Objective: There are nearly 786,000 Americans with end-stage renal disease (ESKD), of which 71% rely on life-saving hemodialysis (HD) treatment. HD care costs Medicare annually in excess of $70 billion. One primary goal of HD treatment is to remove excess fluid via ultrafiltration. Intradialytic hypotension (IDH), a significant reduction in blood volume due to an imbalance between ultrafiltration and interstitial to intravascular fluid refilling rates, has severe implications for morbidity and mortality. However, fluid and blood volume are not accessible. It has been suggested that knowledge of extracellular fluid and absolute blood volume should improve HD outcomes. Methods: The new estimation approach combines a validated physiological-based fluid volume model during ultrafiltration, the nonlinear least squares method with an uncertainty quantification technique, and the unscented Kalman filter. Results: We develop a novel estimation approach that estimates the underlying model parameters, bounds error estimation due to model uncertainty and measurement noise, reconstructs unmeasured fluid and blood volume, and predicts personalized outcomes (hematocrit), during HD treatment. Finally, we test the performance of our approach using actual HD data. Conclusion: The extracellular (plasma, interstitial) fluid volume, absolute blood volume, and fluid shift/refill parameters can be estimated and bounded by the Fisher information matrix lower bounds. In addition, fluid volume corrections and personalized predictions for the blood volume evolution can be achieved during ultrafiltration by fitting the underlying parameters to a patient's data. Significance: This novel estimation algorithm, readily available for integration in current HD machines, could improve HD treatment outcomes.