CN111885491A - Wi-Fi fingerprint-based indoor fire-fighting spraying area positioning system - Google Patents

Wi-Fi fingerprint-based indoor fire-fighting spraying area positioning system Download PDF

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CN111885491A
CN111885491A CN202010747659.9A CN202010747659A CN111885491A CN 111885491 A CN111885491 A CN 111885491A CN 202010747659 A CN202010747659 A CN 202010747659A CN 111885491 A CN111885491 A CN 111885491A
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CN111885491B (en
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郝新厂
王宝凤
赵志华
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Zhejiang Ruihua Fire Technology Co ltd
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Huzhou Shiyuan Technology Co ltd
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W4/00Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/02Services making use of location information
    • H04W4/021Services related to particular areas, e.g. point of interest [POI] services, venue services or geofences
    • AHUMAN NECESSITIES
    • A62LIFE-SAVING; FIRE-FIGHTING
    • A62CFIRE-FIGHTING
    • A62C31/00Delivery of fire-extinguishing material
    • A62C31/02Nozzles specially adapted for fire-extinguishing
    • A62C31/05Nozzles specially adapted for fire-extinguishing with two or more outlets
    • AHUMAN NECESSITIES
    • A62LIFE-SAVING; FIRE-FIGHTING
    • A62CFIRE-FIGHTING
    • A62C37/00Control of fire-fighting equipment
    • GPHYSICS
    • G08SIGNALLING
    • G08BSIGNALLING OR CALLING SYSTEMS; ORDER TELEGRAPHS; ALARM SYSTEMS
    • G08B17/00Fire alarms; Alarms responsive to explosion
    • GPHYSICS
    • G08SIGNALLING
    • G08BSIGNALLING OR CALLING SYSTEMS; ORDER TELEGRAPHS; ALARM SYSTEMS
    • G08B25/00Alarm systems in which the location of the alarm condition is signalled to a central station, e.g. fire or police telegraphic systems
    • G08B25/01Alarm systems in which the location of the alarm condition is signalled to a central station, e.g. fire or police telegraphic systems characterised by the transmission medium
    • G08B25/10Alarm systems in which the location of the alarm condition is signalled to a central station, e.g. fire or police telegraphic systems characterised by the transmission medium using wireless transmission systems
    • GPHYSICS
    • G08SIGNALLING
    • G08BSIGNALLING OR CALLING SYSTEMS; ORDER TELEGRAPHS; ALARM SYSTEMS
    • G08B7/00Signalling systems according to more than one of groups G08B3/00 - G08B6/00; Personal calling systems according to more than one of groups G08B3/00 - G08B6/00
    • G08B7/06Signalling systems according to more than one of groups G08B3/00 - G08B6/00; Personal calling systems according to more than one of groups G08B3/00 - G08B6/00 using electric transmission, e.g. involving audible and visible signalling through the use of sound and light sources
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W4/00Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/02Services making use of location information
    • H04W4/023Services making use of location information using mutual or relative location information between multiple location based services [LBS] targets or of distance thresholds
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W4/00Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/30Services specially adapted for particular environments, situations or purposes
    • H04W4/33Services specially adapted for particular environments, situations or purposes for indoor environments, e.g. buildings
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W4/00Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/30Services specially adapted for particular environments, situations or purposes
    • H04W4/35Services specially adapted for particular environments, situations or purposes for the management of goods or merchandise

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Abstract

The invention discloses an indoor fire-fighting spraying area positioning system based on Wi-Fi fingerprints, and aims to solve the problem that the positioning delay of a fire-fighting spraying area in a large or complex indoor environment is large. The invention comprises a field information acquisition device at a spraying area end and a monitoring and positioning device at a server end, wherein a Wi-Fi fingerprint database of indoor spraying area position information and each position information is firstly established, then when a fire disaster occurs, the field information acquisition device is activated to acquire the field Wi-Fi fingerprint information and send the field Wi-Fi fingerprint information to the server end, when the server end receives the field Wi-Fi fingerprint information, the fingerprint information in the fingerprint database nearest to the field fingerprint information is found through a nearest neighbor fingerprint matching algorithm, the alarm position of the fire disaster can be obtained, an alarm prompt is sent to a console, the specific position of the fingerprint information is displayed in real time on a console interface and is sent at the same time, the fire disaster in the spraying area can be positioned quickly and dynamically in real time, the fastest response time is strived for fire fighting, and the fire hazard is reduced.

Description

Wi-Fi fingerprint-based indoor fire-fighting spraying area positioning system
Technical Field
The invention relates to the technical field of indoor positioning, in particular to an indoor fire-fighting spraying area positioning system based on Wi-Fi fingerprints.
Background
In an indoor environment, a Global Positioning System (GPS), a network assisted global positioning system (a-GPS), a Global Navigation Satellite System (GNSS), and the like have been widely used in various aspects of people's daily life, and can basically meet the requirements of most applications. However, in indoor environments, these well-positioned systems are no longer suitable due to problems such as shadowing by buildings, multipath propagation of wireless signals, etc. In recent years, various services based on positions in indoor environments enable indoor position perception to become one of the hotspots of research in the industrial and academic fields, and indoor positioning has more and more extensive application scenes, such as personnel navigation in airports/railway stations/shopping malls, position-based service push, mines, hospitals, security and intrusion detection and prevention and the like.
Currently, there are many indoor positioning technologies relying on different infrastructures, such as positioning technologies based on zigbee, bluetooth, USB, infrared and RFID, etc., and most of these positioning technologies are based on ranging, such as time of arrival (TOA), time difference of arrival (TDOA), etc., which are not only expensive to deploy and complex to calculate, but also not suitable for indoor fire location. In addition, the existing automatic fire alarm system is generally composed of two parts, namely a fire detector and a fire alarm. When a fire disaster occurs, a sound and light alarm signal is usually sent out, and workers on the scene can manually find the position of the fire disaster, so that the efficiency is low, and rescue delay is easily caused.
Disclosure of Invention
The invention provides an indoor fire-fighting spraying area positioning system based on Wi-Fi fingerprints, aiming at solving the problem that the positioning delay of a fire-fighting spraying area in a large or complex indoor environment is large.
In order to achieve the purpose, the invention adopts the following technical scheme:
the utility model provides an indoor fire control sprays regional positioning system based on Wi-Fi fingerprint which characterized in that, this system comprises two parts, including the on-the-spot information acquisition equipment of regional end of spraying and the monitoring positioning equipment of server end, the on-the-spot information acquisition equipment of regional end of spraying includes switch module, on-the-spot collection module and wireless communication module, the monitoring positioning equipment of server end includes fingerprint database and control cabinet, and this system operation includes following step:
(1) establishing a Wi-Fi fingerprint database of the position information and each position information of the indoor spraying area;
(2) when a fire disaster happens, a switch module in information acquisition equipment at a spraying area end site is activated, the information acquisition module acquires Wi-Fi fingerprint information f at the site, namely, the Received Signal Strength (RSS) data of all Wi-Fi Access Points (AP) are acquired, and then the Wi-Fi fingerprint information f is sent to a server end by a wireless communication module; (3) when the server receives the field Wi-Fi fingerprint information, the server calculates the received field fingerprint information F and all fingerprint information F in the fingerprint database through a nearest neighbor fingerprint matching algorithmiHas a Euclidean distance D betweeniAll Euclidean distances DiSorting according to descending order to obtain the fingerprint information in the original database corresponding to the minimum Euclidean distance, namely finding the fingerprint information F in the fingerprint database nearest to the field fingerprint information FiThe alarm position of the fire can be obtained, an alarm prompt is sent to the console, and the specific position of the fire alarm is displayed in real time on the interface of the console and is sent at the same time.
Because the position of the fire detector or the spray head is fixed in the indoor fire-fighting spray area, which is different from the common indoor positioning, the mobile equipment and the user position point thereof can move, the key point of the indoor fire-fighting positioning is quick, accurate and high efficiency, the system takes the position of the fire detector or the spray head as the reference point when constructing the fingerprint database, and the field acquisition equipment is arranged at the reference point position when activating the acquisition stage on the field, thus, the basic positioning algorithm can meet the requirement of the system for fire-fighting positioning, the fingerprint information with the nearest Euclidean distance to the fingerprint information f sent from the field can be found in the fastest time, namely, the position where the fire alarm occurs can be quickly found, the obtained position does not need to be weighted or probability algorithm subsequently, the fire alarm position is a certain point in the reference point established in the constructed fingerprint database, and the specific position accuracy is higher, a large amount of time cost is saved for the development of fire rescue work, the fastest reaction time is strived for fire protection, and the fire hazard is reduced.
Further, the step (1) of constructing a Wi-Fi fingerprint database of the indoor spraying area position information and each position information comprises the following steps:
(11) setting a plurality of said Reference Points (RP) in said indoor spray zone;
(12) detecting, at each of said Reference Points (RP), all Received Signal Strength (RSS) data from all of said Wi-Fi Access Points (APs);
(13) information related to Received Signal Strength (RSS) data for all of the Wi-Fi Access Points (APs) for each of the reference points, constituting a location fingerprint for the reference point;
(14) associating the location fingerprint of each of the reference points with the location coordinates (x) of the reference pointi,yi) And recording the data to the Wi-Fi fingerprint database.
Further, step (11) of setting a plurality of said reference points within said chamber comprises the steps of:
(111) a fire detector or a spray head is arranged at the position of each spraying area in the room;
(112) and the positions of the fire detectors or the spray heads of all the spraying areas are used as the reference points.
The positioning speed of indoor fire fighting is the first factor, the position of a fire detector or a spray head is used as a reference point, the later-stage nearest neighbor fingerprint matching algorithm positioning is facilitated, the algorithm time is saved, and the fastest reaction time is strived for fire rescue work.
Further, the field information acquisition device in the step (2) is installed at an indoor fire detector or a spray head, namely the field information acquisition device is located at the reference point, the field information acquisition device is installed at the fire detector (a smoke detector, a flame detector and the like) or the spray head, when the detector gives an alarm or the spray head starts spraying water, a switch module in the field information acquisition device is activated, the information acquisition module acquires field Wi-Fi fingerprints, and the wireless communication module sends the field Wi-Fi fingerprints acquired by the current detector to the server end in real time.
Further, when the server receives Wi-Fi fingerprint information from the scene in the step (3), the received fingerprint information F is defined with each fingerprint information F in the fingerprint database before the nearest neighbor fingerprint matching algorithmiThe RSS difference from the kth access point AP in between is:
dik=|rk-rik|;
the received fingerprint information F is compared with each fingerprint information F in the fingerprint databaseiThe RSS disparity vectors from all access points AP in between are:
(di1,di2,...,dim)。
further, obtaining fingerprint information F in the original database corresponding to the minimum Euclidean distance through a nearest neighbor fingerprint matching algorithmiThe method comprises the following steps:
(31) calculating the received fingerprint information F and the fingerprint information F in the fingerprint databaseiRSS difference vector between: (d)i1,di2,...,dim);
(32) And (3) selecting abnormal access points by using the 3 standard deviation intervals of the normal distribution mean as normal ranges, wherein if the t-th access point is abnormal, the RSS difference of the access point is as follows: dit=0;
(33) Calculating the received fingerprint information F and the fingerprint information F in the fingerprint databaseiThe Euclidean distance between them is:
Figure BDA0002608920760000031
(34) in the same way, the fingerprint information F is calculated and all the fingerprint information F in the fingerprint databasei(1. ltoreq. i. ltoreq.n) by the Euclidean distance Di(1≤i≤n);
(35) Sorting all Euclidean distances in a descending order, and taking the distance at the minimum value position in all Euclidean distances as a fire occurrence alarm position, namely:
Figure BDA0002608920760000032
wherein, l is argmin1≤i≤nDi
When a fire disaster occurs, the on-site information acquisition equipment in the spraying area is activated, real-time Wi-Fi fingerprint information is sent to the server side, the specific position of a detector or a spray head for spraying water is obtained at the server side through a nearest neighbor fingerprint matching algorithm according to the fingerprint information received on site, and the specific position of the fire disaster alarm can be accurately and quickly obtained by the algorithm and displayed on a console interface because the position of a plurality of reference points in the fingerprint database is one of the installation positions of the on-site acquisition equipment.
In the whole fire process, the fire spread range can relate to a plurality of indoor areas, so that in a control console, the specific position of a fire source can be quickly positioned according to the position of a detector, the fire spreading condition can be known through the alarm time of a position detector adjacent to the detector, or the fire spreading condition can be known in real time by seeing the opening time of a spray head in the control console, and therefore the fire spreading condition can be known in real time. When people and materials are evacuated and rescued, the optimal evacuation and rescue route can be given according to the position without an alarm detector or a water spray nozzle, the system can realize real-time, rapid and dynamic positioning when a fire disaster occurs in a spraying area, strives for the fastest reaction time for fire control, reduces the fire hazard,
drawings
FIG. 1 is a system framework diagram of the present invention.
Fig. 2 is a schematic diagram of the system architecture of the present invention.
Detailed Description
The invention is further described with reference to the following figures and detailed description.
As shown in fig. 1, an indoor fire-fighting spraying area positioning system based on Wi-Fi fingerprint is composed of two parts, namely an information acquisition device at a spraying area end and a monitoring positioning device at a server end, wherein the information acquisition device at the spraying area end comprises a switch module, an on-site acquisition module and a wireless communication module, the monitoring positioning device at the server end comprises a fingerprint database and a console, and the system comprises the following three stages: sampling and constructing a fingerprint database, exciting a field acquisition device to transmit a field acquisition fingerprint, and positioning and calculating.
As shown in fig. 2, in the stage of sampling and constructing the fingerprint database, namely in the stage of constructing the Wi-Fi fingerprint database of the indoor spraying area position information and each position information, arranging a plurality of Reference Points (RP) in the indoor spraying area, installing fire detectors or spray heads at the positions of the reference points in the indoor spraying areas, the positions of the fire detectors or the spray heads of all the spraying areas are used as the reference point positions, detecting, at each of said Reference Points (RP), all Received Signal Strength (RSS) data coming from all said Wi-Fi Access Points (AP), information related to the Received Signal Strength (RSS) data of all said Wi-Fi Access Points (AP) of each said reference point, constituting a location fingerprint of said reference point, associating the location fingerprint of each said reference point with the location coordinates (x) of said reference point.i,yi) And recording the data to the Wi-Fi fingerprint database.
Assuming that there are m access points, n reference points and the reference point location information is known in the indoor environment, the fingerprint database is:
F=(F1,F2,...,Fi,...,Fn)T(1)
Fi=(xi,yi,ri1,ri2,...,rim)(i=1,2,...,n) (2)
in the formula (1), F isAn n × m matrix, in formula (2), FiRepresents the fingerprint of the ith reference point, and 1 ≦ i ≦ n, where (x) is in formula (2)i,yi) Coordinates representing the ith reference point, rik(1. ltoreq. K. ltoreq.m) represents the RSS value of the kth access point at the ith reference point.
As shown in fig. 2, in the stage of activating the field collecting device to send the field collected fingerprint, the field information collecting device is installed at the position of the indoor fire detector or the indoor spray head, namely, the position of the field information acquisition equipment is the reference point position, when a fire disaster happens, a switch module in the information acquisition equipment of the spraying area field is activated, the field information acquisition equipment is arranged at the position of an indoor fire detector or a spray head and is arranged at the position of a fire detector (a smoke detector, a flame detector and the like) or the spray head, when the detector gives an alarm or the spray head starts to spray water, a switch module in the on-site information acquisition equipment is activated, the information acquisition module acquires on-site Wi-Fi fingerprints, the wireless communication module sends the collected field Wi-Fi fingerprint of the current detector to the server end in real time, and the collected field Wi-Fi fingerprint information is as follows:
f=(r1,r2,...,rm) (3)
in the formula (3), rk(1 ≦ k ≦ m) represents the RSS value for the kth access point at the active device.
As shown in fig. 2, in the positioning calculation stage, when the server receives the live Wi-Fi fingerprint information, the received fingerprint information F and each fingerprint information F in the fingerprint database are defined firstiThe RSS difference from the kth access point AP in between is:
dik=|rk-rik| (4)
then, the received fingerprint information F is compared with each fingerprint information F in the fingerprint databaseiThe RSS disparity vectors from all access points AP in between are:
(di1,di2,...,dim) (5)
the specific nearest neighbor fingerprint matching algorithm comprises the following steps:
calculating the received fingerprint information f and fingerprint databaseFingerprint information F iniRSS difference vector between:
(di1,di2,...,dim) (6)
selecting abnormal access points by using 3 standard deviation intervals of the normal distribution mean as normal ranges, wherein if the t-th access point is abnormal, the RSS difference of the access point is as follows:
dit=0 (7)
considering that some APs are abnormal due to some environmental or equipment factors, the influence of the abnormal APs needs to be eliminated during calculation, experiments show that RSS difference vectors from all the APs meet normal distribution, and abnormal access points can be selected by taking 3 standard deviation intervals of the mean value of the normal distribution as the normal range.
Calculating the received fingerprint information F and the fingerprint information F in the fingerprint databaseiThe Euclidean distance between them is:
Figure BDA0002608920760000061
in the same way, the fingerprint information F is calculated and all the fingerprint information F in the fingerprint databasei(1. ltoreq. i. ltoreq.n) by the Euclidean distance Di(1≤i≤n);
Sorting all Euclidean distances in a descending order, and taking the distance at the minimum value position in all Euclidean distances as a fire occurrence alarm position, namely:
Figure BDA0002608920760000062
wherein, l is argmin1≤i≤nDi(10)
Through the algorithm process, the fingerprint information F in the fingerprint database nearest to the field fingerprint information F is foundi(1. ltoreq. i. ltoreq. n), i.e. (x)l,yl) Is the alarm position of fire.
At the server side, the specific position of the detector or the spray head for spraying water is obtained through a nearest neighbor fingerprint matching algorithm according to the fingerprint information received on site, and the specific position of the fire alarm can be accurately and quickly obtained through the algorithm and displayed on a console interface because the position of a plurality of reference points in a fingerprint database is one of the installation positions of the on-site acquisition equipment.
In the whole fire process, the fire spread range can relate to a plurality of indoor areas, so that in a control console, the specific position of a fire source can be quickly positioned according to the position of a detector, the fire spreading condition can be known through the alarm time of a position detector adjacent to the detector, or the fire spreading condition can be known in real time by seeing the opening time of a spray head in the control console, and therefore the fire spreading condition can be known in real time. When people and materials are evacuated and rescued, the optimal evacuation and rescue route can be given according to the position without an alarm detector or a water spray nozzle, the system can realize real-time, rapid and dynamic positioning when a fire disaster occurs in a spraying area, strives for the fastest reaction time for fire control, reduces the fire hazard,
because the indoor fire-fighting spray area is provided with the fire detector or the spray head is fixed, the indoor fire-fighting spray area is different from general indoor positioning, the mobile equipment and the user position point thereof can move, and the key point of the indoor fire-fighting positioning is rapidness, accuracy and high efficiency. The system takes the position of a fire detector or a spray head as a reference point when a fingerprint database is established, and field acquisition equipment is installed at the position of the reference point when an acquisition stage is activated on site, so that the basic positioning algorithm can meet the requirement of fire protection positioning of the system, the fingerprint information with the nearest Euclidean distance to the fingerprint information f sent from the field can be found in the fastest time, namely, the position where fire alarm occurs is quickly found, the obtained position does not need to be weighted or subjected to probability algorithm subsequently, and the fire alarm position is a certain point in the established reference point in the established fingerprint database, so that the specific position accuracy is higher, a large amount of time cost is saved for the development of fire rescue work, the fastest reaction time is strived for fire protection, and the fire hazard is reduced. In summary, the system can realize real-time, rapid and dynamic positioning when a fire disaster occurs in a spraying area, strive for the fastest reaction time for fire fighting, and reduce the fire hazard.

Claims (6)

1. The utility model provides an indoor fire control sprays regional positioning system based on Wi-Fi fingerprint which characterized in that, this system comprises two parts, including the on-the-spot information acquisition equipment of regional end of spraying and the monitoring positioning equipment of server end, the on-the-spot information acquisition equipment of regional end of spraying includes switch module, on-the-spot collection module and wireless communication module, the monitoring positioning equipment of server end includes fingerprint database and control cabinet, and this system operation includes following step:
(1) establishing a Wi-Fi fingerprint database of the position information and each position information of the indoor spraying area;
(2) when a fire disaster happens, a switch module in information acquisition equipment at a spraying area end site is activated, the information acquisition module acquires Wi-Fi fingerprint information f at the site, namely, the Received Signal Strength (RSS) data of all Wi-Fi Access Points (AP) are acquired, and then the Wi-Fi fingerprint information f is sent to a server end by a wireless communication module;
(3) when the server receives the field Wi-Fi fingerprint information, the server calculates the received field fingerprint information F and all fingerprint information F in the fingerprint database through a nearest neighbor fingerprint matching algorithmiHas a Euclidean distance D betweeniAll Euclidean distances DiSorting according to descending order to obtain the fingerprint information in the original database corresponding to the minimum Euclidean distance, namely finding the fingerprint information F in the fingerprint database nearest to the field fingerprint information FiThe alarm position of the fire can be obtained, an alarm prompt is sent to the console, and the specific position of the fire alarm is displayed in real time on the interface of the console and is sent at the same time.
2. The Wi-Fi fingerprint based indoor fire sprinkler zone positioning system of claim 1, wherein the step (1) of building a Wi-Fi fingerprint database of indoor sprinkler zone location information and each location information comprises the steps of:
(11) setting a plurality of said Reference Points (RP) in said indoor spray zone;
(12) detecting, at each of said Reference Points (RP), all Received Signal Strength (RSS) data from all of said Wi-Fi Access Points (APs);
(13) information related to Received Signal Strength (RSS) data for all of the Wi-Fi Access Points (APs) for each of the reference points, constituting a location fingerprint for the reference point;
(14) associating the location fingerprint of each of the reference points with the location coordinates (x) of the reference pointi,yi) And recording the data to the Wi-Fi fingerprint database.
3. A Wi-Fi fingerprint based indoor fire sprinkler zone location system according to claim 2, wherein step (11) sets the plurality of reference points at the indoor sprinkler zone, comprising the steps of:
(111) a fire detector or a spray head is arranged at the position of each spraying area in the room;
(112) and the positions of the fire detectors or the spray heads of all the spraying areas are used as the reference points.
4. The Wi-Fi fingerprint based indoor fire sprinkler zone location system of claim 1 or 3, wherein the field information collection device in step (2) is installed at an indoor fire detector or sprinkler location, i.e., the field information collection device location is the reference point location.
5. The Wi-Fi fingerprint-based indoor fire sprinkler zone location system of claim 1, wherein prior to step (3), the received fingerprint information F is defined with each fingerprint information F in the fingerprint databaseiThe RSS difference from the kth access point AP in between is: dik=|rk-rikIf yes, the received fingerprint information F and each fingerprint information F in the fingerprint databaseiThe RSS disparity vectors from all access points AP in between are: (d)i1,di2,...,dim)。
6. A Wi-Fi fingerprint based indoor fire sprinkler zone location system of claim 5, wherein the nearest neighbor fingerprint matching algorithm in step (3) comprises the steps of:
(31) calculating the received fingerprint information F and the fingerprint information F in the fingerprint databaseiRSS difference vector between: (d)i1,di2,...,dim);
(32) And (3) selecting abnormal access points by using the 3 standard deviation intervals of the normal distribution mean as normal ranges, wherein if the t-th access point is abnormal, the RSS difference of the access point is as follows: dit=0;
(33) Calculating the received fingerprint information F and the fingerprint information F in the fingerprint databaseiThe Euclidean distance between them is:
Figure FDA0002608920750000021
(34) in the same way, the fingerprint information F is calculated and all the fingerprint information F in the fingerprint databasei(1. ltoreq. i. ltoreq.n) by the Euclidean distance Di(1≤i≤n);
(35) Sorting all Euclidean distances in a descending order, and taking the distance at the minimum value as the fire occurrence alarm position, namely:
Figure FDA0002608920750000022
wherein, l is argmin1≤i≤nDi
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