Mother-of-six Anita Rose, 57, left her house to take her springer spaniel named Bruce for a walk in Brantham, Suffolk at around 5am on Wednesday, cops said.
She was found by a member of the public along the country path with serious head injuries at around 6.25am and taken to Addenbrooke's Hospital in Cambridge.
Detective Superintendent Mike Brown, from Suffolk Police's Major Investigation Team - speaking at the force's headquarters on Monday, made an appeal for information.
He said officers are looking for a pink jacket that Ms Rose was believed to have been wearing immediately before the incident.
The officer said police would be releasing a map showing the route they believe Ms Rose walked, and want to speak to anyone who saw anything on Wednesday in the areas shown on the map.
The map has now been released.
He added: "Our investigation team continue to progress a large number of inquiries to establish the circumstances surrounding Anita's injuries and her subsequent death.
"This work includes house-to-house inquiries, searches at the scene and surrounding areas where Anita was found as well as searching through CCTV footage and ongoing forensic work.
"We know that Anita had left her house at approximately 5am to take her dog, a springer spaniel named Bruce, for a walk.
"At approximately 6.25am on Wednesday, a member of the public found Anita laying unconscious on a track near the water treatment works and a railway line off Rectory Lane and called an ambulance.
"Officers were then called by the East of England Ambulance Service shortly after 8am."
Officers have been able to locate and recover Anita's missing iPhone following appeals to trace it.
A tribute issued by Anita's family read: "Our mum was well known and loved in the community.
"She was brutally taken from us devastatingly too early, and we have been robbed of so much time with her.
"She wasn't just a mum of six, she was also a grandma to 13, a long-term partner, a mother-in-law and a special friend to so many.
"Someone somewhere must know something, and we urge them to come forward.
"We want to thank everyone for their love and support.
"All we ask is for everyone to cherish their time with their family and loved ones."
Mr Brown said Ms Rose was taken to Addenbrooke's Hospital in Cambridge having sustained "serious head injuries", and she died on Sunday morning.
"Residents will continue to see an additional police presence and officers patrolling and engaging in the area over the coming days as our investigation continues," he said.
"I recognise that many people will feel concern, but I can reassure you that we are working hard to identify what has taken place and this investigation is a priority for the constabulary.
"If people are concerned about going for a walk I would advise them to remain vigilant, to tell someone where you are going, what time you are expected to be back and let them know when you are home.
"Anita's family continue to be supported by specially trained officers as part of the investigation and we appreciate that this is a very difficult time for them at the moment and therefore I would ask people not to speculate on social media about this incident.
"Information from the public is always a key part of an investigation and I'm again appealing for any information on the whereabouts of Anita's pink jacket.
"We know that Anita was wearing a pink zip-up jacket which we believe she had on immediately prior to the incident.
"This missing jacket is described as being made of waterproof material and believed to be from an outdoor clothing brand, possibly Regatta.
"To help us with this we will be releasing a map detailing the route we believe Anita walked on Wednesday morning.
"We're keen to speak to anyone who saw anything on Wednesday in the areas shown on the map or anyone travelling on trains towards Ipswich or Manningtree on that morning who saw anything that they think may be of use to the investigation.
"We are also keen to speak to anyone living in the area that has CCTV or a Ring doorbell.
"I'm extremely grateful for the support of the community and that the media has given us so far.
"The assistance we have received is absolutely key to our investigation.
"Anyone with information that may assist the inquiry is asked to contact Suffolk Police quoting 37/41580/24 or to get online on the Major Incident Public Portal which can be found on Suffolk Constabulary's web page."
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