Abstract

In sensor-driven dynamic systems, missing data can severely degrade parameter estimation accuracy. This article investigates the impact of missing data on phase estimation in a mass-spring-damper system using an information-theoretic framework based on the Cramér-Rao Lower Bound (CRLB). Closed-form CRLB expressions are derived for four scenarios: complete data, missing completely at random (MCAR) deletion, MCAR-based imputation, and missing at random (MAR) missingness via a selection-weighted formulation. These bounds are used as theoretical benchmarks to evaluate classical imputation methods (last observation carried forward (LOCF), linear interpolation) and advanced approaches (Kalman filtering, Rauch-Tung-Striebel (RTS) smoothing, Bayesian inference, and transformer-based imputation) through Monte Carlo simulations. Empirical results show that classical imputation introduces substantial bias and variance, while advanced methods improve stability but neither outperform direct estimation from available samples nor approach the complete-data or MCAR CRLBs, even under realistic model-parameter mismatch. Normality tests confirm approximately Gaussian estimator behavior, supporting the validity of the CRLB-based analysis. Under MAR conditions, estimation from observed samples consistently yields the lowest variance, highlighting the importance of explicitly accounting for the missingness mechanism in parameter estimation.

Department(s)

Electrical and Computer Engineering

Comments

Intelligent Systems Center, Grant None

Keywords and Phrases

Cramer-Rao lower bound (CRLB); mass-spring-damper; missing data; phase estimation; sensor data imputation

International Standard Serial Number (ISSN)

1557-9662; 0018-9456

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2026 Institute of Electrical and Electronics Engineers, All rights reserved.

Publication Date

01 Jan 2026

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