CN112566055B - Indoor positioning algorithm based on radio frequency fingerprint matching - Google Patents

Indoor positioning algorithm based on radio frequency fingerprint matching Download PDF

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CN112566055B
CN112566055B CN202011355524.4A CN202011355524A CN112566055B CN 112566055 B CN112566055 B CN 112566055B CN 202011355524 A CN202011355524 A CN 202011355524A CN 112566055 B CN112566055 B CN 112566055B
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鹿建银
胡敦
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Chaohu University
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • H04W4/30—Services specially adapted for particular environments, situations or purposes
    • H04W4/33—Services specially adapted for particular environments, situations or purposes for indoor environments, e.g. buildings
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
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Abstract

The invention relates to an indoor positioning algorithm based on radio frequency fingerprint matching, which is used for sensing an access point by deploying a small number of radio signal strength positioning areas, building a reference node, performing mobile positioning and RSSI mapping relation by utilizing linear regression and solving the problem of characteristic radio frequency fingerprints. And acquiring the position of space off-line training through the radio frequency fingerprint to establish a fingerprint model. Simulation results show that the accumulated positioning error is reduced, the positioning precision is improved by 1 to 2 meters, and the positioning precision reaches 100 percent in 2.5 meters.

Description

Indoor positioning algorithm based on radio frequency fingerprint matching
Technical Field
The invention relates to an indoor positioning algorithm of a wireless sensor network, in particular to an indoor positioning algorithm based on radio frequency fingerprint matching.
Background
At present, the indoor positioning technology has been deeply applied in many fields, such as intelligent care for the aged, intelligent medical treatment, intelligent navigation, intelligent industrial manufacturing, warehouse logistics, etc., and the improvement of service level and management efficiency is obvious. In the aspect of intelligent navigation based on the navigation technology, the intelligent navigation system can be used for navigation to guide a user to reach a destination, can realize interaction between a service party and a terminal consumer, can realize independent navigation, or can realize more accurate marketing management. In the medical field, hospitals provide electronic medical guidance services and the like to patients using indoor navigation. In the aspect of personnel and article real-time location, can realize the accurate location to personnel, goods and materials, equipment, provide the support for other services. For the aspect of personnel management, the real-time position of the positioned object can be provided, post management and scheduling management are optimized, help is provided for simplifying the work flow, and support is provided for improving the efficiency. For the aspect of equipment management, the method can realize active response when the equipment is required to be called, quickly lock the real-time position of the equipment and shorten the time consumed in the process of searching the equipment. Meanwhile, the data statistics function can be realized, such as inventory clearing, access management and the like, and support is provided for intelligent asset management. In the aspect of movement track query, the historical track of a positioned target in a certain period of time can be checked at any time, and event tracing can be realized by querying the historical track. In the aspect of the electronic fence, by arranging the electronic fence in a certain area, when positioned personnel or goods and materials enter or leave the area without authorization, the system immediately warns, so that accidents of the personnel are prevented, or goods and materials are guaranteed, the area is safe, and the like. In the aspect of one-key alarm seeking, a one-key alarm function can be integrated on the intelligent positioning terminal, when a person is in danger or meets an accident, a manager can be informed to rescue by pressing the one-key alarm button, the position of the alarm person is locked, and quick rescue is realized. In the aspect of data statistics and analysis, comprehensive data statistics can be realized, the information such as the number of regional real-time personnel and equipment, heat distribution, access time and the like can be checked, and omission in personnel management is avoided.
At present, many scientific research institutions exist at home and abroad, and a plurality of scholars perform indoor positioning technology. The position fingerprint matching is realized by utilizing the Gaussian kernel function, the error is reduced by adopting the Kalman filtering algorithm, the positioning precision of the moving target within 3m is 100 percent, and the single positioning time is within 1 s. A location fingerprint positioning method based on a support vector machine is provided. In the off-line stage, the strength of the position signal received by each region is used as a training sample set of a Support Vector Machine (SVM) to obtain an optimal classification model. And in the online stage, the information monitored in real time is used as a test set, and is predicted by means of a support vector machine classification model, so that the region to which the information belongs is judged, and a better positioning effect is obtained. The WiFi positioning result under the mobile scene is preliminarily corrected by utilizing the personal trace, and the corrected result is evaluated by defining the confidence space with self-adaptive size, so that the unreliable WiFi positioning estimation is eliminated before data fusion, and the accuracy and the robustness of the positioning system are improved. From the perspective of improving the reliability of the signal strength, the scheme of integrating comprehensive analysis theory and practice is used for carrying out deep analysis on the signal strength characteristic of the ZigBee technology. In order to improve the successful matching efficiency of the position fingerprints, the fingerprint database is required to be correspondingly processed, namely, the fingerprint database is subjected to clustering division, and the positioning function of a target area is realized. And the Kalman filtering with better real-time property is selected to realize the positioning and tracking of the moving target. And optimizing the selection of an initial clustering center according to the standard deviation of the received signal strength, then clustering the fingerprint data, and finally carrying out online positioning. Not only shortens the positioning time, but also can effectively improve the positioning precision. Aiming at an indoor position fingerprint positioning algorithm, a fingerprint database is established in an off-line mode and on-line positioning is carried out in an actual scene, and a double filtering processing scheme is introduced to solve the problem that collected signals are interfered by environmental factors in two stages. Aiming at the problems that fingerprint matching efficiency is low and universality exists, an improved algorithm is provided on the basis of a neighbor method, and hierarchical optimization is provided on the basis of a weighted K neighbor method. The improved algorithm can effectively improve the matching efficiency of the position fingerprint database, and meanwhile, the indoor positioning precision is also improved. And partitioning the indoor space to be monitored, measuring each node to obtain the wireless signal intensity of each node, and storing the wireless signal intensity into the created radio frequency fingerprint database. And calculating the distance between the beacon node and the unknown node, wherein the smaller the distance between the beacon node and the unknown node is, the larger the function of the beacon node and the unknown node on the positioning of the beacon node is, and providing a clustering algorithm (improved equivalent parameter algorithm) to obtain a better positioning effect.
The scheme disclosed by the above is a research on indoor positioning technology, and a good positioning effect is obtained.
The existing radio frequency fingerprint matching indoor positioning algorithm (mainly NN, KNN4, Bayes) generally has the following problems:
(1) in the radio frequency positioning algorithm, radio frequency signal instability caused by time mobility exists, and positioning performance is affected.
(2) The positioning accuracy is not high.
Disclosure of Invention
Based on the technology mentioned in the background technology and the problem mentioned in the background technology, the invention aims to provide an indoor positioning algorithm based on radio frequency fingerprint matching, which is used for sensing an access point, building a reference node, performing mobile positioning, obtaining an RSSI mapping relation and processing a characteristic radio frequency fingerprint by a method of deploying a small number of radio signal strength positioning areas and utilizing linear regression. And acquiring the position of space off-line training through the radio frequency fingerprint to establish a fingerprint model. Simulation results show that the accumulated positioning error is reduced, the positioning precision is improved by 1 to 2 meters, and the positioning precision reaches 100 percent in 2.5 meters.
In order to achieve the above purpose, the invention adopts the technical scheme that: an indoor positioning algorithm based on radio frequency fingerprint matching comprises the following steps:
1) modeling a positioning algorithm model:
firstly, collecting RF radio frequency signal intensity, constructing a signal intensity vector and a fingerprint database, wherein the average value of the received signal intensity of each position is shown as the formula (1):
Figure GDA0003510655540000031
wherein, FIIndicating the signal strength of the ith fingerprint,
Figure GDA0003510655540000032
representing the signal strength of the N fingerprints,
Figure GDA0003510655540000033
representing the average value of the RSS of the Nth AP measured on the ith reference point;
the fingerprint database composed of the positions is shown as formula (2):
{f1,f2,L,fi} {l1,l2,L,li} (2)
wherein, { f1,f2,L,fiDenotes the signal strength of each fingerprint, { l1,l2,L,liDenotes the set of actual positions of the 1, 2.. i node fingerprints;
the position sample S of the node to be measured is shown in formula (3):
S＝{s1,s2,L,sN}T (3)
wherein, { s }1,s2,L,sNMeans actual measurementA sample fingerprint;
applying the probability type positioning hope method to model data;
that is, the signal strengths of the signal access points AP are independent, and the signal strength value of the jth AP received in the f-th observation of the mobile terminal is shown in formula (4):
Figure GDA0003510655540000034
in the formula (4), liRepresenting the actual position of the fingerprint of the ith node, Oj(t) indicates that the measured node received an RSS value from the j AP, μ is the mean and σ is the standard deviation;
estimating probability of possibility by using a kernel density-based estimation function, as shown in equation (5):
Figure GDA0003510655540000035
in the above formula (5), w represents the kernel width, describing the most critical part data of kernel density estimation; x represents the received signal strength of the jth AP transmission, y represents the mean value of x, and σ represents the standard deviation of x; as shown in equation (6), the kernel density estimation model based on the likelihood function:
Figure GDA0003510655540000036
in the above equation (6), the size j of the training sample is from 1 to p, K is a function of kernel density estimation, o (t) represents the RSS value r from the jth AP received by the real measuring pointj；
Calculated at the known signal vector m (< wf)1,RSSI1＞＜wf2,RSSI2＞L＜wfN,RSSIN>) to find the position at P, the model formula is as follows:
max(P(p|m)) (7)
in the above formula (7), p represents a certain position, and m represents a signal vector;
after a signal vector value of a P position is obtained, the probability of P (m | P) is obtained;
Figure GDA0003510655540000041
assuming that each WiFi signal is independent, the above equation is simplified to obtain:
Figure GDA0003510655540000042
in the above formula (11), wfiRepresents a Mac address, and the value of the Mac address is from 0 to N; p represents a specific location within the grid; m represents the semaphore corresponding to the p position; solving for P (wf)i＝RSSIiP), i.e. the position in the grid where p is solved for, the Mac address is wfiAnd the signal strength is RSSIiThe probability of occurrence;
calculating the signal space generalized distance is shown as formula (13):
Figure GDA0003510655540000043
in the above formula (13), LPRepresenting the similarity between the online real measurement sample and the offline proof in the fingerprint database; n represents the number of APs; rhoijIndicating that the ith sampling point of the fingerprint database receives the RSS value of the jth AP node; when p is 1, RSS is manhattan distance, and when p is 2, RSS is euclidean distance; selecting the database vector with the minimum mapping distance from the calculation results, and taking the corresponding position coordinate as a result;
2) and positioning the radio frequency fingerprint.
Further, in step 1), the probabilistic positioning method includes modeling the position data and the radio frequency signal strength data at the position.
Further, in step 1), max (P | m)) is obtained, and the max is obtained by bayesian conversion, as shown in equation (8):
Figure GDA0003510655540000051
in the above formula (8), p represents a certain position, and m represents a signal vector; the denominator p (m) represents the probability of occurrence of the signal vector m, and is a constant, neglected, so the above equation is converted into:
Figure GDA0003510655540000052
in the formula (9), P (P) represents the probability of occurrence of the P position, P (m | P) represents the probability of occurrence of the signal vector m at the P position, and the probability of occurrence of the P position is equalized, and the following formula is obtained by simplifying the formula:
max(P(p|m))＝max(P(m|p)) (10)
in the above formula (10), max (P (m | P) represents that P positions are found on the geographic space, exhaustion is performed, the probability of the signal vector m appearing at each point on the space is calculated, and the point with the maximum probability is found;
after the signal vector value of the P position is obtained, the probability of P (m | P) is obtained.
Further, in step 1), selecting a database vector of the mapping with the minimum distance in the calculation result, and when the probabilities of encountering two grids are almost similar, assisting in selection by a weighted interpolation method:
Figure GDA0003510655540000053
in the above-mentioned formula (14),
Figure GDA0003510655540000054
denotes weighted interpolation, wi denotes weight, p denotes position, and m denotes a signal vector corresponding to the position of p.
Further, in step 2), a radio frequency fingerprint database is created before the radio frequency fingerprint is positioned.
Furthermore, in the off-line stage, firstly, a plurality of fingerprint data, namely wireless signals, are collected indoors, the wireless signals are collected by defining a plurality of grid points to collect the wireless signal intensity, and a unique fingerprint is corresponding to one position and is stored in a fingerprint database; when positioning is carried out, wireless signals which are collected in advance by the mobile terminal and stored in the fingerprint database are compared, and the found fingerprint position with the highest similarity is used as the estimated position of the node to be solved.
The invention has the technical effects that: the method comprises the steps of deploying a small number of radio signal strength positioning areas, sensing access points, utilizing linear regression, building reference nodes, performing mobile positioning, obtaining RSSI mapping relation, and processing the problem of characteristic radio frequency fingerprints. And acquiring the position of space off-line training through the radio frequency fingerprint to establish a fingerprint model. Simulation results show that the accumulated positioning error is reduced, the positioning precision is improved by 1 to 2 meters, and the positioning precision reaches 100 percent in 2.5 meters.
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FIG. 1 is a diagram of the correspondence between locations and fingerprints according to the present invention;
FIG. 2 is a schematic diagram of a wireless RF fingerprint location in accordance with the present invention;
FIG. 3(a) is a flowchart of fingerprint acquisition according to the present invention;
FIG. 3(b) is a flow chart of fingerprint matching according to the present invention;
FIG. 4 is a flow diagram of an online location module in accordance with the present invention;
fig. 5 is a comparison graph of positioning performance for different numbers of APs applied in the embodiment of the present invention;
FIG. 6 is a comparison graph of the localization performance of different ROI ranges applied in the embodiment of the present invention;
FIG. 7 is a graph of cumulative probability of error for different fingerprint location algorithms applied in an embodiment of the present invention;
FIG. 8 is a comparison graph of accumulated positioning errors for different positioning algorithms involved in embodiments of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The indoor positioning algorithm based on radio frequency fingerprint matching has the beneficial effects that:
(1) the accumulated error in the positioning process is reduced, the positioning precision is improved by 1 to 2 meters, and the positioning precision reaches 100 percent in 2.5 meters.
(2) In the off-line stage, the position of the mobile terminal is predicted by deploying a small number of radio signal strength positioning areas and adopting a positioning area selection mechanism, so that the radio frequency signal instability caused by the time mobility is avoided, and the influence of the Access Point (AP) facility change on the positioning performance is avoided.
(3) The radio frequency positioning algorithm provided by the application is superior to NN, KNN4 and Bayes algorithms in positioning accuracy, the accumulated errors of NN, KNN4 and Bayes experiments are 2.0813 meters, 1.3958 meters and 1.9554 meters respectively, and the accumulated error of the application is only 0.835029 meters.
An indoor positioning algorithm based on radio frequency fingerprint matching comprises the following steps:
1) modeling a positioning algorithm model:
firstly, collecting RF radio frequency signal intensity, constructing a signal intensity vector and a fingerprint database, wherein the average value of the received signal intensity of each position is shown as a formula (1):
Figure GDA0003510655540000071
wherein, FIIndicating the signal strength of the ith fingerprint,
Figure GDA0003510655540000072
representing the signal strength of the N fingerprints,
Figure GDA0003510655540000073
representing the average value of the RSS of the Nth AP measured on the ith reference point;
the fingerprint database composed of the positions is shown as formula (2):
{f1,f2,L,fi} {l1,l2,L,li} (2)
wherein, { f1,f2,L,fiDenotes the signal strength of each fingerprint, { l1,l2,L,liDenotes the set of actual positions of the 1 st, 2.. i node fingerprints;
the position sample S of the node to be measured is shown in formula (3):
S＝{s1,s2,L,sN}T (3)
wherein, { s }1,s2,L,sNRepresents the measured sample fingerprint;
the present invention will be applied to probabilistic positioning hopes (methods);
probabilistic positioning is intended to model data, including location data and radio frequency signal strength data at a location, using a statistical or machine learning method to account for its uncertainty due to interference from complex environmental factors. The research of the wireless positioning technology is mainly focused on a probabilistic positioning algorithm.
Specifically, the method comprises the following steps:
the signal strength between the signal access points AP is independent, and the signal strength value of the jth AP received in the f-th observation value of the mobile terminal is shown in formula (4):
Figure GDA0003510655540000074
in the formula (4), liRepresenting the actual position of the fingerprint of the ith node, Oj(t) indicates that the measured node received an RSS value from the j AP, μ is the mean and σ is the standard deviation;
the probability is estimated by using a kernel density estimation function, wherein the kernel density estimation function has no parameter estimation and no hypothesis exists, but the feature of the data distribution is researched by developing the mode based on the data sample, and the feature is also one of Gaussian kernel density functions, as shown in formula (5):
Figure GDA0003510655540000081
in the above formula (5), w represents the kernel width, which describes the most critical part data of kernel density estimation, but in the gaussian kernel method, the kernel width is generally expressed by standard deviation;
x represents the received signal strength of the jth AP transmission, y represents the mean of x, and σ represents the standard deviation of x. As shown in equation (6), the kernel density estimation model based on the likelihood function:
Figure GDA0003510655540000082
in the above equation (6), the size j of the training sample is from 1 to p, K is a function of kernel density estimation, o (t) represents the RSS value r from the jth AP received by the real measuring pointj(ii) a In order to improve the positioning accuracy, the maximum likelihood estimation and a K-Nearest Neighbor (KNN) clustering algorithm are combined, the position of K is selected according to the maximum likelihood probability, then the estimated position is calculated, and the positioning error can be reduced;
calculated at the known signal vector m (< wf)1,RSSI1＞＜wf2,RSSI2＞L＜wfN,RSSIN>) to find the position at P and maximize the probability of this case, the model formula is as follows:
max(P(p|m)) (7)
in the above formula (7), p represents a certain position, and m represents a signal vector.
Preferably, the direct calculation formula (7) has a very high difficulty, and is obtained through bayes transformation, as shown in formula (8):
Figure GDA0003510655540000083
in the above formula (8), p represents a certain position, and m represents a signal vector; the denominator p (m) represents the probability of occurrence of the signal vector m, which is constant and therefore will be ignored, so the above equation is converted into:
Figure GDA0003510655540000084
in the formula (9), P (P) represents the probability of occurrence of the P position, P (m | P) represents the probability of occurrence of the signal vector m at the P position, and the probability of occurrence of the P position is equalized, and the following formula is obtained by simplifying the formula:
max(P(p|m))＝max(P(m|p)) (10)
in the above equation (10), max (P (m | P) represents that P positions are found in the geographic space, the exhaustion is performed, the probability of the signal vector m occurring at each point in the space is calculated, and the point with the maximum probability is found.
After the signal vector value of the P position is obtained, the probability of P (m | P) can be obtained.
Figure GDA0003510655540000091
Assuming that each WiFi signal is independent, the above equation is simplified to obtain:
Figure GDA0003510655540000092
in the above formula (11), wfiRepresents a Mac address, and the value of the Mac address is from 0 to N; p represents a specific location within the grid; m represents the semaphore corresponding to the p position; solving for P (wf)i＝RSSIiP), i.e. the position in the grid at which p is solved, Mac address wfiAnd the signal strength is RSSIiThe occurrence probability is matched based on the probability, so that accidental errors in the positioning process are eliminated to a certain extent, and the positioning accuracy and robustness are improved;
calculating the signal space generalized distance is shown as formula (13):
Figure GDA0003510655540000093
in the above formula (13), LPRepresenting the similarity between the online real measurement sample and the offline proof in the fingerprint database; n represents the number of APs; rhoijIndicating that the ith sampling point of the fingerprint database receives the RSS value of the jth AP node; when p is 1, RSS is manhattan distance, and when p is 2, RSS is euclidean distance; in the calculation result, the database vector of the mapping with the minimum distance is selected, and the position coordinate corresponding to the database vector is used as the result.
Further, when the probabilities of encountering two lattices are almost similar, the selection is assisted by a weighted interpolation method:
Figure GDA0003510655540000094
in the above-mentioned formula (14),
Figure GDA0003510655540000095
representing weighted interpolation, wi representing weight, p representing position, and m representing signal vector corresponding to p position;
that is, mobile terminals such as mobile phones and the like detect the signal strength (RSSI) corresponding to each WiFi (Mac address) around, that is, the signal vector (< wf) is collected1,RSSI1＞＜wf2,RSSI2＞L＜wfN,RSSIN>) value; the server transmits the signal vector to the positioning engine after receiving the user request, the positioning engine transmits information such as the positioning position (x, y), the positioning precision and the like to the server, and finally the server transmits the positioning result information to the user.
2) Radio frequency fingerprint positioning:
the radio frequency fingerprint positioning algorithm comprises a training module and a positioning module, and a radio frequency fingerprint database is also required to be established; in the off-line stage, firstly, a plurality of fingerprint data, namely wireless signals, are collected indoors, the wireless signals are defined to be collected by grid points, one position corresponds to one unique fingerprint, and the fingerprint data is stored in a fingerprint database; when positioning is carried out, wireless signals which are collected in advance by mobile terminals such as mobile phones and stored in a fingerprint database are compared, and the found fingerprint position with the highest similarity is used as the estimated position of the node to be solved; the corresponding relationship between the position and the fingerprint in the off-line stage is shown in fig. 1, a rectangular grid area is covered by two signal access points AP, and 28 grid points coexist in 4 rows and 7 columns in the grid area; in order to reduce the complexity of fingerprint retrieval, a 'joint clustering' method is adopted, namely all grid points of information obtained from the same AP form a Cluster (Cluster), and a Cluster determining method is adopted, namely the probability that the signal intensity of a certain AP can be monitored according to each grid point.
The main task of the online phase is to perform positioning according to the RSSI signal strength received by a Mobile Station (MS), and fig. 2 shows the principle of the fingerprint positioning algorithm in indoor positioning. And taking the average value of the RSSI signal strength in a period of sampling time as a position fingerprint and storing the position fingerprint, and then calling a corresponding algorithm to calculate the position of the node.
3) The positioning algorithm flow comprises the following steps:
the fingerprint acquisition stage of the wireless radio frequency fingerprint positioning algorithm is responsible for data sampling, data acquisition, data management and organization to establish a fingerprint database, and a fingerprint acquisition flow chart is shown in figure 3 (a); in the fingerprint comparison stage, fingerprints are collected in real time and matched with the fingerprints in the fingerprint database, as shown in fig. 3 (b); the online positioning stage is responsible for receiving real-time observation of fingerprints and positioning the node to be detected by using historical position data;
the training process comprises the steps of building a fingerprint database, managing a time migration process and building a positioning equipment model; firstly, establishing a fingerprint database; then, according to the time and the mobile terminal device identification, the fingerprint processing time and the device relocation process migration, the module is optional; according to the characteristics of a fingerprint model after fingerprint training, a positioning module comprises a time offset mode, the mobile terminal equipment comprises a mobile phone migration model and a fingerprint model, and the positioning module also comprises three parts of selection of a target positioning area (ROI), selection of an information Access Point (AP) and calculation of posterior probability.
Referring to fig. 4, a specific flow shown in fig. 4 is provided, when a real-time observation fingerprint positioning engine is operated, an ROI and an information access point AP are selected depending on a mapping relationship between a migration of observation time and a mobile terminal migration model, and this step is mainly to reduce complexity and difficulty of calculation; then starting a Bayesian positioning stage, calculating posterior probability and screening the node estimation position with the maximum probability from the posterior probability; at the moment, based on the experience posterior probability and the threshold value for controlling the posterior probability process, if the result is larger than the threshold value, the returned result is the estimated position of the node, otherwise, the global positioning is realized in the free space, and then the new result obtained by positioning is returned.
In a 100m × 100m area, dividing the area into 50 × 50 grids (2 m × 2m each), collecting a group of fingerprints in the middle of each grid, storing the fingerprints in a database, wherein each fingerprint record describes that the RSSI value from each AP is received at the grid point for 5 to 15 minutes, and the measurement terminal equipment is a mobile phone and a notebook computer, and the direction setting is different.
Specific examples are given below:
the method specifically comprises the following steps:
1) selecting a positioning AP:
setting the number of the APs as 2, 3, 5, 6 and 10 respectively to study the variation trend of the positioning accuracy, and generating a state diagram similar to normal distribution along with the increment of the number; fig. 5 is a comparison graph of positioning performance of different AP numbers. It can be known that, when the positioning accuracy is the highest, the number of the information access points AP is 3 and 5; when the positioning error is 3m, the positioning accuracy can reach about 85 percent. When the number of the information access points AP is set to 10, the positioning accuracy is reduced, which is the worst case of the positioning performance. When the number of the selected information access points AP can meet the requirement of distinguishing the fingerprint characteristics of the positioning area, the positioning precision is in the best state. When the number of the information access points AP is 2, fingerprint characteristics are not easy to distinguish; meanwhile, when the number of the APs reaches 10, signals of some APs are difficult to distinguish, so that the risk of observing noise is increased, the overall performance of the network is reduced, and the positioning effect is also reduced. But when 3 to 5 APs are used, better positioning accuracy is obtained. It can be known that whether the number of APs is proper or not directly affects the accuracy of positioning.
2) And (3) positioning ROI area selection:
and analyzing the positioning area, referring to fig. 6, wherein D is the radius of the positioning ROI, selecting different values of D and the positioning ROI not used, respectively performing experiments and analyzing and comparing the results in the global range, and the experimental results are shown in fig. 6.
As can be seen from fig. 6, the positioning accuracy is highest when D is 2 and D is 3, and particularly the positioning accuracy at 3m has reached about 90%. However, as the positioning region is gradually enlarged, the positioning accuracy is gradually reduced. The main reason is that indoor Wi-Fi signal propagation is interfered by factors such as fading, space-time and multipath structure, the observation fingerprint received by the mobile terminal in real time is not necessarily perfectly matched with the fingerprint of the training fingerprint database, and the probability of success in matching the observation fingerprint with the fingerprints at other positions is increased along with the increase of the positioning range. Particularly, in the global state, the positioning area range is not selected in advance, and the positioning result is not stable because the self-selection of the positioning area range is not performed by using the previous positioning information of the mobile terminal such as a mobile phone. Therefore, the ROI selection and the selection of the positioning radius D based on the historical position improve the positioning accuracy and improve the positioning stability. The positioning area selection mechanism of the embodiment predicts the position of the mobile terminal such as a mobile phone and the like, operates in a positioning stage, and has no direct relation with an information access point AP and a wireless radio frequency fingerprint (an off-line stage) in a positioning scene, so that the influence caused by radio frequency signal instability factors and the change of hardware equipment such as the AP and the like due to the mobility of time is avoided. Meanwhile, when the radius D of the positioning area is respectively 2, 3, 5 and 6, the positioning accuracy is higher when the positioning radius is 2, and particularly the positioning accuracy can reach about 90% when the error distance is 3 m. But as the scale of network coverage increases, the positioning performance also begins to degrade. The simulation result shows that the method not only improves the positioning performance, but also reduces the positioning overhead.
3) Difference comparison of error accumulation:
the fingerprint location algorithm of this example is compared to the cumulative probability distribution of errors for other location algorithms, as shown in FIG. 7. The method is evaluated through an error accumulation distribution function, the error distance is set to be 0-5 m, and under the condition of error probability distribution, the error distance reaches 100% when the error distance is 5 m, namely the accurate positioning precision of the method is 5 m, which is improved relative to the outdoor positioning precision, but the positioning precision is not high for the complex indoor environment. The positioning accuracy of the proposed NEW-FR is obviously higher than that of a KNN positioning algorithm, a Bayes positioning algorithm and a KK positioning algorithm, and the cumulative probability is close to 1 at 2.5 meters, namely the NEW-FR (short for indoor positioning algorithm based on radio frequency fingerprint matching in the application) has 100% probability positioning accuracy within 2.5 meters. While KNN has 90% probability positioning accuracy reaching 4.5 meters. Because KNN does not take into account the time-varying characteristics of the signal, the positioning accuracy is affected, in less than 1 meter, by about 30%. The weighted K nearest neighbor algorithm can reduce errors by adopting a method of averaging a plurality of reference point samples, so that better positioning accuracy is obtained. The Bayes algorithm has higher positioning accuracy than the NN algorithm, and the positioning range is reduced by the calculation of the positioning distribution probability based on the probability distribution of fingerprint matching, so that part of noise interference can be eliminated.
As shown in FIG. 8, the positioning accumulated error statistics of the four positioning algorithms of KNN, Bays, KK and New-FR are shown, the NEW-FR algorithm is superior to other algorithms in positioning accuracy, and the accumulated errors of NN, KNN4, NEW-FR and Bayes experiments are 2.0813 meters, 1.3958 meters, 0.835029 meters and 1.9554 meters respectively.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (6)

1. An indoor positioning algorithm based on radio frequency fingerprint matching is characterized by comprising the following steps:
1) modeling a positioning algorithm model:
firstly, collecting RF radio frequency signal intensity, constructing a signal intensity vector and a fingerprint database, wherein the average value of the received signal intensity of each position is shown as a formula (1):
Figure FDA0003510655530000011
wherein, FIIndicating the signal strength of the ith fingerprint,
Figure FDA0003510655530000012
which represents the strength of the N fingerprint signals,
Figure FDA0003510655530000013
representing the average value of the RSS of the Nth AP measured on the ith reference point;
the fingerprint database composed of the positions is shown as formula (2):
{f1,f2,L,fi} {l1,l2,L,li} (2)
wherein, { f1,f2,L,fiDenotes the signal strength of each fingerprint, { l1,l2,L,liDenotes the set of actual positions of the 1 st, 2.. i node fingerprints;
the position sample S of the node to be measured is shown in formula (3):
S＝{s1,s2,L,sN}T (3)
wherein, { s }1,s2,L,sNRepresents the measured sample fingerprint;
applying the probability type positioning hope method to model data;
that is, the signal strengths of the signal access points AP are independent, and the signal strength value of the jth AP received in the f-th observation of the mobile terminal is shown in formula (4):
Figure FDA0003510655530000014
in the formula (4), liRepresenting the actual position of the fingerprint of the ith node, Oj(t) indicates that the measured node received an RSS value from the j AP, μ is the mean and σ is the standard deviation;
estimating probability of possibility by using a kernel density-based estimation function, as shown in equation (5):
Figure FDA0003510655530000015
in the above formula (5), w represents the kernel width, describing the most critical part data of kernel density estimation; x represents the received signal strength of the jth AP transmission, y represents the average value of x, and sigma represents the standard deviation of x; as shown in equation (6), the kernel density estimation model based on the likelihood function:
Figure FDA0003510655530000021
in the above equation (6), the training sample size j is from 1 to p, K is a function of kernel density estimation, o (t) represents the RSS value r from the jth AP received by the real measuring pointj；
Calculated at the known signal vector m (< wf)1,RSSI1＞＜wf2,RSSI2＞L＜wfN,RSSIN>) to find the position at P, the model formula is as follows:
max(P(p|m)) (7)
in the above formula (7), p represents a certain position, and m represents a signal vector;
after a signal vector value of a P position is obtained, the probability of P (m | P) is obtained;
Figure FDA0003510655530000022
assuming that each WiFi signal is independent, the above equation is simplified to obtain:
Figure FDA0003510655530000023
in the above formula (11), wfiRepresents a Mac address, and the value of the Mac address is from 0 to N; p represents a specific location within the grid; m represents the semaphore corresponding to the p position; solving for P (wf)i＝RSSIiP), i.e. the position in the grid where p is solved for, the Mac address is wfiAnd the signal strength is RSSIiThe probability of occurrence;
calculating the signal space generalized distance is shown as formula (13):
Figure FDA0003510655530000024
in the above formula (13), LPRepresenting the similarity between the online real measurement sample and the offline proof in the fingerprint database; n represents the number of APs; rhoijIndicating that the ith sampling point of the fingerprint database receives the RSS value of the jth AP node; when p is 1, RSS is manhattan distance, and when p is 2, RSS is euclidean distance; in the calculation result, selecting the database vector mapped with the minimum distance, and taking the corresponding position coordinate as a result;
2) and positioning the radio frequency fingerprint.
2. The indoor positioning algorithm based on radio frequency fingerprint matching as claimed in claim 1, wherein: in step 1), the probabilistic positioning expectation method comprises position data and modeling of radio frequency signal strength data at the position.
3. The indoor positioning algorithm based on radio frequency fingerprint matching as claimed in claim 1, wherein: in step 1), max (P | m)) is obtained, and the max is obtained by bayesian conversion, as shown in equation (8):
Figure FDA0003510655530000031
in the above formula (8), p represents a certain position, and m represents a signal vector; the denominator p (m) represents the probability of occurrence of the signal vector m, and is a constant, neglected, so the above equation is converted into:
Figure FDA0003510655530000032
in the formula (9), P (P) represents the probability of occurrence of the P position, P (m | P) represents the probability of occurrence of the signal vector m at the P position, and the probability of occurrence of the P position is equalized, and the following formula is obtained by simplifying the formula:
max(P(p|m))＝max(P(m|p)) (10)
in the above formula (10), max (P (m | P) represents finding P position in the geographic space, performing exhaustive enumeration, calculating the probability of signal vector m appearing at each point in the space, and finding out the point with the maximum probability;
after the signal vector value of the P position is obtained, the probability of P (m | P) is obtained.
4. The indoor positioning algorithm based on radio frequency fingerprint matching as claimed in claim 1, wherein: in the step 1), selecting a database vector with minimum distance mapping in a calculation result, and when the probability of encountering two grids is similar, selecting the database vector with the minimum distance mapping in an auxiliary manner by a weighted interpolation method:
Figure FDA0003510655530000033
in the above-mentioned formula (14),
Figure FDA0003510655530000034
denotes weighted interpolation, wi denotes weight, p denotes position, and m denotes a signal vector corresponding to the position of p.
5. The indoor positioning algorithm based on radio frequency fingerprint matching as claimed in claim 1, wherein: and 2), establishing a radio frequency fingerprint database before positioning the radio frequency fingerprint.
6. The indoor positioning algorithm based on radio frequency fingerprint matching as claimed in claim 5, wherein: in the off-line stage, firstly, a plurality of fingerprint data, namely wireless signals, are collected indoors, the wireless signals are defined to be collected by grid points, one position corresponds to one unique fingerprint, and the fingerprint data is stored in a fingerprint database; when positioning is carried out, wireless signals which are collected in advance by the mobile terminal and stored in the fingerprint database are compared, and the found fingerprint position with the highest similarity is used as the estimated position of the node to be solved.
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