The woman who was knifed to death on the Greenstead estate in Colchester yesterday may have been targeted because she was wearing a hijab.
Detectives have also said there are "immediate similarities" between her death and that of James Attfield, who was stabbed more than 100 times in Castle Park earlier this year.
Officers now want to hear from anyone who used the Salary Brook Trail between 8.30am and 11am and are at the location this morning speaking to any members of the public in the area who normally use the pathway.
Detective Superintendent Tracy Hawkings said: "We have not yet been able to formally identify the victim but we believe we know who she is and specially trained family liaison officers are speaking with her family now.
"We urgently need to speak to anyone who saw a woman in her early 30s walking through the Greenstead estate yesterday morning.
"She is believed to have left her home in Woodrow Way and then made her way down across Avon Way onto the Salary Brook Trail. It is possible she may have got onto the trail at one of several entrances on Avon Way towards St Andrews Avenue.
"At the time she was wearing a dark navy blue full length robe, called an Abaya, and a patterned multi-coloured headscarf, known as a Hijab. She also had with her a black bag, with orange panels, which she was carrying on a shoulder strap.
"If anyone saw her or was in this area yesterday morning we would ask them to call us."
Detectives would also like residents to check their gardens and rubbish bins for any discarded weapons or blood stained clothing.
They are asking for anyone who has CCTV footage which covers any part of the Greenstead estate between Woodrow Way and the Salary Brook Trail to make contact with them so that it can be viewed.
Det Supt Hawkings said: "A forensic post-mortem is due to be carried out this afternoon to establish the cause of death but at this time it would appear that a knife or other bladed weapon was used in this attack.
"The victim also suffered facial injuries but the cause of these has yet to be established.
"We have no further detail on the murder weapon or weapons at this time but if anyone comes across any suspicious items which they think could be connected to this murder we would ask them to call us."
Det Supt Hawkings said the investigation team were keeping an open mind about the motive for the attack and at this time it did not appear that anything had been stolen from the victim.
"There are some immediate similarities between this murder and that of James Attfield but there are also a large number of differences as well," she said.
"There is no current known motive for this attack and we are keeping an open mind and exploring all possible avenues of investigation.
"We are also conscious that the dress of the victim will have identified her as likely being a Muslim and this is one of the main lines of the investigation but again there is no firm evidence at this time that she was targeted because of her religion."
Police will be carrying out additional reassurance patrols in the Greenstead area while the investigation continues.
One man currently remains in custody and is being questioned by detectives after being arrested in connection with this investigation yesterday evening.
Detective Superintendent Hawkings added: "We are obviously as concerned as the rest of the community about this murder.
"Officers will be carrying out additional patrols and we will be dedicating all of our available resources to trying to find the person or persons responsible.
"Someone in Colchester must have information or suspicions about someone who may be responsible for this horrific crime. We would urge them to get in touch as soon as possible so that we can progress our investigation."
Anyone with any information that could assist the enquiry is asked to contact the Major Investigation Team on 01245 282103, Essex Police on 101 or they can contact Crimestoppers anonymously on 0800 555 111.
