Kalman filters are widely used for real-time estimation of dynamic systems, and they sometimes need to be implemented on energy-constrained devices. A Kalman filter implementation from unreliable memories is considered, where the flipping probability of a bit in a memory cell directly depends on its energy consumption. The degradation in estimation performance caused by the noise in the memory is theoretically investigated. Updated equations are then developed for the Kalman filter, taking into account the new source of noise from the unreliable memory. Finally, a method is proposed to optimize the bit energy allocation in the memory, and it is shown from numerical simulations that this method allows for important energy gains.