CN113759309A - Indoor mobile target positioning method and device and computer equipment - Google Patents

Indoor mobile target positioning method and device and computer equipment Download PDF

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CN113759309A
CN113759309A CN202111012495.6A CN202111012495A CN113759309A CN 113759309 A CN113759309 A CN 113759309A CN 202111012495 A CN202111012495 A CN 202111012495A CN 113759309 A CN113759309 A CN 113759309A
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曹宁
马利
毛明禾
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Hohai University HHU
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
    • G01S5/0294—Trajectory determination or predictive filtering, e.g. target tracking or Kalman filtering
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
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    • H03H17/00—Networks using digital techniques
    • H03H17/02—Frequency selective networks
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Abstract

The invention discloses a method for positioning an indoor moving target, which comprises the following steps: establishing a state equation and an observation model of the motion of an unknown moving target node; according to a state equation, obtaining a one-step predicted value and a covariance matrix of the system state quantity and an observation Sigma point set through a group of Sigma point sets calculated by UT and corresponding weights thereof; calculating an observation predicted value of observing a Sigma point set according to the observation model to obtain an observation predicted value of the system; and according to a cost function based on the maximum correlation entropy, fusing an observation predicted value of the system, obtaining an observation covariance matrix and an observation cross covariance matrix of a reconstructed observation model, determining a Kalman gain matrix, estimating a system state quantity, and determining the position coordinate of an unknown moving target node. The indoor positioning method based on the MCUKF can better complete indoor positioning under the condition that non-Gaussian noise occurs in measurement noise, the positioning precision is higher than that of the indoor positioning methods of LS, EKF and UKF, and the robustness is also higher than that of the indoor positioning methods of LS, EKF and UKF.

Description

Indoor mobile target positioning method and device and computer equipment
Technical Field
The invention relates to the field of indoor positioning, in particular to an indoor moving target positioning method, device and computer equipment based on maximum correlation entropy unscented Kalman Filter (MCUKF).
Background
In recent years, indoor positioning is increasingly demanded. Due to the application scene of huge indoor positioning scale and high commercial value, the indoor positioning system is widely applied to the fields of medical centers, intelligent homes, shopping centers, positioning and tracking of personnel in mines, tracking of goods and the like. Indoor positioning systems based on RSS have received much attention as soon as they are available, due to the advantage that they do not require specific hardware. As Kalman filtering based on MMSE (minimum mean square error) criterion is an optimal state estimation method, the method is also introduced into indoor positioning and achieves better effect. Besides, some modified algorithms of kalman filtering, such as Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), etc., are also applied to the indoor positioning system. However, in an actual indoor environment, due to a very complex environment, a wireless signal is prone to phenomena such as reflection, diffraction and refraction, and meanwhile, changes of surrounding environments such as temperature, humidity and obstacles and non-line-of-sight and the like can also have certain influences on propagation of the wireless signal, so that the indoor positioning system is often influenced by multimodal heavy-tailed non-gaussian noise due to the factors, the accuracy of the kalman filter based on the MMSE criterion is greatly reduced, and even filtering divergence is caused, so that the indoor positioning system cannot be normally used.
Disclosure of Invention
In view of the foregoing, it is desirable to provide a method, an apparatus and a computer device for positioning an indoor moving target.
The embodiment of the invention provides a method for positioning an indoor moving target, which comprises the following steps: the positioning system is composed of a plurality of wireless access point AP nodes arranged indoors and an unknown moving target node, wherein the number of the wireless access point AP nodes is more than or equal to 3; the positioning method comprises the following steps:
establishing a state equation of the motion of an unknown moving target node;
establishing an observation model of unknown moving target node motion;
according to a state equation, obtaining a one-step predicted value and a covariance matrix of the system state quantity through a group of Sigma point sets calculated by unscented transformation UT and corresponding weights thereof; according to the predicted value of the first step, calculating a new Sigma point set again through unscented transformation UT, substituting the new Sigma point set into the observation model, and obtaining an observation Sigma point set;
calculating an observation predicted value of an observation Sigma point set according to the observation model, and obtaining the observation predicted value of the system through weighted summation;
according to a cost function based on the maximum correlation entropy, fusing an observation predicted value of the system to obtain an observation covariance matrix and an observation cross covariance matrix of a reconstructed observation model; determining a Kalman gain matrix according to the observation covariance matrix and the observation cross covariance matrix;
estimating a system state quantity and a covariance matrix according to the Kalman gain matrix; and determining the position coordinates of the unknown moving target nodes according to the estimated system state quantity and the covariance matrix.
Further, the establishing of the state equation of the unknown moving target node motion includes:
taking the position and the speed of an unknown mobile target node as state quantities
Figure RE-GDA0003339816540000021
Establishing a state equation of the motion of an unknown moving target node; and the motion of the unknown moving target node is described by the change of x (k) at time step k, and the expression is as follows: x (k +1) ═ f (x (k)) + ω (k)
Figure RE-GDA0003339816540000022
Wherein (x, y) is the spatial location coordinates of the unknown node;
Figure RE-GDA0003339816540000023
the speed of the unknown node in the x direction and the y direction respectively; f (x (k)) is the system matrix,
Figure RE-GDA0003339816540000024
w (k) is process noise, and the sampling time interval is set as T ═ 1 s; the abbreviation is: x (k +1) ═ f (x (k)) + w (k).
Further, the establishing an observation model of the unknown moving target node motion includes:
acquiring an RSSI value of an unknown mobile target node received from a known wireless Access Point (AP) node;
and establishing an observation model by taking the RSSI value as an observed quantity.
Further, the establishing an observation model by using the RSSI value as an observed quantity includes:
taking the weighted average of RSSI values of different known wireless access point AP nodes as an observed quantity, and establishing an observation model by adopting a logarithmic distance path loss model; and the expression of the observation model is as follows:
Z(k)＝h(x(k))+v(k)
Figure RE-GDA0003339816540000031
wherein the logarithmic distance path loss model has a general formula: RS (d) ═ RS (d)0)+10λlg(d/d0)+θdB(ii) a Rs (d) is the path loss in dB for a distance d between the transceivers; RS (d)0) Is a short distance d0Reference path loss of time, d0Taking 1 meter; λ is a loss factor; thetadBIs a normal random variable;
Figure RE-GDA0003339816540000032
v (k) is the observation noise,
Figure RE-GDA0003339816540000036
is the coordinate vector, X, of the Lth known wireless access point AP nodekIs the coordinate vector of the unknown moving target node at the kth moment.
Further, the obtaining a set of observed Sigma points comprises:
a set of sampling points, called the Sigma point set, is obtained from the UT transform:
Figure RE-GDA0003339816540000037
Figure RE-GDA0003339816540000038
Figure RE-GDA0003339816540000039
calculating the corresponding weight of the sampling point as follows:
Figure RE-GDA0003339816540000041
Figure RE-GDA0003339816540000042
Figure RE-GDA00033398165400000413
form 2n +1 Sigma point sets according to the system equation:
Figure RE-GDA00033398165400000414
the predicted value and covariance matrix of the system state quantity are:
Figure RE-GDA0003339816540000045
Figure RE-GDA0003339816540000046
from the one-step predicted values, the UT transform is again used to generate a new Sigma point set:
Figure RE-GDA0003339816540000047
Figure RE-GDA00033398165400000415
Figure RE-GDA00033398165400000416
substituting the predicted new Sigma point set into the observation model to obtain a corresponding observed Sigma point set:
Figure RE-GDA00033398165400000417
wherein n is the dimension of the state; x0The sampling point when i is 0; xiIs the ith Sigma sample point;
Figure RE-GDA00033398165400000411
is the sample mean of the Sigma set; p is the variance of the state vector; λ is a scaling parameter;
Figure RE-GDA00033398165400000412
weight values of the covariance and the mean, respectively; alpha is a distribution state parameter of the sampling point; beta is more than or equal to 0 and is a non-negative weight coefficient; xi(k +1 | k) is a one-step predicted value of the Sigma sampling point;
Figure RE-GDA0003339816540000051
and P (k +1 |. k) is a one-step predicted value and covariance matrix of the system state quantity, respectively, and Q (k) is process noise; zi(k +1 | k) is the observed Sigma sample point.
Further, the system's observed predictions are as follows:
Figure RE-GDA0003339816540000052
further, the determining a kalman gain matrix includes:
reconstructing the observation model to obtain the following nonlinear model:
Figure RE-GDA0003339816540000053
wherein the content of the first and second substances,
Figure RE-GDA0003339816540000054
E[r(k)rT(k)]＝R(k)
Figure RE-GDA0003339816540000055
left-multiplying both sides of the reconstructed observation model by S-1(k) Due to S-1(k)＝ST(K) The following equation is obtained:
Figure RE-GDA0003339816540000056
Figure RE-GDA0003339816540000057
wherein the content of the first and second substances,
Figure RE-GDA0003339816540000058
e(k)＝ST(k)φ(k)
then element e of line j in e (k)j(k)，ej(k)＝dj(k)-mj(x(k))。
According to the nature of the correlation entropy, the cost function based on the correlation entropy is:
Figure RE-GDA0003339816540000061
when the cost function J (-) is maximum, the optimal estimate of the state is obtained, then the optimal estimate of x (k) is:
Figure RE-GDA0003339816540000062
order to
Figure RE-GDA0003339816540000063
The above formula yields:
Figure RE-GDA0003339816540000064
this gives:
Figure RE-GDA0003339816540000065
the modified covariance was found to be:
Figure RE-GDA0003339816540000066
wherein the content of the first and second substances,
Φ(k)＝diag(GΥ(e1(k),…,GΥ(en+m(k))))
Figure RE-GDA0003339816540000067
Figure RE-GDA0003339816540000071
the actual state is not known in practice, let
Figure RE-GDA0003339816540000072
Namely, it is
Figure RE-GDA0003339816540000073
Then there is
Figure RE-GDA0003339816540000074
The modified observed covariance was:
Figure RE-GDA0003339816540000075
then the covariance of the system's observations
Figure RE-GDA0003339816540000076
The following steps are changed:
Figure RE-GDA0003339816540000077
cross covariance matrix
Figure RE-GDA0003339816540000078
Comprises the following steps:
Figure RE-GDA0003339816540000079
the Kalman gain matrix K (k) is:
Figure RE-GDA00033398165400000710
further, the updating the system state quantity and the covariance matrix according to the kalman gain matrix includes:
computing state updates
Figure RE-GDA00033398165400000711
And a covariance update P (k +1 |. k + 1);
Figure RE-GDA00033398165400000712
Figure RE-GDA00033398165400000713
an embodiment of the present invention further provides an indoor mobile target positioning device, including: the positioning system is composed of a plurality of wireless access point AP nodes arranged indoors and an unknown moving target node, wherein the number of the wireless access point AP nodes is more than or equal to 3; the positioning device further comprises:
the state equation establishing module is used for establishing a state equation of the motion of the unknown moving target node;
the observation model establishing module is used for establishing an observation model of unknown moving target node motion;
the observation Sigma point set determining module is used for obtaining a one-step predicted value and a covariance matrix of the system state quantity through a group of Sigma point sets calculated by the unscented transformation UT and corresponding weights thereof according to the state equation; according to the predicted value of the first step, calculating a new Sigma point set again through unscented transformation UT, substituting the new Sigma point set into the observation model, and obtaining an observation Sigma point set;
the system observation predicted value determining module is used for calculating the observation predicted value of the observation Sigma point set according to the observation model and obtaining the observation predicted value of the system through weighted summation;
the Kalman gain matrix determination module is used for fusing the observation predicted value of the system according to the cost function based on the maximum correlation entropy determined by the property of the correlation entropy to obtain an observation covariance matrix and an observation cross covariance matrix for reconstructing an observation model; determining a Kalman gain matrix according to the observation covariance matrix and the observation cross covariance matrix;
the moving target determining module is used for updating the system state quantity and the covariance matrix according to the Kalman gain matrix; and determining the position coordinates of the unknown moving target nodes according to the updated system state quantity and the covariance matrix.
An embodiment of the present invention further provides a computer device, including: the positioning system is composed of a plurality of wireless access point AP nodes arranged indoors and an unknown moving target node, wherein the number of the wireless access point AP nodes is more than or equal to 3;
establishing a state equation of the motion of an unknown moving target node;
establishing an observation model of unknown moving target node motion;
according to a state equation, obtaining a one-step predicted value and a covariance matrix of the system state quantity through a group of Sigma point sets calculated by unscented transformation UT and corresponding weights thereof; according to the predicted value of the first step, calculating a new Sigma point set again through unscented transformation UT, substituting the new Sigma point set into the observation model, and obtaining an observation Sigma point set;
calculating an observation predicted value of an observation Sigma point set according to the observation model, and obtaining the observation predicted value of the system through weighted summation;
according to a cost function based on the maximum correlation entropy, fusing an observation predicted value of the system to obtain an observation covariance matrix and an observation cross covariance matrix of a reconstructed observation model; determining a Kalman gain matrix according to the observation covariance matrix and the observation cross covariance matrix;
updating a system state quantity and a covariance matrix according to the Kalman gain matrix; and determining the position coordinates of the unknown moving target nodes according to the updated system state quantity and the covariance matrix.
Compared with the prior art, the indoor positioning method, the indoor positioning device and the computer equipment provided by the embodiment of the invention have the following beneficial effects:
aiming at the problem that an indoor positioning system is generally influenced by multimodal heavy-tailed non-Gaussian noise in a complex indoor environment, the invention provides an indoor positioning method based on maximum cross-correlation entropy criterion (MCC) and an Unscented Kalman Filter (UKF), namely based on maximum cross-correlation entropy unscented Kalman filter (MCUKF). In addition, indoor positioning experiments are carried out on an indoor positioning method based on LS, EKF and UKF and an indoor positioning method based on MCUKF, and the results show that: the indoor positioning precision of the indoor positioning method based on LS, EKF and UKF is lower than that of the MCUKF method of the design; meanwhile, an indoor positioning method based on MCUKF under four different nuclear widths is analyzed, and the effect of the proposed method is optimal when upsilon ═ 10 is obtained. The indoor positioning method based on the MCUKF can better complete indoor positioning under the condition that non-Gaussian noise occurs in measurement noise, the positioning precision is higher than that of the indoor positioning methods of LS, EKF and UKF, and the robustness is also higher than that of the indoor positioning methods of LS, EKF and UKF. Namely, the MCUKF has better estimation effects on the state estimation and the position positioning of the unknown node than the traditional Extended Kalman Filtering (EKF) and Unscented Kalman Filtering (UKF) and has stronger robustness in the environment of multimodal heavy-tailed non-Gaussian observation noise.
Drawings
FIG. 1 is a flow diagram of a method for locating an indoor moving object provided in one embodiment;
FIG. 2 is a comparison graph of positioning accuracy for different positioning algorithms provided in one embodiment;
FIG. 3 is a comparison of MCUKF algorithm dynamic positioning for different kernel widths as provided in one embodiment;
FIG. 4 is a comparison graph of localized RMSE at different core widths as provided in one example.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
In one embodiment, referring to fig. 1, a method for positioning an indoor moving target is provided, which specifically includes:
the MCUKF indoor positioning method reconstructs observation information based on a non-linear regression method of MCC, and enhances the robustness of the UKF to non-Gaussian noise.
Setting L wireless Access Point (AP) nodes in an indoor field, wherein the coordinate of the ith AP node is (x)l,yl) And L is 1,2, … L. The moving unknown node can receive the signal strength from the AP node and takes the position and the speed of the moving unknown node as state quantities
Figure RE-GDA0003339816540000101
(x, y) are the spatial unknown coordinates of the unknown node,
Figure RE-GDA0003339816540000102
the velocity of the unknown node in the x direction and the y direction respectively is described by the change of x (k) at the time step k, and the expression is as follows: x (k +1) ═ f (x (k)) + ω (k)
Figure RE-GDA0003339816540000103
Wherein the content of the first and second substances,
Figure RE-GDA0003339816540000104
w (k) is process noise, and the sampling time interval is assumed to be T ═ 1 s.
It can also be abbreviated as: x (k +1) ═ f (x (k)) + w (k).
The RSSI ranging technique is also called signal strength ranging, and is calculated based on a radio propagation path loss model. In such a complicated and changeable indoor environment, traditional wireless signal transmission models such as a free space model are no longer applicable, and the current more common models are a logarithmic distance path loss model and the like, which are verified in various practical environments, and the general models are as follows:
RS(d)＝RS(d0)+10λlg(d/d0)+θdB
in indoor positioning, RSSI values may be extracted from the transceivers of the mobile nodes, and the observed model of predicted RSSI values employs a logarithmic range path loss model (i.e., the RSSI values are predicted using the logarithmic range path loss model to form the observed model of RSSI values). In order to enhance the anti-interference capability of the positioning system to other external wireless signals, the obtained weighted average of the signal strength of multiple measurements of different known nodes is obtained
Figure RE-GDA0003339816540000111
As an observed quantity.
Z(k)＝h(x(k))+v(k)
Figure RE-GDA0003339816540000112
Wherein the content of the first and second substances,
Figure RE-GDA0003339816540000113
v (k) is the observation noise,
Figure RE-GDA0003339816540000114
is the coordinate vector of the Lth known node, XkIs the coordinate vector of the unknown node moving at the kth time.
It should be noted that, in the conventional observation model, it is assumed that the noise is gaussian distributed, and now the noise changes, and is a non-gaussian noise with multiple peaks and heavy tails, and needs to be reconstructed; 2. the traditional observation model is constructed based on the criterion of minimum mean square error; the current criterion is changed by adopting the maximum cross-correlation entropy criterion, the criterion is changed, and the observation model needs to be reconstructed if the originally established observation model is not consistent.
The maximum correlation entropy unscented Kalman filtering MCUKF positioning algorithm comprises the following specific processes:
(1) first, a set of sampling points (called Sigma point set) and their corresponding weights are obtained according to UT transform:
Figure RE-GDA0003339816540000115
(initial value)
Figure RE-GDA00033398165400001111
Figure RE-GDA00033398165400001112
(2) The corresponding weights of these samples transformed by UT are calculated as follows:
Figure RE-GDA0003339816540000118
Figure RE-GDA0003339816540000119
Figure RE-GDA00033398165400001113
(3) then 2n +1 Sigma point sets are formed according to the system equation:
Figure RE-GDA00033398165400001210
(4) the one-step prediction and covariance matrix of the system state quantity are as follows:
Figure RE-GDA0003339816540000122
Figure RE-GDA0003339816540000123
(5) the UT transform is then used again to generate a new Sigma point set based on the predicted values from the previous step.
Figure RE-GDA0003339816540000124
Figure RE-GDA00033398165400001211
Figure RE-GDA00033398165400001212
(6) Substituting the predicted new Sigma point set into the observation equation to obtain the corresponding observed Sigma point set
Figure RE-GDA00033398165400001213
(7) Obtaining an observation predicted value of an observation Sigma point set in the step (3), and obtaining a mean value predicted by the system through weighted summation, wherein the mean value is as follows:
Figure RE-GDA0003339816540000128
reconstructing the observation model to obtain the following nonlinear model:
Figure RE-GDA0003339816540000129
wherein the content of the first and second substances,
Figure RE-GDA0003339816540000131
E[r(k)rT(k)]＝R(k)
Figure RE-GDA0003339816540000132
(9) left-multiplying both sides of the reconstructed observation model by S-1(k) Due to S-1(k)＝ST(K) Then the following equation is obtained:
Figure RE-GDA0003339816540000133
Figure RE-GDA0003339816540000134
wherein the content of the first and second substances,
Figure RE-GDA0003339816540000135
e(k)＝ST(k)φ(k)
then element e of line j in e (k)j(k) Is ej(k)＝dj(k)-mj(x(k))。
(10) According to the property of the correlation entropy, the cost function based on the correlation entropy is
Figure RE-GDA0003339816540000136
When the function J (-) is maximal, the optimal estimate of the state can be obtained, and then the optimal estimate of x (k) is
Figure RE-GDA0003339816540000137
Then, order
Figure RE-GDA0003339816540000138
The above formula can be obtained:
Figure RE-GDA0003339816540000141
this gives:
Figure RE-GDA0003339816540000142
then, a modified covariance is obtained as
Figure RE-GDA0003339816540000143
Wherein:
Φ(k)＝diag(GΥ(e1(k),…,GΥ(en+m(k))))
Figure RE-GDA0003339816540000144
Figure RE-GDA0003339816540000145
(11) the actual state is not known in practice, let
Figure RE-GDA0003339816540000146
Namely, it is
Figure RE-GDA0003339816540000147
Then there are:
Figure RE-GDA0003339816540000148
the modified observed covariance was:
Figure RE-GDA0003339816540000149
the covariance observed by the system becomes:
Figure RE-GDA00033398165400001410
then, the cross covariance matrix is:
Figure RE-GDA00033398165400001411
kalman gain matrix of
Figure RE-GDA00033398165400001412
(12) Finally, a state update and a covariance update are calculated
Figure RE-GDA0003339816540000151
Figure RE-GDA0003339816540000152
Example 1
In order to fully verify the rationality of the MCUKF method, a Zigbee indoor positioning system based on CC2530 is adopted for carrying out experiments, an unknown node and four AP points are arranged in the Zigbee indoor positioning system based on CC2530, the four AP points are randomly distributed, and the coordinates of the AP points are determined. And then, acquiring signal intensity data by using a PC (personal computer) under the static condition of an unknown node, acquiring 3min for each point, selecting 50 groups of data from the data, carrying out test analysis on the error distribution characteristics of the 4 AP signal intensities received by the unknown node, and analyzing the result of Kolmogorov-Smirnov test, wherein if the test rejects a zero hypothesis on a 15% significant level, the signal intensities from the unknown node to the 4 APs are all in non-normal distribution. The signal strength of the AP received by the unknown node is in a non-Gaussian distribution state, and the ranging errors of the unknown node and the known AP are also non-Gaussian noise. Therefore, the signal intensity distribution is superposed according to several Gaussian distributions, the signal intensity distribution is fitted through a mixed Gaussian model, and the proposed MCUKF positioning algorithm is calculated according to the distribution, as shown in FIG. 2.
As shown in figure 2, because of introducing the maximum correlation entropy, MCUKF can be known by comparing with other positioning algorithms, MCUKF reduces the requirement on the distribution characteristic of observation noise, can carry out filtering processing on observation data better, positioning accuracy is obviously improved, especially when other algorithm positioning errors are larger, the accuracy of the MCUKF positioning algorithm is obviously improved, and therefore the MCUKF positioning algorithm is stronger in robustness compared with other algorithms and stronger in adaptive environment capacity.
Example 2
In a practical and complex indoor environment, the positioning accuracy is often influenced by the multi-peak heavy-tail non-Gaussian noise, which can cause the accuracy of the traditional non-linear filtering algorithm to be reduced or even diverged, so that a non-linear robust filtering method aiming at the multi-peak heavy-tail non-Gaussian noise needs to be researchedThe maximum correlation entropy makes the filtering robust against non-gaussians. The following is a verification by a specific simulation experiment, and a suitable core width is selected by comparative analysis. Four APs are deployed in an indoor positioning area, corresponding coordinates of the four APs are A1(0,0), A2(0,10), A3(10,0) and A4(10,10), and state vectors of unknown nodes in an experiment are set
Figure RE-GDA0003339816540000161
The initial true state is provided by LS (position unit m, speed unit m/s)
Figure RE-GDA0003339816540000162
The initial state estimation error covariance matrix is set to P (0 | 0) ═ diag ([1,0.5,1, 0.5)]) The process noise is Q-N (0,0.1), and the observed non-Gaussian noise is comprehensively analyzed according to the signal intensity of the test
Figure RE-GDA0003339816540000163
To find the optimal core width, four different core widths were first selected for experimentation, with the core widths set to γ respectively1＝5，Υ2＝10，Υ3＝20，Υ 450. The results of the experiment are shown in FIGS. 3 and 4 below.
The MCUKF algorithm dynamic positioning comparison at four kernel widths as shown in fig. 3, the comparison of positioning accuracy as shown in fig. 4, and the kernel width y selected by MCUKF as shown in fig. 3 and 43When the indoor positioning precision is 10, the indoor positioning precision is the highest, and the performance effect is the best.
In one embodiment, an indoor positioning device is provided, the device comprising: the positioning system is composed of a plurality of wireless access point AP nodes arranged indoors and an unknown moving target node, wherein the number of the wireless access point AP nodes is more than or equal to 3;
and the state equation establishing module is used for establishing a state equation of the motion of the unknown moving target node.
And the observation model establishing module is used for establishing an observation model of the unknown moving target node motion.
The observation Sigma point set determining module is used for obtaining a one-step predicted value and a covariance matrix of the system state quantity through a group of Sigma point sets calculated by the unscented transformation UT and corresponding weights thereof according to the state equation; and according to the predicted value in one step, calculating a new Sigma point set again through the unscented transformation UT, substituting the new Sigma point set into the observation model, and obtaining an observation Sigma point set.
And the system observation predicted value determining module is used for calculating the observation predicted value of the observation Sigma point set according to the observation model and obtaining the observation predicted value of the system through weighted summation.
The Kalman gain matrix determination module is used for fusing the observation predicted value of the system according to the cost function based on the maximum correlation entropy determined by the property of the correlation entropy to obtain an observation covariance matrix and an observation cross covariance matrix for reconstructing an observation model; and determining a Kalman gain matrix according to the observation covariance matrix and the observation cross covariance matrix.
The moving target determining module is used for updating the system state quantity and the covariance matrix according to the Kalman gain matrix; and determining the position coordinates of the unknown moving target nodes according to the updated system state quantity and the covariance matrix.
For specific definition of the indoor positioning device, reference may be made to the definition of the indoor positioning method above, and details are not described here. The modules in the indoor positioning device can be wholly or partially realized by software, hardware and a combination thereof. The modules can be embedded in a hardware form or independent from a processor in the computer device, and can also be stored in a memory in the computer device in a software form, so that the processor can call and execute operations corresponding to the modules.
In one embodiment, a computer device is provided, comprising: the positioning system is composed of a plurality of wireless access point AP nodes arranged indoors and an unknown moving target node, wherein the number of the wireless access point AP nodes is more than or equal to 3;
and establishing a state equation of the motion of the unknown moving target node.
And establishing an observation model of the unknown moving target node motion.
According to a state equation, obtaining a one-step predicted value and a covariance matrix of the system state quantity through a group of Sigma point sets calculated by unscented transformation UT and corresponding weights thereof; and according to the predicted value in one step, calculating a new Sigma point set again through the unscented transformation UT, substituting the new Sigma point set into the observation model, and obtaining an observation Sigma point set.
And calculating an observation predicted value of the observation Sigma point set according to the observation model, and obtaining the observation predicted value of the system through weighted summation.
According to a cost function based on the maximum correlation entropy, fusing an observation predicted value of the system to obtain an observation covariance matrix and an observation cross covariance matrix of a reconstructed observation model; and determining a Kalman gain matrix according to the observation covariance matrix and the observation cross covariance matrix.
Updating a system state quantity and a covariance matrix according to the Kalman gain matrix; and determining the position coordinates of the unknown moving target nodes according to the updated system state quantity and the covariance matrix.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by hardware instructions of a computer program, which can be stored in a non-volatile computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. Any reference to memory, storage, database or other medium used in the embodiments provided herein can include at least one of non-volatile and volatile memory. Non-volatile Memory may include Read-Only Memory (ROM), magnetic tape, floppy disk, flash Memory, optical storage, or the like. Volatile Memory can include Random Access Memory (RAM) or external cache Memory. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM), among others.
The technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features. Furthermore, the above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (10)

1. An indoor mobile target positioning method comprises the following steps: the positioning system is composed of a plurality of wireless access point AP nodes arranged indoors and an unknown moving target node, wherein the number of the wireless access point AP nodes is more than or equal to 3; the positioning method is characterized by comprising the following steps:
establishing a state equation of the motion of an unknown moving target node;
establishing an observation model of unknown moving target node motion;
according to a state equation, obtaining a one-step predicted value and a covariance matrix of the system state quantity through a group of Sigma point sets calculated by unscented transformation UT and corresponding weights thereof; according to the predicted value of the first step, calculating a new Sigma point set again through unscented transformation UT, substituting the new Sigma point set into the observation model, and obtaining an observation Sigma point set;
calculating an observation predicted value of an observation Sigma point set according to the observation model, and obtaining the observation predicted value of the system through weighted summation;
according to a cost function based on the maximum correlation entropy, fusing an observation predicted value of the system to obtain an observation covariance matrix and an observation cross covariance matrix of a reconstructed observation model; determining a Kalman gain matrix according to the observation covariance matrix and the observation cross covariance matrix;
estimating a system state quantity and a covariance matrix according to the Kalman gain matrix; and determining the position coordinates of the unknown moving target nodes according to the estimated system state quantity and the covariance matrix.
2. The indoor moving-object positioning method of claim 1, wherein the establishing of the state equation of the unknown moving-object node motion comprises:
taking the position and the speed of an unknown mobile target node as state quantities
Figure RE-FDA0003339816530000011
Establishing a state equation of the motion of an unknown moving target node; and the motion of the unknown moving target node is described by the change of x (k) at time step k, and the expression is as follows: x (k +1) ═ f (x (k)) + ω (k)
Figure RE-FDA0003339816530000012
Wherein (x, y) is the spatial location coordinates of the unknown node;
Figure RE-FDA0003339816530000013
the speed of the unknown node in the x direction and the y direction respectively; f (x (k)) is the system matrix,
Figure RE-FDA0003339816530000021
w (k) is process noise, and the sampling time interval is set as T ═ 1 s; the abbreviation is: x (k +1) ═ f (x (k)) + w (k).
3. An indoor moving-object positioning method as claimed in claim 2, wherein said establishing an observation model of unknown moving-object node motion comprises:
acquiring an RSSI value of an unknown mobile target node received from a known wireless Access Point (AP) node;
and establishing an observation model by taking the RSSI value as an observed quantity.
4. The indoor moving-object positioning method of claim 3, wherein the establishing an observation model using the RSSI value as an observed quantity comprises:
taking the weighted average of RSSI values of different known wireless access point AP nodes as an observed quantity, and establishing an observation model by adopting a logarithmic distance path loss model; and the expression of the observation model is as follows:
Z(k)＝h(x(k))+v(k)
Figure RE-FDA0003339816530000022
wherein the logarithmic distance path loss model has a general formula:
Figure RE-FDA0003339816530000023
rs (d) is the path loss in dB for a distance d between the transceivers; RS (d)0) Is a short distance d0Reference path loss of time, d0Taking 1 meter; λ is a loss factor;
Figure RE-FDA0003339816530000024
is a normal random variable;
Figure RE-FDA0003339816530000025
v (k) is the observation noise,
Figure RE-FDA0003339816530000026
is the coordinate vector, X, of the Lth known wireless access point AP nodekIs the coordinate vector of the unknown moving target node at the kth moment.
5. The indoor moving object positioning method of claim 4, wherein the obtaining an observed Sigma point set comprises:
a set of sampling points, called the Sigma point set, is obtained from the UT transform:
Figure RE-FDA0003339816530000031
Figure RE-FDA0003339816530000032
Figure RE-FDA0003339816530000033
calculating the corresponding weight of the sampling point as follows:
Figure RE-FDA0003339816530000034
Figure RE-FDA0003339816530000035
Figure RE-FDA0003339816530000036
form 2n +1 Sigma point sets according to the system equation:
Figure RE-FDA0003339816530000037
the predicted value and covariance matrix of the system state quantity are:
Figure RE-FDA0003339816530000038
Figure RE-FDA0003339816530000039
from the one-step predicted values, the UT transform is again used to generate a new Sigma point set:
Figure RE-FDA00033398165300000310
Figure RE-FDA00033398165300000311
Figure RE-FDA00033398165300000312
substituting the predicted new Sigma point set into the observation model to obtain a corresponding observed Sigma point set:
Figure RE-FDA0003339816530000041
wherein n is the dimension of the state; x0The sampling point when i is 0; xiIs the ith Sigma sample point;
Figure RE-FDA0003339816530000042
is the sample mean of the Sigma set; p is the variance of the state vector; λ is a scaling parameter;
Figure RE-FDA0003339816530000043
weight values of the covariance and the mean, respectively; alpha is a distribution state parameter of the sampling point; beta is more than or equal to 0 and is a non-negative weight coefficient; xi(k +1 | k) is a one-step predicted value of the Sigma sampling point;
Figure RE-FDA0003339816530000044
and P (k +1 |. k) is a one-step predicted value and covariance matrix of the system state quantity, respectively, and Q (k) is process noise; zi(k +1 | k) is the observed Sigma sample point.
6. The indoor moving object positioning method of claim 5, wherein the system's observation prediction is as follows:
Figure RE-FDA0003339816530000045
7. the indoor moving object locating method of claim 6, wherein the determining a Kalman gain matrix comprises:
reconstructing the observation model to obtain the following nonlinear model:
Figure RE-FDA0003339816530000046
wherein the content of the first and second substances,
Figure RE-FDA0003339816530000047
E[r(k)rT(k)]＝R(k)
Figure RE-FDA0003339816530000051
left-multiplying both sides of the reconstructed observation model by S-1(k) Due to S-1(k)＝ST(K) The following equation is obtained:
Figure RE-FDA0003339816530000052
Figure RE-FDA0003339816530000053
wherein the content of the first and second substances,
Figure RE-FDA0003339816530000054
e(k)＝ST(k) phi (k) then, e (k) the element e of the jth linej(k)，ej(k)＝dj(k)-mj(x(k))。
According to the nature of the correlation entropy, the cost function based on the correlation entropy is:
Figure RE-FDA0003339816530000055
when the cost function J (-) is maximum, the optimal estimate of the state is obtained, then the optimal estimate of x (k) is:
Figure RE-FDA0003339816530000056
order to
Figure RE-FDA0003339816530000057
The above formula yields:
Figure RE-FDA0003339816530000058
this gives:
Figure RE-FDA0003339816530000061
the modified covariance was found to be:
Figure RE-FDA0003339816530000062
wherein the content of the first and second substances,
Φ(k)＝diag(Gγ(e1(k),…,Gγ(en+m(k))))
Figure RE-FDA0003339816530000063
Figure RE-FDA0003339816530000064
the actual state is not known in practice, let
Figure RE-FDA0003339816530000065
Namely, it is
Figure RE-FDA0003339816530000066
Then there is
Figure RE-FDA0003339816530000067
The modified observed covariance was:
Figure RE-FDA0003339816530000068
then the covariance of the system's observations
Figure RE-FDA0003339816530000069
The following steps are changed:
Figure RE-FDA00033398165300000610
cross covariance matrix
Figure RE-FDA00033398165300000611
Comprises the following steps:
Figure RE-FDA00033398165300000612
the Kalman gain matrix K (k) is:
Figure RE-FDA00033398165300000613
8. the method of claim 7, wherein updating the system state quantities and covariance matrix based on the Kalman gain matrix comprises:
computing state updates
Figure RE-FDA0003339816530000071
And a covariance update P (k +1 |. k + 1);
Figure RE-FDA0003339816530000072
Figure RE-FDA0003339816530000073
9. an indoor mobile target positioning device comprising: the positioning system is composed of a plurality of wireless access point AP nodes arranged indoors and an unknown moving target node, wherein the number of the wireless access point AP nodes is more than or equal to 3; characterized in that, the positioner still includes:
the state equation establishing module is used for establishing a state equation of the motion of the unknown moving target node;
the observation model establishing module is used for establishing an observation model of unknown moving target node motion;
the observation Sigma point set determining module is used for obtaining a one-step predicted value and a covariance matrix of the system state quantity through a group of Sigma point sets calculated by the unscented transformation UT and corresponding weights thereof according to the state equation; according to the predicted value of the first step, calculating a new Sigma point set again through unscented transformation UT, substituting the new Sigma point set into the observation model, and obtaining an observation Sigma point set;
the system observation predicted value determining module is used for calculating the observation predicted value of the observation Sigma point set according to the observation model and obtaining the observation predicted value of the system through weighted summation;
the Kalman gain matrix determination module is used for fusing the observation predicted value of the system according to the cost function based on the maximum correlation entropy determined by the property of the correlation entropy to obtain an observation covariance matrix and an observation cross covariance matrix for reconstructing an observation model; determining a Kalman gain matrix according to the observation covariance matrix and the observation cross covariance matrix;
the moving target determining module is used for updating the system state quantity and the covariance matrix according to the Kalman gain matrix; and determining the position coordinates of the unknown moving target nodes according to the updated system state quantity and the covariance matrix.
10. A computer device comprising a memory and a processor, the memory storing a computer program, wherein the processor when executing the computer program implements the steps of the method of any of claims 1-8.
CN202111012495.6A 2021-08-31 2021-08-31 Indoor mobile target positioning method and device and computer equipment Pending CN113759309A (en)

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