·n·log10(d) + noise
d_est   = 10 ^ ((TxPower − RSSI) / (10·n))

Instead of solving a fresh least-squares fix every frame, this tracker runs an Extended Kalman Filter over a constant-velocity motion model — the same estimator class used in real dead-reckoning / sensor-fusion pipelines. The state is position and velocity, x = [px, py, vx, vy]:

predict:  x⁻ = F·x        P⁻ = F·P·Fᵀ + Q
measure:  r̂ᵢ = ‖(px,py) − beaconᵢ‖
          Hᵢ = [ (px−bxᵢ)/r̂ᵢ , (py−byᵢ)/r̂ᵢ , 0, 0 ]
          Kᵢ = P⁻·Hᵢᵀ / (Hᵢ·P⁻·Hᵢᵀ + R)
          x  = x⁻ + Kᵢ·(dᵢ − r̂ᵢ)     P = (I − Kᵢ·Hᵢ)·P⁻

Each active beacon's range applies its own scalar correction in turn every frame, and the motion model itself predicts forward between updates — so unlike a pure algebraic solve, the filter keeps producing a (growing-uncertainty) estimate even with only one or two beacons visible, rather than becoming undefined. The dashed circle around each beacon is literally its current noisy range estimate; where several circles cross is the raw geometric fix the filter is correcting toward. The solid ellipse around the red marker is the filter's own 95% position-uncertainty ellipse, drawn from the eigenvalues of its covariance matrix — it visibly shrinks with more beacons and lower noise, and swells when the geometry is poor.

Filter motion trust q sets the process-noise (assumed acceleration variance) — low q makes the filter trust its constant-velocity prediction and smooth over noisy readings (at the cost of lag when the phone changes direction); high q makes it snap to each new measurement. Note that because a fixed dB noise σ converts to a smaller metre-noise at higher n (division by n in the exponent), raising the path-loss exponent alone can look like it tightens the fix in this model — in a real cluttered room, a higher n usually also brings additional multipath bias that this simplified noise model does not add, so watch the trilateration circles' spread for the honest picture, not RMSE alone.

BLE beacon Range circle (noisy) Phone (true) EKF estimate True path Estimated path