With the widespread use of new energy vehicles and the large-scale application of energy storage, lithium-ion batteries are facing resource shortages. Sodium-ion batteries, due to their affordability and abundant resources, are considered a promising energy storage technology. Accurately assessing their health status is crucial to ensuring the efficient performance and long lifespan of batteries. This study combines the techniques of time-series convolutional neural networks and unscented Kalman filtering to propose a novel health status estimation framework. The time-series convolutional neural network leverages its high parallelism and ability to capture long-term dependencies to provide strong support for estimation, while the unscented Kalman filter ensures the robustness of state estimation. Through experimental validation on three sodium-ion batteries, this method demonstrates excellent estimation results, with an average absolute error of 4.52%, average root mean square error of 4.09%, and model fitting up to 93.63%. This research not only provides an efficient estimation method for the health status of sodium-ion batteries but also offers valuable insights for battery management and maintenance in practical applications, aiming to further enhance battery performance, safety, and lifespan.