This paper is the first of a two-part series on a novel method of power system state estimation that makes use of information theory to calculate an accurate real-time power system model from a set of analog and digital measurements. This proposed minimum-information-loss (MIL) method is distinguished in that it seamlessly unifies the maximum a-posteriori estimation of both analog and digital quantities such as bus voltages and switch statuses. Both analog and digital estimation residuals are obtained. MIL takes into account the a priori probabilities of the quantities to be measured and the losses incurred along the measurement's information channels with noise when minimizing the overall loss of information. For the identification of network topology errors and switch statuses, MIL processes digital data directly without using auxiliary analog pseudo-measurements. It is shown that the well-known weighted-least-square (WLS) estimation is obtained as a special case of the comprehensive MIL state estimation. © 2013 IEEE.