CN106646358A - Multi-error model IMM algorithm for indoor wireless positioning - Google Patents

Abstract

The present invention provides a multi-error model IMM (Interacting Multiple Model) algorithm for indoor wireless positioning. In the traditional IMM algorithm, generally, two states need to perform filtering processing, one of the two states is a sight distance state, and the other one thereof is a non-sight distance state. However, the two states cannot fully describe the channel condition in the actual indoor environment. There are a plurality of different errors in the actual environment, and the multi-error model IMM algorithm for indoor wireless positioning extends the model state. That the multi-error model IMM algorithm for indoor wireless positioning is introduced about the complex indoor environment having various barriers is an effective means to eliminate errors. When the number of the models in the multi-error model IMM algorithm matches the reality, the elimination performance of the algorithm is the best, and the performances of the algorithm which has the number of the models more than the reality are better than the performances of the algorithm which has the number of the models less than the reality. The multi-error model is introduced not to increase the complexity of the IMM algorithm, and therefore, the multi-error model IMM algorithm is an efficient method for error elimination in the indoor environment with a plurality of different errors.

Description

IMM algorithm of multi-error model for indoor wireless positioning

Technical Field

The invention relates to the technical field of wireless positioning networks, in particular to an IMM algorithm of a multi-error model for indoor wireless positioning.

Background

The most widely used today is the GPS positioning system. But GPS is not suitable for indoor environments due to the shelter of buildings. However, the wireless sensor network positioning provides the possibility of indoor positioning by adopting various ranging modes and combining node information with known positions.

As a brand-new information acquisition and processing technology, the wireless sensor network has wide application prospect in the related positioning fields of environment monitoring, target tracking and the like. Determining the position of an event or the position of a sensor node acquiring information is one of the most basic functions of a wireless sensor network, and monitoring information without position information is usually meaningless.

The wireless sensor network positioning methods are more, and currently, the wireless sensor network positioning methods are most commonly divided according to whether distance measurement is needed or not, namely a distance-Based positioning algorithm (Range-Based) and a distance-Free positioning algorithm (Range-Free). Distance-based positioning algorithms include time of signal Transmission (TOA) -based, time difference of signal Transmission (TDOA) -based, angle of arrival (AOA) -based, and Received Signal Strength Indication (RSSI) -based measurement methods. The positioning method based on the RSSI has low cost and higher positioning accuracy, but is easily influenced by factors such as reflection, multipath propagation, antenna gain, barrier obstruction and the like in an actual environment; especially, the RSS signal is greatly influenced by the obstruction of the obstacle. Therefore, the elimination of the error caused by the obstacle has been the direction of efforts of researchers.

When a target node (MN) moves indoors, it always frequently switches between line-of-sight and non-line-of-sight due to signal propagation conditions. An Interactive Multiple Model (IMM) algorithm is introduced to handle this transition state. Simulation and experiments of a plurality of researchers prove that the algorithm mechanism is superior to a general method of identifying non-line-of-sight and then eliminating non-line-of-sight errors. The conventional IMM algorithm simply divides the signal propagation state into line-of-sight and non-line-of-sight to process. However, through practical measurement, the difference of the error caused by different obstacles in the room to the non-line-of-sight is large.

Disclosure of Invention

The invention aims to provide an IMM algorithm of a multi-error model to further eliminate errors caused by obstacles. Simulation results and experiments show that the IMM algorithm adopting the multi-error model is superior to the traditional single-error model algorithm.

In order to achieve the purpose, the invention is realized by the following technical scheme:

AN IMM algorithm of a multi-error model is used for indoor wireless positioning of a target node MN, and a channel model between the MN and AN anchor node AN comprises a line-of-sight model and a non-line-of-sight model, wherein the non-line-of-sight model is divided into 3 different non-line-of-sight models according to the statistical result of AN indoor environment channel state; the IMM algorithm is divided into four phases: inputting interaction, filtering a model, updating the probability of the model and outputting interaction;

(1) input interaction

In the input interaction process, all states and model conditional probabilities obtained in the last cycle are used for recalculating an input state and input state error covariance matrix for each model; firstly, calculating the interaction probability of the model:

c_k，j＝Σ_ip_iju_k，i(n-1)

wherein u is_k，i|j(n | n-1) represents the transition probability that the k-th AN inputs the filtering result of the model i to the model j at the time n-1; p_ijThe model transition probability of the Markov chain represents the probability of transition from the model i to the model j; u. of_k，i(n-1) is the model probability of the kth AN at time n-1 model i, c_kjRepresenting the Kth anchor nodeThe prediction probability of the model j is a normalized variable; then covariance update:

wherein, P_k，i(n-1| n-1) represents the posterior probability of the ith model at time n-1,is an initial state estimate that contains an initial ranging value,is the hybrid state estimate of model i; and then calculating the input value of the model j at the moment n:

the model conversion probability of the Markov chain is as follows:

and satisfy p₁₁+p₁₂+p₁₃+p₁₄＝1，p₂₁+p₂₂+p₂₃+p₂₄＝1，p₃₁+p₃₂+p₃₃+p₃₄＝1，p₄₁+p₄₂+p₄₃+p₄₄＝1；

(2) Filtering calculation of each model

Because the measurement noise under LOS and NLOS is different, 4 different Kalman filters are adopted to carry out filtering processing on the measurement distance;

(3) model probability update

And calculating model likelihood and model probability while filtering each model, and obtaining the model likelihood according to observed and measured residuals in the model under the assumption that the model likelihood obeys Gaussian distribution:

Λ_k，j(n)＝N(V_k，j(n)；0，S_k，j(n))

wherein S is_k，j(n)＝GP_k，j(n|n-1)G^T，G＝[1 0]，Λ_k，j(n) denotes a residual V_k，j(n) has a mean value of zero and a variance of S_k，j(n), G is a matrix of rows and columns,

u_k，j(n)＝1/c_kΛ_k，j(n)c_k，j

c_kjrepresenting the predicted probability of model j for the kth anchor node.

(4) Output interaction

The final estimated distance is

Further, the kalman filtering algorithm is divided into 2 steps: predicting and updating; firstly, a prediction process based on Kalman filtering KF:

P_k，j(n|n-1)＝F_dP_k，0j(n|n-1)F_d ^T

F_dis a matrix, Fd ═ 1, T; 0,1]

Followed by measurement update of KF

K_a，k，j(n)＝P_k，j(n|n-1)G^T[GP_k，j(n|n-1)G^T]^-1

P_k，j(n|n)＝[I-K_a，k，j(n)G]P_k，j(n|n-1)

d_k ^mes(n) is the initial distance value measured by the hardware module, typically a value that contains measurement noise.

The invention has the beneficial effects that: for a complex indoor environment with various obstacles, the IMM algorithm with the multi-error model is introduced, and is a means for effectively eliminating errors; when the number of models in the IMM algorithm of the multi-error model is matched with the actual number, the elimination performance of the algorithm is optimal, and the performance of the algorithm when the number of models is more than the actual number is better than the performance when the number of models is less than the actual number; the complexity of the IMM algorithm cannot be increased by introducing the multi-error model, so that the IMM algorithm of the multi-error model is an effective method for eliminating errors in an indoor environment with various different obstacles.

Drawings

FIG. 1 is a graph of a target node and anchor nodes in an indoor environment;

FIG. 2 is a schematic diagram of channel state statistics of a complex indoor environment;

FIG. 3 is a diagram of a conventional IMM algorithm framework;

FIG. 4 is a schematic diagram of transition probabilities of Markov chains;

FIG. 5 is a diagram of a Markov state transition matrix;

FIG. 6 is a diagram of 4 different obstacle models for an actual environment;

fig. 7 shows that there are 5 different error models for the actual environment.

Detailed description of the preferred embodiments

The present invention will be described in further detail with reference to the following detailed description and accompanying drawings.

The system model of the invention is as follows: when the MN moves indoors, it is assumed that at time t, the distance between the MN and M Anchor Nodes (ANs) can be expressed as:

wherein,indicating the measured distance between the mth AN and the MN. Fig. 1 is an indoor environment of a MN, and fig. 2 is its corresponding channel conditions. At time t, the distance state vector between the MN and the mth AN is represented as follows:

D_m(t)＝[h_m(t),V_m(t)]^Tm＝1,2,3,…,M

wherein h is_m(t) denotes the distance, V, between the mth AN and the MN_m(t) represents the speed of the MN, M being the number of ANs. The state transition equation for MN is as follows:

D_m(t)＝FD_m(t-1)+Cω_d(t-1)

wherein,

T_irepresenting the sampling time interval, ω_d(t-1) represents the independent identically distributed Gaussian process noise. The state vector of the MN at each time t is defined as:

where (x (t), y (t)) represent the coordinates of the MN at time t,representing the speed of the MN in the x and y directions. The state update equation for MN is:

X(t)＝AX(t-1)+Bω(t-1) t＝1,2,3,…,T

x (t-1) represents the posterior probability at time t-1.

Wherein d (x (t)) [ d ]₁(X(t)),d₂(X(t)),…,d_M(X(t))]^TRepresenting the Euclidean distance between MN and ANSeparating; n (t) ═ n₁(t),n₂(t),…,n_M(t)]^TIs the distance measurement noise with the mean value of the error being mu_dThe variance isAccording to different sight distance and non sight distance states:

with respect to the models LOS, NLOS1, NLOS2, NLOS3, that is, the model variables obey N (μ, σ)²) Wherein the mean μ is 0m, 1.659m, 4.048m, 7.845m, respectively, the corresponding variance σ²1.5747, 1.76, 3.0886, 2.728, respectively. Too many introduced models lead to too high algorithm complexity and can meet the requirement of real-time positioning and rapid ranging positioning. Therefore, according to the requirements in the real-time positioning and tracking process, models LOS, NLOS1, NLOS2 and NLOS3 are selected.

As shown in fig. 3, the conventional IMM algorithm is divided into four phases: input interaction, model filtering, model probability updating and output interaction. The IMM algorithm is a recursive algorithm. The general idea is to perform Kalman filtering respectively through different error models to perform optimization processing. Therefore, the method is particularly suitable for performing IMM extension of the multi-error model.

(1) Input interaction

And in the input interaction process, the covariance matrix of the input state and the input state errors is recalculated for each model by using all the states and the model conditional probabilities obtained in the last cycle. Firstly, calculating the interaction probability of the model:

c_k，j＝Σ_ip_iju_k，i(n-1)

wherein u is_k，i|j(n | n-1) represents the transition probability that the k-th AN inputs the filtering result of the model i to the model j at the time n-1; p_ijThe model transition probability of the Markov chain represents the probability of transition from the model i to the model j; u. of_k，i(n-1) is the model probability of the kth AN at time n-1 model i, c_kjThe predicted probability of model j, which represents the kth anchor node, is a normalized variable. Then covariance update:

wherein, P_k，i(n-1| n-1) represents the posterior probability of the ith model at time n-1.

And then calculating the input value of the model j at the moment n:

the model transition probability of the Markov chain is shown in FIG. 4: wherein, P11+ P12 is 1, and P21+ P22 is 1.

(2) Filtering calculation of each model

Because the measurement noise under LOS and NLOS is different, 2 different Kalman filters are adopted to carry out filtering processing on the measurement distance. The Kalman filtering algorithm is divided into 2 steps: and (4) predicting and updating. First is a prediction process based on KF:

Pk,j(n|n-1)＝FdPk,0j(n|n-1)FdT

followed by measurement update of KF

K_a，k，j(n)＝P_k，j(n|n-1)G^T[GP_k，j(n|n-1)G^T]^-1

P_k，j(n|n)＝[I-K_a，k，j(n)G]P_k，j(n|n-1)

(3) Model probability update

And calculating model likelihood and model probability while filtering each model, and obtaining the model likelihood according to observed and measured residuals in the model under the assumption that the model likelihood obeys Gaussian distribution:

Λk，j(n)＝N(Vk，j(n)；0，Sk，j(n))

wherein S is_k，j(n)＝GP_k，j(n|n-1)G^T，G＝[1 0]，Λ_k，j(n) denotes a residual V_k，j(n) has a mean value of zero and a variance of S_k，j(n) a gaussian density function.

u_k，j(n)＝1/c_kΛ_k，j(n)c_k，j

(4) Output interaction

The final estimated distance is

IMM of the multiple error model of the present invention

In the conventional IMM algorithm, two states are generally filtered, one is a line-of-sight state and the other is a non-line-of-sight state. However, these two states do not sufficiently describe the channel conditions in a practical indoor environment. As shown in FIG. 2, various errors exist in the actual environment, so the invention expands the model state. The expanded markov state transition matrix is represented as follows:

the transition probability matrix is as follows:

and satisfy p₁₁+p₁₂+p₁₃+p₁₄＝1，p₂₁+p₂₂+p₂₃+p₂₄＝1，p₃₁+p₃₂+p₃₃+p₃₄＝1，p₄₁+p₄₂+p₄₃+p₄₄＝1。

Then, simulation verification is carried out, 5 anchor nodes with known positions are arranged, and MN moves in an indoor environment with the speed of 20m by 35m, the speed is 0.5m/s, and the total length is 50 m. The sampling interval is 1s and the total number of samples is 100. The environment in which the MN is located and the propagation state of the channel between the MN and each AN are shown in fig. 1 and fig. 2, respectively.

Fig. 5 shows a cumulative distribution diagram of positioning errors when 4 different error models actually exist in the indoor environment, and the two-model algorithm and the 4-model algorithm are used for error elimination. Clearly, the algorithm using multiple models outperforms the two models. However, a new problem also arises after the error model is expanded, namely how to adopt the error model in the algorithm can effectively eliminate the non-line-of-sight error. Therefore, the present invention first counts the error of the signal due to the common indoor obstacle, as shown in table 1 below.

TABLE 1 common indoor obstacle to signal noise

Obstacle	Mean value (m)	Variance (variance)
			Line of sight (without obstacles)	0	1.5747
Desk baffle	1.659	1.76
			Glass door	4.048	3.0886
Human body	7.845	2.728
			Furniture of table and chair	9.762	3.635
Wall with a plurality of walls	11.93	5.7657

As can be seen from table 1, the noise interference of different obstacles to the signal is very different. Figure 6 has demonstrated that the multiple-error model performs significantly better than the conventional two models in an environment where there are many different obstacles. Therefore, the introduction of multiple error models is necessary.

In order to further study the performance of the multi-error model IMM algorithm in processing complex indoor environments, the performance of the multi-error model IMM in the presence of different numbers of obstacles in actual environments is further analyzed, as shown in fig. 7.

Fig. 7 depicts a cumulative localization error profile for 5 different obstacles in a real environment under an IMM algorithm using only EKF, 2 to 6 different error models. As can be seen from FIG. 6, when the number of error models in the IMM algorithm is exactly matched with the actual environment, the error elimination effect is optimal, as shown by the light blue solid line in the figure. And researching other unmatched conditions to find that the error elimination effect is worse when the difference between the number of models used in the IMM algorithm and the actual environment is larger. The research of the invention discovers that: firstly, an IMM algorithm of a multi-error model is introduced, so that errors of a complex environment with multiple obstacles can be eliminated; and secondly, when the number of models in the IMM algorithm of the multi-error model is matched with the actual environment, the error elimination effect is optimal. In order to further study the relation between the IMM algorithm of the multi-error model and the obstacle types in the actual environment, further analysis is performed herein, as shown in Table 2.

Table 2 positioning error statistical table with different quantities of IMM algorithm and actual obstacle for multi-error model

Number of error models	II	III	Fourthly	Five of them	Six ingredients
						II	4.2	4.8	5.4	5.6	6.7
III	9.8	6.3	6.8	6.9	6.6
						Fourthly	12.1	11.4	7.5	7.6	7.8
Five of them	15.7	12.6	11.2	7.2	8.1
						Six ingredients	17.8	14.9	12.6	11.2	10.8

The first row represents the number of error models used in the algorithm and the first column represents the actual number of error models. It can be seen from the table that the cancellation effect is always the best when the error model numbers match. When the models do not match, the number of models in the algorithm is better than the number of models in the algorithm. Table 3 describes the algorithm complexity of different error models in the IMM algorithm of the multiple error model. As can be seen from Table 3, there is no significant difference in complexity between the different error models. Therefore, extending the error model of the IMM does not increase the complexity of the algorithm.

TABLE 3 IMM Algorithm complexity for different model numbers

Number of models	EKF	II	III	Fourthly	Five of them	Six ingredients
							Complexity(s)	0.217	0.286	0.336	0.393	0.428	0.488

In conclusion, for a complex indoor environment with various obstacles, the IMM algorithm with the multi-error model is an effective error elimination means; when the number of models in the IMM algorithm of the multi-error model is matched with the actual number, the elimination performance of the algorithm is optimal, and the performance of the algorithm when the number of models is more than the actual number is better than the performance when the number of models is less than the actual number; the complexity of the IMM algorithm cannot be increased by introducing the multi-error model, so that the IMM algorithm of the multi-error model is an effective method for eliminating errors in an indoor environment with various different obstacles.

The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (2)

1. An IMM algorithm of a multi-error model, which is used for indoor wireless positioning of a target node MN, and is characterized in that: the channel model between the MN and the anchor node AN comprises a line-of-sight model and a non-line-of-sight model, wherein the non-line-of-sight model is divided into 3 different non-line-of-sight models according to the indoor environment channel state statistical result; the IMM algorithm is divided into four phases: inputting interaction, filtering a model, updating the probability of the model and outputting interaction;

(1) input interaction

In the input interaction process, all states and model conditional probabilities obtained in the last cycle are used for recalculating an input state and input state error covariance matrix for each model; firstly, calculating the interaction probability of the model:

$u_{k,i|j}\left(n\right|n-1)=\left(\frac{1}{c_{k,j}}\right)p_{ij}{u}_{k,i}(n-1)$

c_k，j＝∑_ip_iju_k，i(n-1)

wherein u is_k，i|j(n | n-1) represents the transition probability that the k-th AN inputs the filtering result of the model i to the model j at the time n-1; p_ijThe model transition probability of the Markov chain represents the probability of transition from the model i to the model j; u. of_k，i(n-1) is the model probability of the kth AN at time n-1 model i, c_kjThe prediction probability of the model j representing the Kth anchor node is a normalized variable; then covariance update:

$\begin{array}{c}{P}_{k,0j}(n-1|n-1)\\ =\underset{i}{\mathrm{\Σ}}\{P_{k,i}(n-1|n-1)+\[{\hat{D}}_{k,i}(n-1|n-1)-{\hat{D}}_{k,0j}(n-1|n-1)\]\\ \×{\[{\hat{D}}_{k,i}(n-1|n-1)-{\hat{D}}_{k,0j}(n-1|n-1)\]}^T\}\×u_{k,i|j}(n-1|n-1)\end{array}$

wherein, P_k，i(n-1| n-1) represents the posterior probability of the ith model at time n-1,is an initial state estimate that contains an initial ranging value,is the hybrid state estimate of model i; and then calculating the input value of the model j at the moment n:

${\hat{D}}_{k,0j}\left(n\right)=\underset{i}{\Σ}{\hat{D}}_{k,i}|(n-1|n-1)u_{k,i|j}\left(n\right|n-1)$

the model conversion probability of the Markov chain is as follows:

$P=\left[\begin{array}{cccc}{p}_{11}& p_{12}& p_{13}& p_{14}\\ p_{21}& p_{22}& p_{23}& p_{24}\\ p_{31}& p_{32}& p_{33}& p_{34}\\ p_{41}& p_{42}& p_{43}& p_{44}\end{array}\right]$

and satisfy p₁₁+p₁₂+p₁₃+p₁₄＝1，p₂₁+p₂₂+p₂₃+p₂₄＝1，p₃₁+p₃₂+p₃₃+p₃₄＝1，p₄₁+p₄₂+p₄₃+p₄₄＝1；

(2) Filtering calculation of each model

Because the measurement noise under LOS and NLOS is different, 4 different Kalman filters are adopted to carry out filtering processing on the measurement distance;

(3) model probability update

And calculating model likelihood and model probability while filtering each model, and obtaining the model likelihood according to observed and measured residuals in the model under the assumption that the model likelihood obeys Gaussian distribution:

Λ_k，j(n)＝N(V_k，j(n)；O，S_k，j(n))

wherein S is_k，j(n)＝GP_k，j(n|n-1)G^T，G＝[1 0]，Λ_k，j(n) denotes a residual V_k，j(n) has a mean value of zero and a variance of S_k，j(n), G is a matrix of rows and columns,

u_k，j(n)＝1/c_kΛ_k，j(n)c_k，j

$c_k=\underset{j}{\Σ}{\mathrm{\Λ}}_{k,j}\left(n\right)c_{k,j}$

(4) output interaction

${\hat{D}}_k\left(n\right|n)=\underset{j}{\Σ}{\hat{D}}_{k,j}\left(n\right|n)u_{k,j}\left(n\right)$

$P_k\left(n\right|n)=\underset{j}{\mathrm{\Σ}}\{P_{k,j}\left(n\right|n)+\[{\hat{D}}_{k,j}\left(n\right|n)-{\hat{D}}_k\left(n\right|n)\]\×{\[{\hat{D}}_{k,j}\left(n\right|n)-{\hat{D}}_k\left(n\right|n)\]}^T\}{u}_{k,j}\left(n\right)$

The final estimated distance is

${\hat{d}}_k\left(n\right)=G{\hat{D}}_k\left(n\right|n).$

2. The IMM algorithm of claim 1, wherein: the Kalman filtering algorithm is divided into 2 steps: predicting and updating; first is a prediction process based on KF:

${\hat{D}}_{k,j}\left(n\right|n-1)=F_d{\hat{D}}_{k,0j}(n-1|n-1)$

P_k，j(n|n-1)＝F_dP_k，0j(n|n-1)F_d ^T

followed by measurement update of KF

K_a，k，j(n)＝P_k，j(n|n-1)G^T[GP_k，j(n|n-1)G^T]^-1

P_k，j(n|n)＝[I-K_a，k，j(n)G]P_k，j(n|n-1)

$V_{k,j}\left(n\right)=d_k^{mes}\left(n\right)-G{\hat{D}}_{k,j}\left(n\right|n-1)$

${\hat{D}}_{k,j}\left(n\right|n)={\hat{D}}_{k,j}\left(n\right|n-1)+K_{a,k,j}\left(n\right)V_{k,j}\left(n\right).$