State–space methods are central to estimation and control but remain underexplored in modelling portfolio dynamics with transaction costs. This paper presents the Covariance–Calibrated Portfolio Filter (CCPF), a Kalman-based estimation and decision framework for stochastic financial systems influenced by trade-dependent frictions. This work proposes a novel, financially grounded output equation that explicitly embeds wealth, excess return, and transaction effects within the measurement model, completing the state–space representation. An adaptive covariance calibration mechanism further aligns estimation accuracy with performance-oriented criteria. Theoretical analysis establishes detectability and stabilisability conditions, ensuring the model's consistency for control and estimation. Numerical experiments on Tehran Stock Exchange data demonstrate the CCPF's effectiveness in denoising financial trajectories, reconstructing latent holdings, and improving excess-return estimation. By integrating stochastic estimation, feedback control, and adaptive decision principles, this work advances robust dynamic-system design under uncertainty.
Bahrmand et al. (Mon,) studied this question.