(AP) -- A cruise ship battered by a major storm in the Atlantic Ocean returned to its New Jersey port on Wednesday night.

Royal Caribbean's Anthem of the Seas docked at Bayonne's Cape Liberty shortly after 9 p.m., its passengers cheering wildly. It was escorted by two tugboats and a Coast Guard vessel.

"I could kiss the ground" a woman cried as she rushed toward the cruise terminal, where passengers were reunited with family members. "Free at last," shouted a man.

The ship was carrying 4,500 passengers and 1,600 crew members when it departed Saturday on a seven-day cruise to the Bahamas. But the 1,141-foot vessel sailed into a major winter storm on Sunday.

Powerful winds and waves as high as 30 feet tossed the vessel around. Royal Caribbean said four passengers reported minor injuries and the ship sustained some damage to its public areas and staterooms.

Gerald Rogers of Allentown, Pennsylvania, was taking his first cruise with his family. He said it was a "pretty traumatic experience" for those aboard the ship.

"It was really leaning and the water kept coming above our window," Rogers said. "It looked like we were in an aquarium looking out."

Alison Crowley of Manasquan, New Jersey, who was traveling with her four children and her parents, described the situation as "pretty scary." But she said, "The captain did a great job for what he had to deal with."

Bill Baumgartner, a senior vice president with Royal Caribbean, said the ship's passengers and crew had "a terrifying weather experience."

"We are very sorry and apologize to the guests who had to go through this," he told The Associated Press.

Passengers will get a full refund and a certificate toward 50 percent off a future cruise.