Carolanne Jackson, 50, who ran an antiques business from her home, was found tied up in the kitchen of her cottage in Wooburn Green, near High Wycombe, Buckinghamshire, on Sunday morning. She died from asphyxiation and had severe head wounds.
Police believe she could have been beaten by a burglar trying to force her to give details of how to get into her safe, where a large amount of jewels were stored.
Detectives are also studying possibly links with an unsolved murder of another 50-year-old woman killed two years ago at her home about 20 miles away from the latest assault.
Police said the intruder may have waited for Ms Jackson to return from a trip abroad on Friday night and entered her homeas she was unloading her car.
It was disclosed yesterday that Ms Jackson had called the police in February after being followed by a vehicle near her home. She later saw a man standing outside her house. Police searched the area with tracker dogs but could find no sign of the stalker.
Superintendent Alan Partridge, leading the murder investigation, also said there had been other earlier incidents when Ms Jackson had complained about being followed. She was very security-conscious and her home was protected by an alarm system.
Supt Partridge said: "It is my firm suspicion that regrettably Ms Jackson had been targeted by someone who knew what sort of trade she was in.
"Someone suspected she might have items at her home which would be of value." He added: "It is likely they had been hanging around the area waiting for her and, indeed, may have been in the area in earlier days or weeks."
The assailant tied her hands and feet and took a Rolex watch from her body, with other jewellery. The cottage was searched, but the police have been unable to open the house safe to discover whether anything has been stolen from it.
It is unclear how she died. There were no strangulation marks on her throat and a murder weapon, such as a pillow, which may have been used to suffocate her, has yet to be identified. Ms Jackson, who lived alone, was described as a decent woman and regular churchgoer.
Police are examining possible links with the murder of Janet Brown, 50, a nurse who was found battered to death at her farmhouse in Radnage, Buckinghamshire, two years ago. Supt Partridge said there were certain similarities between the cases but there were no strong links to indicate the killer was the same person.
Mrs Brown was found naked and handcuffed at her home. She had been beaten to death, but had not been sexually assaulted.
Burglary was discounted as the motive after it was discovered that nothing had been taken. Her murder remains unsolved.
Stanley Jackson, the father of Ms Jackson, said yesterday that he believed her killer was also responsible for the death of Mrs Brown. He said: "You can never be sure, but I believe the killer is the same man.
"Carolanne was a lovely woman, a lovely lady. She knew a lot of people through her jewellery business and they all thought so much of her," he added.