FARNBOROUGH, England (Reuters) - Raytheon Co on Tuesday said it was cautiously optimistic after hitting key milestones in recent months on a long-delayed and over-budget program to develop a ground control system for next-generation GPS satellites.

"Things are progressing well. We've overcome a lot of the challenges, but there are still some in front of us," David Wajsgras, president of Raytheon's Intelligence, Information and Services business, told Reuters at the Farnborough International Airshow.

Wajsgras said Raytheon would continue to work closely with the U.S. Air Force to ensure the success of the program, which is facing a "live or die" Pentagon review after breaching critical cost thresholds earlier this year.

He said Raytheon had put its best resources and people to work to resolve the program's issues.

"I would put us as cautiously optimistic," Wajsgras said. "We feel good about the progress we've made."

Defense Undersecretary Frank Kendall told reporters this week that Raytheon's work on the program was "a mixed bag", showing progress in some areas but continuing problems in others. He said he still hoped Raytheon could get the program under control since it was critically needed.

Air Force Secretary Deborah James on June 30 declared the program had breached congressional cost thresholds, triggering a mandatory review that could lead to the program's termination.

The review will conclude in October, but Kendall told reporters it would be "very disruptive" to stop the program at this point and start over.

The Pentagon earlier this year said the estimated cost of Raytheon's Operational Control System (OCX) had risen 16.3 percent, or $586.4 million, to $4.2 billion in 2015, even before a two-year delay that would further inflate costs.

The new estimated cost was not immediately available. The program was expected to cost just $1.5 billion when Raytheon won the contract in 2010.

The Air Force said Raytheon had briefed its progress on process improvements, including increased automation in software development, platform deployment, and other changes in their software approach at a deep dive review last week.

(Reporting by Andrea Shalal; Editing by Mark Potter)