1. A method for providing integrity for a hybrid navigation system using a Kalman filter, the method comprising: receiving signals from a plurality of global navigation satellite system (GNSS) satellites at a vehicle; obtaining inertial measurements from one or more inertial sensors on the vehicle; determining a main navigation solution for one or more of roll, pitch, platform heading, and true heading for the vehicle using data from the signals from a plurality of GNSS satellites and the inertial measurements; determining a plurality of sub-solutions for the main navigation solution using solution separation; determining a separation between the main navigation solution and each of the sub-solutions; determining a separation variance between the main navigation solution and each of the sub-solutions; determining a threshold for detection of a satellite failure based on the separation variances and an allowable false alert rate; and determining a protection limit that bounds error in the main navigation solution based on the threshold and an allowable missed detection probability, wherein determining a protection limit comprises: determining a plurality of limits, one or more for each sub-solution and one or more for the main navigation solution, by calculating an estimation error variance for the respective sub-solution and main navigation solution and using a multiplier set based on the allowable missed detection probability, wherein the estimation error variance for each sub-solution and the main navigation solution is calculated using a transpose of an error mapping vector for the one or more of roll, pitch, platform heading, and true heading, a respective error covariance matrix, and the respective error mapping vector; and selecting a limit from the plurality of limits as the protection limit.