An A319 Captain's Pitot System failed followed shortly by the Air Data Reference 1 (ADR1) failure. The Flight Crew continued to their destination in Alternate Law.

Narrative

We were in cruise flight; west of ICT when we received an ECAM that the captains pitot system failed. The result was a loss of associated PFD indications. We assigned flying duties and followed ECAM procedures. We switched the Captain's instruments to ADR3 per ECAM and all indications returned to normal. A few minutes later; we lost ADR1. We were in Alternate Law. We noticed that the circuit breaker for the Captain's Pitot System was poppped. I contacted Company and talked to Dispatch and Maintenance Control. Maintenance Control advised us NOT to reset the circuit breaker; we agreed with that advice. We determined that we would continue to our destination since the weather was clear and dry the remainder of the route. We monitored our instruments and flight controls carefully the rest of the flight. We spent considerable time briefing our approach as we were going to degrade to direct law. We briefed the first flight attendant of the situation. We also advised Approach Control. The approach and landing were as briefed and uneventful. This is a system failure.