1. A navigation system for a vehicle having a receiver operable to receive a plurality of signals from a plurality of transmitters, the navigation system comprising: a processor; and a memory device having stored thereon machine-readable instructions that, when executed by the processor, enable the processor to: determine a set of error estimates corresponding to pseudo-range measurements derived from the plurality of signals, determine an error covariance matrix for a main navigation solution using ionospheric-delay data, and using a solution separation technique, determine at least one protection level value based on the error covariance matrix.