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The wilderness manhunt for a 73-year-old seasoned outdoorsman suspected of gunning down his daughter-in-law before disappearing into a vast state forest has hit a brick wall, and at least one survival expert believes it could be weeks before he is found.

Eugene Palmer, of Haverstraw, N.Y., allegedly shot and killed his son's estranged wife, 39-year-old Tammy Palmer, a mother of two, in what family members said was a bitter domestic dispute. Palmer was found shot to death Sept. 24 outside her home. Haverstraw Police Chief Charles Miller told FoxNews.com Monday that he believes Palmer, a retired park ranger and avid hunter, is hiding in nearby Harriman State Park -- a 46,000-acre woodland filled with caves and root cellars that straddles Rockland and Orange counties.

"We’re just hoping we get a sighting or something concrete to go on," Miller said of the search for Palmer, a diabetic who police believe is armed with a shotgun and rifle.

"He’s a woodsman who goes up there all the time," said Miller. "He knows how to cover his scent."

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Survival expert Mykel Hawke said Palmer's chances of staying alive in the park depend on a variety of factors -- including his age and the level of preparation for the outdoors.

"If it was hasty, I give him seven days," Hawke told FoxNews.com. "If it was planned, he could go 30 days -- given that he’s an outdoorsman and knows the lay of the land.

"I’d say he might have gone in there looking to check out," said Hawke, a retired U.S. Army Special Forces officer and co-star of the Discovery Channel's "Man, Woman, Wild," which aired until last January.

Hawke said Palmer will need a heat source as the weather gets colder, and a clean water supply.

"He obviously knows he’s being hunted, so a fire would be a big footprint," said Hawke. "Police should look for rock structures that are close to water sources."

Interviews with family members suggest the fatal shooting was premeditated.

The man reportedly told his granddaughter a day before the alleged murder that "I'm going to take your mother down, mark my words."

Palmer's sister, Elaine Babcock, also told reporters that her brother showed up at her house after the shooting and confessed to the killing.

"He just came in and said, 'Here's money to pay my taxes with, I’ve had enough. I shot and killed Tammy. Give me an hour to get away and then do whatever you have to do — call the police…whatever you have to do,’ and then he just took off,'" Elaine Babcock told CBS-TV.

Police found Palmer's green 1995 Dodge pickup camper in Harriman State Park a day after the shooting. The vehicle, which was impounded, was discovered about a half mile from Palmer's Haverstraw home.

Miller said he is unsure whether Palmer, who suffered a heart attack last year, is carrying medication with him. He said authorities have subpoenaed Palmer's medical records for more information on his condition.

The Haverstraw police, with the assistance of bloodhounds and New York State Police, have scoured the park over the last week.

Miller said one of the dogs detected a scent that led him to a campsite, where the trail went cold.

"The dog followed it up to a local campsite and then he lost the scent," Miller said. "I’m not even sure it was him."

Miller dismissed the suggestion that Palmer might have crossed into the 16,000-acre military reservation around West Point, where trespassers are prohibited. The reservation is north of Harriman State Park.

Miller also said searches of the land by helicopter have so far proved fruitless.

"We’re not searching by air anymore because the helicopters aren’t really seeing much on the ground," he said. "The leaves are too full right now and there's not a lot of openings."

Authorities are urging any hikers who may encounter Palmer to "walk away" and call police.