You can still detect any kind of faulty input to the UKF system equations using the innovation sequence and an appropriate chi-square test applied to the innovation covariance of the filter.
For such detection your filter must be sensitive to the faults in the inputs (e.g. a filter with low process noise covariance, Q).
If there is a possibility for both measurement and input faults then you may need also a fault isolation process as you need to detect two types of faults both from the innovatiaon sequence. I suggest you to check the following publication in this case for the details of a fault isolation process