Cholinergic receptor activation enables the persistent firing of cortical pyramidal neurons, providing a key cellular basis for theories of spatial navigation involving working memory, path integration, and head direction encoding. The granular retrosplenial cortex (RSG) is important for spatially-guided behaviors, but how acetylcholine impacts RSG neurons is unknown. Here, we show that a transcriptomically, morphologically, and biophysically distinct RSG cell-type - the low-rheobase (LR) neuron - has a very distinct expression profile of cholinergic muscarinic receptors compared to all other neighboring excitatory neuronal subtypes. LR neurons do not fire persistently in response to cholinergic agonists, in stark contrast to all other principal neuronal subtypes examined within the RSG and across midline cortex. This lack of persistence allows LR neuron models to rapidly compute angular head velocity (AHV), independent of cholinergic changes seen during navigation. Thus, LR neurons can consistently compute AHV across brain states, highlighting the specialized RSG neural codes supporting navigation.