Monitoring high-dimensional structures using model-based estimation faces challenges due to limited sensors, necessitating exten- sive sensor channels and high-fidelity models. This conventional approach is hampered by its laborious, expensive, and computationally intensive nature, which is often impractical due to sensor inaccessibility, especially to attain input robustness. While typically input rejection enforces con- ditions on the availability of sufficient measurement channels, this study introduces a cost-effective monitoring method operating in a lagged time domain that can reject the input forces, even with sparse instrumenta- tion. To provide sufficient measurements, the sparse sensor data sampled at a certain time instance is augmented with responses from subsequent time steps, posed as responses sampled from virtual sensors. This eventually mandates employing a unique measurement model that maps state estimates to real and virtual measurements, effectively overcoming the scarcity of physical sensors. Tested on simplified linear time-invariant (LTI) systems, in terms of a lumped mass model, the proposed approach utilizes the traditional Kalman filtering framework. A numerical observability study identifies required instrumentation nodes, successfully estimating unobserved states by fusing real and virtual sensor data. This success suggests the potential exploration of linear time-variant (LTV) systems and extension to parameter estimation towards structural condition monitoring.