Ranging-based position estimators

Ranging measures distance the direct way: a protocol like Wi-Fi RTT (802.11mc) times how long a signal takes to make a round trip between the device and an access point and, since radio waves travel at a known, constant speed (the speed of light), converts that time directly into a distance — no assumption about signal strength or how it decays with distance is needed at all.

Once a distance to an access point is known, the same reasoning as RSSI-based positioning applies: one distance narrows the device down to a circle (2D) or sphere (3D) around that access point; distances to several access points narrow it down to where those circles overlap — multilateration. Because ranging measures distance directly instead of inferring it from a noisy, modeled quantity like signal strength, the resulting distances are typically far more precise, so the circles tend to intersect much more tightly around the true position.

3D robust classes mirror the 2D ones. A RangingReading carries a measured distance (meters), an optional distanceStandardDeviation, and the number of attempted/successful RTT measurement exchanges. As with the RSSI hierarchy, 2D estimators need a minimum of 3 sources and 3D estimators need 4; the indoor classes delegate the actual math to the same com.irurueta.navigation.lateration solvers used by RSSI position estimation — ranging estimators simply feed them measured distances directly instead of distances derived from the path-loss model.

Both linearizations start from the same per-source constraint \((\mathbf{x}-\mathbf{p}_i)\cdot(\mathbf{x}-\mathbf{p}_i) = d_i^2\) and eliminate its quadratic term by subtracting the reference source’s ( ) equation from every other one.

NonLinearRangingPositionEstimator wraps the same Levenberg-Marquardt solver used for RSSI, fitting measured squared distance against the candidate’s squared distance to each source:

minimizing where weights come from each reading’s distanceStandardDeviation (default m if unspecified), optionally combined in quadrature with the source’s position uncertainty when useRadioSourcePositionCovariance is enabled: . The initial position defaults to the centroid of the known source positions unless initialPosition is set. The fit also yields a position covariance and chi-squared value.

RobustRangingPositionEstimator follows the identical sample-and-score structure described in the RSSI hierarchy’s robust section — the residual formula, per-sample scoring, and PROMedS default are the same:

with one notable default difference: useHomogeneousLinearSolver defaults to false for the robust estimators' preliminary-solution step (versus true for the plain linear estimator above). The preliminary solution is always attempted with the (inhomogeneous, by default) linear solver first and then refined with the non-linear solver, seeded at the linear result — this is where linear and non-linear estimation are chained together for every robust variant.

Quality scores in the indoor layer are two separate arrays — sourceQualityScores (per radio source) and fingerprintReadingsQualityScores (per reading) — summed per distance sample. When evenlyDistributeReadings (default true) is enabled, ReadingSorter additionally re-orders sampling priority so that no single source’s readings dominate PROSAC/PROMedS regardless of raw quality-score magnitude.

Static create(…​) factories on RobustRangingPositionEstimator2D/3D build any variant from a RobustEstimatorMethod enum, defaulting to PROMedS.

Main classes used on this page, linked to their source code and Javadoc: