Anchor-Corrected Grey-Box Soft-Sensing Control for Multi-Zone Heating Systems Under Sparse Indoor-Temperature Sensing: Time-Scale Alignment and Common-Mode Residual Compensation

Sparse indoor-temperature sensing limits zone-level heating control in existing buildings. This study evaluates whether an anchor-corrected grey-box controller can retain indoor-air-temperature tracking in one simulated 12-zone TRNSYS Type 56 apartment-block model driven by one weather file. The complete configuration uses one measured anchor among all 12 controlled zones (1/12, 8.3%) and among the six actively heated and evaluated zones (1/6, 16.7%). It combines a fixed, case-specific spatial equivalent heat-transfer coefficient (UA) prior, conditional anchor-residual correction, and recursive virtual-inertia filtering. The primary component-level evidence was a matched-constraint ablation over a selected 21-day heating-period window, comprising seven warm-up days and 14 evaluation days. Anchor correction reduced pooled active-zone RMSE from 3.1 K in static configuration A to 0.5 K in configuration C and reduced the heating-energy proxy from 2.901 to 1.371 GJ. Adding recursive filtering in configuration D increased RMSE to 0.6 K but reduced valve-command total variation from 174.1 to 113.2 and the proxy to 1.312 GJ relative to C, indicating a case-specific smoothing trade-off. In a separate archived 155-day S0–S3 comparison, S3 achieved an active-zone RMSE of 1.0 K and reconstructed radiator heat of 8889.8 kWh; because the strategies did not share fully matched control and actuator constraints, these values describe the combined estimator, controller-update, rate-limit, and saturation effects of the implemented strategies rather than an isolated filter effect. The public-record branch generated one common trajectory for seven withheld targets and is interpreted as a common-mode correction audit. In the measured-radiator audit, the filtered-residual formulation H4 tied the static anchor-offset baseline H1 at approximately 0.4 K on ds1 but was worse on ds2 (0.7 versus 0.6 K). The evidence supports a conditional, case-specific low-sensor architecture, not universal single-anchor transfer, independent zone-state recovery, annual or cross-building performance, or resolved hydraulic-network control.