Beating WLS: state estimation with the SDK

Measurements in, state out, better than weighted least squares on the public test cases. Everything here runs off a shard download — no extra files.

pip install "fdia-graph[se]"     # torch + pandapower

Baseline first

import fdia_graph as fg
from fdia_graph.se import WLS

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

wls = WLS().fit(train)                 # calibrates meter weights from benign residuals
xhat = wls.estimate(test)              # [n, 2N-1] = [theta rad (non-slack) | V pu (all buses)]
print(wls.score(test)["geo"])          # {'angle_mae_deg': 0.108, 'voltage_mae_pu': 6.06e-4}

fit() learns everything from the train split: per-meter error scales (rms of benign residuals at the shard's clean truth) and the chord Jacobian. estimate() returns states already in the truth's angle frame — the state is the classical 2N-1 vector (only the slack ANGLE is fixed, pinned per record to clean[slack]; every voltage magnitude including the slack is estimated, matching production practice and pandapower's estimator), so xhat - truth needs no alignment step.

The better estimator

from fdia_graph.se import SubspacePrior

est = SubspacePrior(rank_frac=0.2, reweight="huber", c=1.5).fit(train)
print(est.score(test)["geo"])          # {'angle_mae_deg': 0.059, 'voltage_mae_pu': 1.47e-4}

The prior restricts the estimate to the low-dimensional subspace benign operation actually occupies (an SVD of the training states), and the Huber reweighting discards measurements the physics cannot explain. On the IEEE 14-bus test partition that is 45 percent lower angle error and 76 percent lower voltage error than the audited WLS baseline (0.108° → 0.059° and 6.06e-4 → 1.47e-4 pu, geometric mean over the seven record classes, v0.7.2 data). Much of the voltage gain comes from the prior learning the generator voltage setpoints from benign history, structure WLS re-estimates from noisy meters at every scan.

Validation-selected hyperparameters per system, from the companion estimation paper:

system	rank_frac	huber c	ResidualRemoval threshold
ieee14	0.20	1.5	4.0
ieee118	0.50	2.5	5.0
ieee300	0.50	6.0	(removal does not help)

What to expect per family

score(test) breaks the result out per attack family, and the split matters:

• Tampering families (Ad bias, As scaling, Ar replay) improve dramatically — they corrupt meters in place, which is what robust weighting exists to reject.
• Stealthy re-solved families (Aq, At, Al) sit near parity for every estimator. They present a physically valid state inside the learned subspace, so no single-scan method can reject them. This is a property of the attacks, not a tuning failure — see the companion paper.
• Benign records improve on the larger systems and can lose slightly on ieee14, where the baseline is already near the noise floor and the subspace truncation bias dominates.

Other arms and your own

AdaptiveWeighting(c=...) and ResidualRemoval(threshold=...) are the classical robust baselines, sharing the same iteration and weights so comparisons are estimator-vs-estimator. To add your own method, subclass SEBase and override one hook:

• _fit_states(x_benign) — learn anything from the benign training states
• _basis() — return a [2N-1, K] basis to restrict the state space (or None for full)
• _solve(z, thsl) — the per-batch solve (thsl is the per-record slack angle reference); self._w_solve(...) gives you the divergence-guarded weighted iteration and self._nres(...) normalized residuals

The classes are verified per-record equivalent to the estimation paper's solver, so results slot directly into its protocol.