We have previously described algorithms for a battery management system (BMS) that uses Kalman filtering (KF) techniques to estimate such quantities as: cell self-discharge rate, state-of-charge (SOC), nominal capacity, resistance, and others. Since the dynamics of electrochemical cells are not linear, we used a non-linear extension to the original KF called the extended Kalman filter (EKF). We were able to achieve very good estimates of SOC and other states and parameters using EKF However, some applications e.g., that of the battery-management-system (BMS) of a hybrid-electric-vehicle (HEV) can require even more accurate estimates than these. To see how to improve on EKF, we must examine the mathematical foundation of that algorithm in more detail than we presented in the prior work to discover the assumptions that are made in its derivation. Since these suppositions are not met exactly in BMS application, we explore an alternative non-linear Kalman filtering techniques known as "sigma-point Kalman filtering" (SPKF), which has some theoretical advantages that manifest themselves in more accurate predictions. The computational complexity of SPKF is of the same order as EKF, so the gains are made at little or no additional cost. The SPKF method as applied to BMS algorithms is presented here in a series of two papers. This first paper is devoted primarily to deriving the EKF and SPKF algorithms using the framework of sequential probabilistic inference. This is done to show that the two algorithms, which at first may look quite different, are actually very similar in most respects; also, we discover why we might expect the SPKF to outperform EKF in non-linear estimation applications. Results are presented for a battery pack based on a third-generation prototype LiPB cell, and compared with prior results using EKE As expected, SPKF outperforms EKF, both in its estimate of SOC and in its estimate of the error bounds thereof. The second paper presents some more advanced algorithms for simultaneous state and parameter estimation, and gives results for a fourth-generation prototype LiPB cell. (c) 2006 Elsevier B.V. All rights reserved.