State estimation — recovering the true state with fdia_graph.se

Given a scan of noisy, possibly attacked measurements, estimate the true bus voltages and angles. Every shard ships a noiseless attack-free clean layer, so the estimate is scored against exact ground truth. The module is sklearn style: one base class owns the shared machinery (the AC measurement model, the chord-Newton solve, meter-weight calibration, the classical 2N-1 state with the slack angle as reference), and each method class changes exactly one thing, so comparing two methods compares estimators, not implementations.

import fdia_graph as fg
from fdia_graph.se import WLS, AdaptiveWeighting, SubspacePrior

train = fg.load("ieee14", split="train")
test  = fg.load("ieee14", split="test")

est  = SubspacePrior(rank_frac=0.2, reweight="huber", c=1.5).fit(train)
xhat = est.estimate(test)   # [n, 2N-1] = [theta rad (non-slack) | V pu (all buses)]
rep  = est.score(test)      # per-family angle/voltage MAE vs the clean truth

Needs the [se] extra (pip install "fdia-graph[se]") and a v0.7.2+ shard (the clean layer is the truth). See also the walkthrough in ../guides/state_estimation.md.

The method classes

Class	What it changes	Knobs
WLS	Nothing — the audited baseline, least squares weighted by accuracy-class meter error	—
AdaptiveWeighting	Iteratively reweighted least squares (the Huber M-estimator)	c
ResidualRemoval	Largest-normalized-residual removal with an observability guard	threshold
SubspacePrior	Restricts the solve to a low-rank benign operating subspace, optionally composed with Huber	rank_frac, reweight

Results — IEEE-14, test split, validation-selected hyperparameters

Angle MAE in degrees per family, geo is the geometric mean over families (full metrics including voltage MAE in results/se_ieee14.json, figure data in the CSV sidecar):

method	benign	Aq	Ad	As	Ar	At	Al	geo
wls	0.008	0.382	0.136	0.246	0.137	0.065	0.180	0.108
huber	0.009	0.384	0.046	0.092	0.038	0.065	0.180	0.068
prior+huber	0.012	0.402	0.027	0.080	0.025	0.064	0.154	0.059

Two readings:

1. Robustness cleans up what it can see. The in-place corruption families (Ad/As/Ar) leave large residuals, so Huber reweighting cuts their angle error 3–5x and the operating-point prior tightens it further (geo 0.108 to 0.059 degrees, and the voltage geo improves 6x, see the JSON).
2. The stealthy families barely move. Aq/At/Al re-solve the physics, so their measurements are consistent and there is nothing for a robust weight or a residual test to reject — every method lands within a few percent of WLS there. Recovering the truth under a stealthy attack is not a weighting problem; it needs temporal information (see ../localization/README.md for the detection side of that same story).

Regenerate

python docs/se/run_se.py                       # IEEE-14, minutes on a laptop
FG_SYSTEM=ieee118 python docs/se/run_se.py     # any system in the ladder

Outputs land in results/: the metrics JSON, the figure, and a CSV data sidecar so the figure can be restyled without re-running.