ashfordeOU Dilution of Precision (gnc-autonomy/navigation/dilution-of-precision)
Use when the task is evaluating GNSS position accuracy from satellite geometry: DOP values, the elevation mask, position error from UERE, and best satellite subset selection.
Domain quick reference
- With N satellite line-of-sight unit vectors (east, north, up in a local ENU frame), the N x 4 geometry matrix H has one row [e, n, u, 1] per satellite; the unit column carries the receiver clock bias solved together with the three position components.
- The normal matrix A = H^T H is 4 x 4; its inverse G maps pseudorange error variance onto the state covariance.
- DOP values are square roots of diagonal sums of G: gdop = sqrt(g00+g11+g22+g33), pdop = sqrt(g00+g11+g22), hdop = sqrt(g00+g11), vdop = sqrt(g22), tdop = sqrt(g33).
- A pseudorange error with standard deviation sigma gives a position error standard deviation of pdop * sigma.
- The elevation mask excludes low satellites whose pseudoranges carry larger atmospheric errors; satellite selection picks the k-subset with the lowest PDOP by exhaustive search over combinations.
Workflow
- Build the geometry matrix H from the satellite unit vectors (at least 4 satellites required).
- Form the normal matrix A = H^T H and invert it by Gauss-Jordan with partial pivoting; singular geometry raises a clear error.
- Read the DOP values off the diagonal and the position error from the user equivalent range error.
- Apply the elevation mask and filter low satellites.
- Select the k-satellite subset with the best geometry (lowest PDOP).
Pitfalls
- Reporting a DOP for a singular geometry (collinear satellites); the inversion must fail loudly, not silently.
- Using the same elevation for every satellite in a synthetic set, which makes the normal matrix singular in (e, n, u, 1) space.
- Confusing HDOP with PDOP (horizontal vs total position).
- Reading position error from GDOP instead of PDOP (GDOP includes the clock term).
Behavior contract (gate 3)
The DOP logic is exercised by the gate 3 contract test: scripts/test_dop.py against scripts/dop_logic.py (stdlib unittest, offline). Run:
python3 scripts/test_dop.py