5g adaptive filtering positioning method in a noise rapidly changing environment

Abstract

The application discloses a 5G adaptive filtering positioning method in a noise sharp change environment, comprising: through a time of arrival and an angle of arrival positioning algorithm, analyzing a positioning filtering process, obtaining index factors influencing positioning accuracy and reliability; based on a variational Bayes adaptive filtering method, 5G channel simulation is carried out on the index factors, and a simulation result is obtained; based on the simulation result, 5G distance and angle observation are extracted, positioning distance is calculated based on the 5G distance and angle observation, and a positioning result is obtained. The application is based on the variational Bayes method, noise covariance matrices in the filtering process are adaptively estimated according to UE-BS distance, UE motion state and LoS / NLoS conditions, has high real-time performance, and can solve the positioning performance decline problem caused by noise sharp change in a complex environment.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of 5G positioning, and particularly relates to a 5G adaptive filtering positioning method in a noise rapidly changing environment. BACKGROUND

[0002] In the past decade, the Internet of Things, cloud computing and intelligent terminals have developed and popularized rapidly, and how to provide more ubiquitous and integrated location services has become the focus of the academic and industrial circles. In an outdoor environment, satellite positioning technology can provide people with convenient positioning services and support vehicle navigation, cargo tracking and other applications; however, satellite navigation technology has the disadvantages of serious obstruction in a complex urban environment and insufficient number of visible stars. Relying solely on the Global Navigation Satellite System (GNSS) will not be able to meet the stringent requirements of high precision, high reliability and low delay for positioning performance proposed by future location service-based application scenarios such as autonomous driving vehicles, intelligent transportation and intelligent manufacturing.

[0003] As an alternative to GNSS, 5G positioning currently provides location information required by various applications for assisted positioning. Moreover, as a revolutionary communication technology, 5G innovatively adopts new technologies such as millimeter waves and large-scale multiple-input multiple-output antennas, and has the characteristics of ultra-high data rate, ultra-low delay and large-scale device connection, which will have the opportunity to greatly expand the coverage of navigation services and achieve unprecedented positioning accuracy and reliability.

[0004] However, 5G positioning currently also has some deficiencies. In a 5G cellular network environment, as a user equipment (UE) moves, the distance between a base station (BS) and the UE also changes rapidly, and near-far effects will cause great changes in the noise covariance observed by 5G. In addition, buildings and trees in urban canyons block, reflect and refract a part of the signal, resulting in non-line-of-sight (NLoS) propagation. NLoS signals will seriously affect the measurement of time of arrival (TOA) and angle of arrival (AOA). In particular, for AOA observations, the error caused by NLoS may be greater than 10°. Therefore, due to the changes in line-of-sight (LoS) / NLoS, the changes in observation noise are further exacerbated.

[0005] The above-mentioned 5G positioning method is usually realized through a fusion filter, such as an extended Kalman filter (EKF). In the EKF, the covariance matrix R of the observation noise is a hyperparameter. The 5G positioning method mentioned at present usually assumes that the observation covariance R is constant. Due to the UE movement and NLoS, the constant observation covariance cannot adapt to the time-varying 5G observation noise, which greatly reduces the positioning accuracy and system convergence. In order to overcome the influence of time-varying measurement noise, adaptive positioning methods appear. The adaptive Kalman filter (AKF) can be used to estimate the time-varying noise covariance. For example, the Sage-Husa AKF (SHAKF) recursively estimates the noise statistics based on the maximum a posteriori criterion. However, as a suboptimal filter, it cannot guarantee to converge to the correct noise covariance matrix, which may lead to divergence of the system. Although this method performs well in the LOS condition, it has deficiencies in more complex scenarios such as NLOS. Therefore, although different adaptive methods are proposed, they are not the best choice for 5G positioning in the scene where the observation noise changes rapidly and greatly. SUMMARY

[0006] In order to meet the demand for more efficient 5G positioning, the present application proposes an adaptive 5G positioning technology based on variational Bayesian adaptive Kalman filter (VBAKF). It can adaptively estimate R to match the actual noise level, has high real-time capability, and can estimate R of EKF according to UE-BS distance, motion state of UE and LoS / NLoS condition.

[0007] To achieve the above-mentioned purpose, the present application provides the following scheme: a 5G adaptive filtering positioning method in a noise rapidly changing environment, comprising:

[0008] Through the positioning algorithm of time of arrival and angle of arrival, the positioning filtering process is analyzed to obtain index factors affecting positioning accuracy and reliability;

[0009] Based on the variational Bayesian adaptive filtering method, 5G channel simulation is performed on the index factors to obtain simulation results;

[0010] Based on the simulation results, 5G distance and angle observation are extracted, and the positioning distance is calculated based on the 5G distance and angle observation to obtain the positioning results.

[0011] Preferably, the index factors include the distance between the user equipment and the base station;

[0012] The process of obtaining the distance between the user equipment and the base station comprises,

[0013] combining measurement values of base stations to obtain an observation vector

[0014] combining the observation vector with a state of the user equipment to obtain a distance between the user equipment and the base station;

[0015] the observation vector is expressed as:

[0016]

[0017] wherein, are zero-mean additive white Gaussian noises, and their standard deviations are and s[n] is a state of the user equipment;

[0018] is a real-valued nonlinear observation function, which links the observation vector with the state of the user equipment through the following equation:

[0019]

[0020]

[0021]

[0022] wherein, denotes a 3D distance between the user equipment and the kth base station;

[0023] and denote distances between the user equipment and the kth base station in x, y and z directions respectively, and p[n] denotes a clock offset of the user equipment relative to a global navigation satellite system time.

[0024] Preferably, the index factor comprises a motion state of the user equipment;

[0025] The process of obtaining the motion state of the user equipment comprises,

[0026] The state of the user equipment is defined as:

[0027]

[0028] wherein, p[n] = [x[n], y[n], z[n]] T and v[n] = [v x [n], v y [n], v z [n]] Tis the 3D position and velocity vector of the user equipment to be estimated, and p[n] and f[n] are two parameters of the user equipment clock model;

[0029] The evolution of the user equipment state is characterized using a continuous white noise acceleration model, assuming that the velocity of the user equipment is constant between two consecutive epochs and is subject to small random variations, and the joint linear model of the state transition is expressed as:

[0030] s[n] = Fs[n - 1] + w[n] (6)

[0031] where the state transition matrix F e 8×8 is given by:

[0032]

[0033] where the four upper-left elements of the matrix F represent the constant velocity model, At represents the interval between two consecutive estimates, and the matrix F C is used to describe the user equipment clock bias;

[0034] It is assumed that the process noise w[n] is a zero-mean Gaussian variable, i.e. w[n] ~ N(0, Q), where Q e 8×8 is a diagonal covariance as follows:

[0035]

[0036] where s v represents the standard deviation of the user equipment velocity, s ε represents the standard deviation of the clock bias noise.

[0037] Preferably, the process of 5G channel simulation of said indicator factor comprises,

[0038] The observation covariance of the Kalman filter is estimated according to the distance between the user equipment and the base station, the motion state of the user equipment and the line-of-sight / non-line-of-sight conditions.

[0039] Preferably, the process of estimating the observation covariance of the Kalman filter according to the distance between the user equipment and the base station, the motion state of the user equipment and the line-of-sight / non-line-of-sight conditions comprises,

[0040] Based on the centralized Kalman filter, the prior state estimate and its covariance matrix P - [n] at the n-th epoch are obtained, represents the prior state estimate, i.e. obtained from the observations but not including y[n], represents the posterior estimate, i.e. obtained from the observations and including y[n];

[0041]

[0042] P - [n]=FP + [n-1]F T +Q[n] (10)

[0043] where F is the state transition matrix given by (7) and Q[n] is the state noise covariance matrix given by (8);

[0044] In centralized Kalman filtering, the formula expression of the posterior estimation process is:

[0045] K[n]=P - [n]H[n] T (H[n]P - [n]H[n] T +R[n]) -1 (11)

[0046]

[0047] P + [n]=(I-K[n]H[n])P - [n] (13)

[0048] where K[n] represents the filter gain at the nth epoch, P + [n] represents the covariance matrix of the posterior estimation, and R[n] represents the covariance matrix of the observation noise;

[0049] Suppose the initial state and the initial covariance matrix are known, the prediction stage of the Kalman filter can be directly applied due to the linear state transition model, and the Jacobian matrix in (11) to (13) is written as the derivative of h with respect to s - [n] is further rewritten as H = H BS ∈ 3K×7 , which represents the element of the matrix in the i-th row and the j-th column.

[0050] Preferably, based on the simulation results, 5G distance and angle observations are extracted, and a process of calculating a positioning distance based on the 5G distance and angle observations includes,

[0051] ​At zero initial time, the system state s[0] and the hyperparameters of noise α0 and β0 are initialized, and then the prediction stage is entered. After observing at a certain n-1 time, the time update is performed according to the system state equation, the mean and variance of the system state variable are predicted, and the time recursion of the variance distribution parameter of the observation noise is performed. According to the maximum entropy constraint theorem, the hyperparameters of the inverse gamma distribution are taken;

[0052] Then the update stage is entered. After obtaining the observation at time n, the noise variance and the system state are estimated. The loop iteration calculation is performed in this way until the algorithm converges, and then the next prediction-update step is continued.

[0053] Preferably, after observing at a certain n-1 time, the time update is performed according to the system state equation, and the process of predicting the mean and variance of the system state variable includes,

[0054] According to the Bayesian criterion, the posterior distribution of the model parameter system state and the 5G measurement noise variance is obtained as:

[0055]

[0056] Wherein:

[0057] p(y BS [n]∣y BS [1:n-1])=∫p(y BS [n]∣s[n],R[n])p(s[n],R[n])(y BS [1:n-1])ds[n]dR[n] (20)

[0058] For the last item in formula (19) p(y BS [n]∣y BS [1:n-1],s[n],R[n]) is assumed that the nth observation y BS [n] is irrelevant to the previous observation, it is simplified to p(y BS [n]∣s[n],R[n]) and for a first-order Markov process, it is also:

[0059]

[0060] Integrating s[n-1] and R[n-1], we get:

[0061] p(s[n],R[n]∣y BS [1:n-1])=∫p(s[n]∣s[n-1])p(R[n]∣R[n-1])p(s[n-1],R[n-1]∣y BS [1:n-1])ds[n-1]dR[n-1] (22)

[0062] In the prediction step, the distribution of the parameters depends on the n-1 observations, and after the time update, the prior distribution of the parameters is obtained (22). After the n-th observation update, the prior is corrected according to the Bayes' rule, and the posterior distribution is obtained (19), which provides the input for the prediction step before the n+1 time.

[0063] Preferably, for the time recursion of the observation noise variance distribution parameters, the process of taking the inverse of the hyperparameters of the inverse gamma distribution according to the maximum entropy constraint theorem comprises,

[0064] Assuming that each parameter in (22) is independent of each other, the system state and the observation noise variance respectively obey Gaussian distribution and inverse gamma distribution:

[0065]

[0066] Where d represents the dimension of the observation, μ and P are two parameters of the Gaussian distribution, and α and β are two parameters of the inverse gamma distribution. Based on the variational Bayes learning, after the n-th observation, a new distribution q(s[n], R[n] | y BS [1:n]) is used to replace p(s[n], R[n] | y BS [1:n]).

[0067] Preferably, the process of obtaining the observation noise variance and the system state at time n after the observation comprises,

[0068] The approximate distribution is considered to be factorizable, i.e. q(s[n], R[n] | y BS [1:n]) = q(s[n])q(R[n]), and the dependence of the parameters s[n] and R[n] on y BS [1:n] in the approximate distribution is omitted. The logarithmic expression of each parameter distribution is calculated as:

[0069]

[0070] Where C represents a normalization factor, representing the expectation of the evidence in (20), which is considered as a constant and omitted in the variational Bayes learning;

[0071] After taking the exponential expression on both sides of (24), q(s[n]) = N(s[n] | μ[n], P[n]), and thus:

[0072]

[0073]

[0074]

[0075] Similarly, for the variable R[n], we have:

[0076]

[0077] Therefore, the variance R[n] still obeys inverse gamma distribution, i.e.:

[0078]

[0079] The parameters of the new distribution are:

[0080]

[0081]

[0082] Considering that:

[0083] E s[n] [s[n]s [n]]=μ[n]μ [n]+P[n] (32)

[0084] Expanding the second term of the above equation, we have:

[0085] E s[n] [((y BS [n]-H[n]s[n]) i ) 2 ]=((y BS [n]-H[n]μ[n]) i ) 2 +(H[n]P[n]H [n]) (33)

[0086] Where μ[n] is the two parameters in the new Gaussian distribution of P[n];

[0087] Due to the properties of inverse gamma distribution, each element in equation (27) can be calculated respectively:

[0088]

[0089] Finally, the convergence of the algorithm is judged, and the calculation of the lower bound function can be expressed as follows:

[0090] F[s[n],R[n]]=E q [ln p(s[n],R[n],y BS [1:n-1])]-E q(R[n]) [ln q(s[n])]-E q(s[n] [ln q(R[n])] (35)

[0091] When |F (m) [s[n],R[n]]-F (m-1)When the lower bound value of two adjacent iterations changes can be ignored, that is, when | [n], R[n]]| < Delta, the algorithm is considered to converge, and the next filtering time is entered.

[0092] Compared with the prior art, the present application has the following advantages and technical effects:

[0093] Based on the variational Bayesian method, the noise covariance matrix in the filtering process can be adaptively estimated according to the UE-BS distance, the motion state of the UE and the LoS / NLoS condition, has high real-time performance, and can solve the problem of positioning performance degradation caused by sharp noise change in a complex environment. BRIEF DESCRIPTION OF DRAWINGS

[0094] The accompanying drawings, which form a part of this application, are included to provide a further understanding of the application and are incorporated in and constitute a part of this application. The embodiments of this application and their description together with the drawings serve to explain the application. In the drawings:

[0095] Figure 1 The figure is a schematic diagram of the system structure of the embodiment of the present application. DETAILED DESCRIPTION

[0096] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict. The present application will be described in detail below with reference to the drawings and in combination with the embodiments.

[0097] It should be noted that the steps shown in the flowchart of the drawings can be executed in a computer system such as a group of computer executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described herein can be executed in an order different from that shown herein.

[0098] As Figure 1 shown, the 5G adaptive filtering positioning method in a noise sharp change environment provided by the present application comprises:

[0099] Through the time of arrival and the angle of arrival positioning algorithm, the positioning filtering process is analyzed to obtain the index factors affecting the positioning accuracy and reliability;

[0100] Based on the variational Bayesian adaptive filtering method, the index factors are simulated by 5G channel simulation to obtain simulation results;

[0101] Based on the simulation results, 5G distance and angle observation are extracted, and the positioning distance is calculated based on the 5G distance and angle observation to obtain the positioning results.

[0102] Further, the system model

[0103] 1、BS observation

[0104] The measurements of the kth BS can be combined into the following joint measurement equation:

[0105]

[0106] where, are zero-mean additive Gaussian white noises, and their standard deviations are and s[n] is the state of the UE. is a real-valued nonlinear observation function that relates the observation vector to the UE state through the following equation:

[0107]

[0108]

[0109]

[0110] where, denotes the 3D distance between the UE and the kth BS. and denote the distances between the UE and the kth BS in the x, y, and z directions, respectively. p[n] denotes the clock bias of the UE with respect to the GNSS system time.

[0111] 2. UE state equation

[0112] The state of the UE is defined as:

[0113]

[0114] where, p[n] = [x[n], y[n], z[n]] T and v[n] = [v x [n], v y [n], v z [n]] T are the 3D position and velocity vectors of the UE to be estimated. p[n] and f[n] are two parameters of the UE clock model. Here, a Continuous White Noise Acceleration (CWNA) model is used to represent the evolution of the UE state. It is assumed that the velocity of the UE is constant between two adjacent epochs and is disturbed by small random changes. The joint linear model of the state transition can be represented as:

[0115] s[n] = Fs[n - 1] + w[n] (6)

[0116] where the state transition matrix F e 8×8 is given by:

[0117]

[0118] where the top-left four elements of the matrix F represent the constant velocity model, Δt represents the interval between two consecutive estimates. The matrix F C The UE clock bias is described. Assume that the process noise w[n] is a zero-mean Gaussian variable, i.e., w[n] ~ N(0, Q), where Q e 8×8 is a diagonal covariance as follows:

[0119]

[0120] where σ v represents the standard deviation of the UE velocity, σ ε represents the standard deviation of the clock bias noise.

[0121] 3. Centralized EKF

[0122] The process of estimating the observation covariance of the Kalman filter according to the distance between the user equipment and the base station, the motion state of the user equipment and the line-of-sight / non-line-of-sight condition comprises,

[0123] represents the prior state estimate, i.e., obtained from the observations but not including y[n]. represents the posterior estimate, i.e., obtained from the observations and including y[n]. For the centralized EKF, the prior state estimate and its covariance matrix P - [n] can be written as follows:

[0124]

[0125] P - [n] = FP + [n-1]F T + Q[n] (10)

[0126] where F is the state transition matrix given in (7) and Q[n] is the state noise covariance matrix given in (8). The posterior estimate process of in the centralized EKF can be written as follows:

[0127] K[n] = P - [n]H[n] T (H[n]P - [n]H[n] T + R[n]) -1 (11)

[0128]

[0129] P+ [n] = (I - K[n]H[n])P - [n] (13)

[0130] where K[n] denotes the filter gain at the nth epoch, P + [n] denotes the covariance matrix of the posteriori estimation. R[n] denotes the covariance matrix of the observation noise, which is also an important parameter related to the positioning performance in the adaptive filtering process. Assume the initial state and the initial covariance matrix are known.

[0131] Due to the linear state transition model, the prediction stage of EKF can be applied directly. The Jacobian matrix in (11) to (13) is written as the derivative of h with respect to s - [n]. If it is rewritten as H = H BS ∈ 3K×7 , it is intuitive that it contains the elements related to the BS. denotes the element in the i-th row and j-th column of the matrix.

[0132] Based on the simulation results, 5G distance and angle observations are extracted, and a process for calculating a positioning distance based on the 5G distance and angle observations includes,

[0133] Like the classic Kalman filter, the variational Bayesian Kalman filter can be divided into two steps: prediction (time update) and update (data update).

[0134] First, initialization, at zero initial time, the system state s[0] and the hyperparameters of the noise α0 and β0 are initialized.

[0135] Then enter the prediction stage, after observing at some n-1 time, according to the system state equation, the time update is performed, first the mean and variance of the system state variable are predicted, as follows:

[0136] μ - [n] = F[n] μ[n-1] (36)

[0137] P - [n] = F[n] P[n-1] F[n] + Q[n] (37)

[0138] For the time recursion of the variance distribution parameter of the observation noise, according to the maximum entropy constraint theorem, the hyperparameters of the inverse gamma distribution are taken:

[0139]

[0140]

[0141] where λ is a varying factor in (0, 1], which is introduced to make the time-varying variance σ 2 It is able to vary with a certain probability distribution, such as inverse gamma distribution, even if the posterior and prior have the same form of probability density function. This will provide algorithmic guarantee and computational convenience for variational Bayesian learning.

[0142] After that, the update phase is entered, and after obtaining the observation at time n, the noise variance and system state can be estimated. It is necessary to calculate (34), (25)-(27), (30), (31) respectively. The specific process of the algorithm is shown in Figure 1 .

[0143] Note that in the above update step, not only the estimation of the system state variable statistical moment such as the mean μ[n] and the covariance P[n] needs to determine the noise variance, but also the calculation of the noise variance needs the hyperparameters α and β, and the known μ[n] and P[n] are also needed in the parameter update equations (30) and (31). The loop iteration calculation is carried out in this way until the algorithm converges, and then the next prediction-update step is continued.

[0144] Further, the VBAKF method

[0145] 1. Preparation

[0146] In order to solve the problems of position estimation and adaptive R estimation, the core task is to estimate a series of parameters θ based on prior knowledge, i.e. 5G AOA / TOA observation y. Through the Bayesian criterion, the posterior distribution of θ is expressed as follows:

[0147]

[0148] One of the key steps is to calculate the denominator of the above formula, also known as the evidence or marginal likelihood function. When the number of parameters increases, the above integral will be difficult or even impossible to solve. Considering the efficiency of numerical calculation methods such as Markov chain Monte Carlo (MCMC) method, variational Bayesian learning can approximately obtain the posterior distribution. This method proposes a VB-based AKF that can approximate the true posterior distribution. Taking the logarithm of the denominator in the above formula and applying the elementary Jensen inequality, we have:

[0149]

[0150] where F(q(θ)) is derived from statistical physics and is the negative of the free energy. The marginal likelihood function can be mathematically processed as:

[0151]

[0152] where, D KL(q(θ) P(θ|y)) is defined as Kullback-Leibler (KL) divergence. When the new distribution q(θ) equals the true posterior p(θ|y), the DKL reaches the minimum value, which is zero, while F(q(θ)) reaches the maximum value. Therefore, we can use F(q(θ)) as a lower bound of Inp(y), and approximate q(θ) to p(θ|y) by maximizing F(q(θ)) continuously. The general solution of q(θ) can be obtained by taking the derivative of F(q(θ)) with respect to q(θ) and setting it to zero as follows:

[0153]

[0154] where, [·] represents the mathematical expectation of q(θ k≠i ). It is assumed that the joint probability density function of the parameter set approximation distribution can be decomposed into the product of independent distribution of each parameter. This assumption is the core of variational Bayesian learning, which has great computational advantage in solving posterior distribution. The theoretical basis of this assumption first appeared in the field of mean field theory, and many papers on variational Bayesian methods have also proved the feasibility and convenience of the theory and its practical application. Therefore, the multivariate joint probability distribution p(θ) can be approximated as the product of the marginal distribution q(θi) of each variable, so that the joint estimation of multiple variables can be easily converted into iterative estimation of the marginal distribution of these variables, thereby greatly reducing the complexity of the calculation.

[0155] According to equation (17), variational Bayesian learning can be summarized as follows: for each parameter to be estimated, a new distribution of the parameter is obtained by calculating the expectation of the joint probability density function with respect to the distribution of other parameters, until the lower bound F(q(θ)) reaches the maximum value. This involves the convergence problem of the variational Bayesian algorithm, that is, to determine when the lower bound reaches the maximum value. The lower bound can be expressed as:

[0156]

[0157] where, [·] represents the expectation of the expression [·] with respect to the random variables in θ i except θ . The lower bound function is a convex function with respect to all q(θ), and increases with the iterative loop estimation. According to the properties of convex functions, the lower bound F[q(θ)] must converge, and the curve gradient tends to be smooth. In this method, the difference between the lower bounds of the adjacent two iterations can be used as a basis for judging convergence. When the difference is less than a certain threshold, it can be judged that the algorithm converges and the estimation result is obtained. Therefore, the variational Bayesian parameter iterative estimation is essentially a gradient descent algorithm.

[0158] It is noted that according to the form of equation (17), if the prior distribution of the parameters to be estimated is reasonably chosen in the Conjugate-Exponential family (CE), its approximate distribution will also be a posterior distribution with the same form but different parameters. The CE family is a widely used distribution family, and most commonly used distributions belong to this family. In the following derivation, we will also see the computational convenience brought by the reasonable choice of CE distribution.

[0159] 2. Parameter estimation derivation

[0160] In this model, the posterior distribution of the parameter system state and 5G measurement noise variance is expressed as:

[0161]

[0162] Where:

[0163] p(y BS [n]∣y BS [1:n-1])=∫p(y BS [n]∣s[n],R[n])p(s[n],R[n])(y BS [1:n-1])ds[n]dR[n] (20)

[0164] For the p(y BS [n]∣y BS [1:n-1],s[n],R[n]) in the second last item of equation (19), assuming that the nth observation y BS [n] is independent of previous observations, it can be simplified to p(y BS [n]∣s[n],R[n]), and for a first-order Markov process, we have:

[0165]

[0166] Integrating s[n-1] and R[n-1], we get the following Chapman-Kolmogorov (CK) equation:

[0167] p(s[n],R[n]∣y BS [1:n-1])=∫p(s[n]∣s[n-1])p(R[n]∣R[n-1])p(s[n-1],R[n-1]∣y BS [1:n-1])ds[n-1]dR[n-1] (22)

[0168] Thus, in the Bayesian filtering theory, each step of the recursive filtering algorithm can be seen as consisting of a prediction (22) and an update (19). In the prediction step, the distribution of the parameters depends on the observations up to n - 1. After the time update, the prior distribution of the parameters is obtained (22). After the update with the n-th observation, the prior is corrected according to the Bayes' rule to obtain the posterior distribution (19), which provides the input for the prediction step at the time n + 1. Moreover, note that in this prediction-update step, the integrals in (20) and (22) cannot be solved analytically, except for some very simple special cases, even if the system has been assumed Gaussian-linear up to now.

[0169] Now assume that the parameters in (22) are independent, and that the system state and the observation noise variance are Gaussian and inverse-Gaussian distributed, respectively, according to the prior knowledge:

[0170]

[0171] where d denotes the dimension of the observation. μ and P are the two parameters of the Gaussian distribution. α and β are the two parameters of the inverse-Gaussian distribution. Based on the variational Bayesian learning, the following approach is proposed: after the n-th observation, replace p(s[n], R[n] \ y BS [1:n]) by a new distribution q(s[n], R[n] \ y BS [1:n]). Similarly, the approximate distribution is also assumed to be factorizable, i.e., q(s[n], R[n] \ y BS [1:n]) = q(s[n])q(R[n]). Here, for notational simplicity, the dependence of the parameters s[n] and R[n] on y BS [1:n] is omitted in the approximate distribution. According to the expression of the general solution (17), the log expression of the parameter distribution is calculated as:

[0172]

[0173] where C denotes the normalization factor, representing the expectation of the evidence in (20), which is considered as a constant and omitted in the variational Bayesian learning.

[0174] After taking the exponential expression on both sides of (24), it is found that q(s[n]) is a Gaussian distribution with a new mean and variance. This is due to the advantage of choosing the prior distribution in the conjugate exponential function domain described before: q(s[n]) = N(s[n] \ μ[n], P[n]), thus we have:

[0175]

[0176]

[0177]

[0178] Similarly, for the variable R[n] we have:

[0179]

[0180] Therefore, the variance R[n] still follows an inverse gamma distribution, i.e.,

[0181]

[0182] The parameters of the new distribution are:

[0183]

[0184]

[0185] The above two equations are also called parameter update equations in variational Bayesian learning, considering that:

[0186] E s[n] [s[n]s [n]]=μ[n]μ [n]+P[n] (32)

[0187] Expanding the second term of the above equation we have:

[0188] E s[n] [((y BS [n]-H[n]s[n]) i ) 2 ]=((y BS [n]-H[n]μ[n]) i ) 2 +(H[n]P[n]H[n]) (33)

[0189] where μ[n] are the two parameters in the new Gaussian distribution of P[n]. Due to the properties of the inverse gamma distribution, each element in equation (27) can be calculated separately:

[0190]

[0191] Finally, the convergence of the algorithm is judged. The lower bound function can be calculated as follows:

[0192] F[s[n],R[n]]=E q [ln p(s[n],R[n],y BS [1:n-1])]-E q(R[n]) [ln q(s[n])]-E q(s[n]) [ln q(R[n])] (35)

[0193] When |F(m) [s[n],R[n]]-F (m-1) When [s[n],R[n]]|<Δ (Δ is a small quantity), that is, the change of the lower bound value in the adjacent two iterations can be ignored, it can be considered that the algorithm converges, and the next filtering time is entered.

[0194] In this way, the formulas (24)-(25) form a variational Bayesian learning algorithm for real-time joint iterative estimation of state variables and observation noise variance. In the following, by combining the algorithm with the Kalman filtering algorithm, a new adaptive filter can be obtained.

[0195] Based on the variational Bayesian method, the noise covariance matrix in the filtering process can be adaptively estimated according to the UE-BS distance, the motion state of the UE and the LoS / NLoS condition, which has high real-time performance and can solve the problem of positioning performance degradation caused by sharp changes in noise in complex environments.

[0196] The above is only a preferred specific embodiment of the present application, but the protection scope of the present application is not limited thereto, any person skilled in the art can easily think of changes or replacements within the technical range disclosed in the present application, which should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A 5G adaptive filtering positioning method for environments with rapidly changing noise, characterized in that, include: By analyzing the positioning filtering process using positioning algorithms based on arrival time and angle of arrival, we can identify the key factors affecting positioning accuracy and reliability. Based on the variational Bayesian adaptive filtering method, the aforementioned index factors are simulated using a 5G channel to obtain simulation results. Based on the simulation results, 5G distance and angle observations are extracted, and the positioning distance is calculated based on the 5G distance and angle observations to obtain the positioning result; The process of extracting 5G distance and angle observations based on the simulation results, and calculating the positioning distance based on the 5G distance and angle observations, includes the following steps: At instant zero, initialize the system state. Hyperparameters of noise and Then, the prediction phase begins. After observation at a certain n-1 time, the system state equation is updated over time to predict the mean and variance of the system state variables. For the time recursion of the observed noise variance distribution parameters, the hyperparameters of the inverse gamma distribution are taken according to the maximum entropy constraint theorem. Then, the update phase begins. After obtaining the observations at time n, the noise variance and system state are estimated. This process is repeated iteratively until the algorithm converges, and then the next prediction-update step is performed. The index factors include the distance between the user equipment and the base station; The process of obtaining the distance between the user equipment and the base station includes, The measurements from the base stations are combined to obtain the observation vector. ; The observation vector Communicate with the user equipment status to obtain the distance between the user equipment and the base station. The observation vector The formula expression is: in, It is zero-mean additive white Gaussian noise, and their standard deviations are respectively , and , It refers to the status of the user equipment; It is a real-valued nonlinear observation function, which uses the following equation to express the observation vector. Related to user equipment status: in, This represents the 3D distance between the user equipment and the k-th base station; , and This represents the distance between the user equipment and the k-th base station in the x, y, and z directions, respectively. This represents the clock offset of the user equipment relative to the time of the Global Navigation Satellite System; The indicator factors include the motion status of the user equipment; The process of acquiring the motion state of the user equipment includes, The state of the user equipment is defined as follows: in, and These are the 3D position and velocity vectors of the user equipment that need to be estimated, and ρ[n] and φ[n] are two parameters of the user equipment clock model; The evolution of user equipment (UE) states is characterized using a continuous white noise acceleration model. It is assumed that the UE's speed is constant between two adjacent epochs and subject to small random variations. The joint linear model of state transitions is expressed as follows: Where the state transition matrix Given below: Among them, matrix The four elements in the top left corner represent a constant velocity model. The matrix represents the interval between two consecutive estimates. Used to describe the clock offset of user equipment; Assuming process noise It is a zero-mean Gaussian variable, that is ,in The diagonal covariance is as follows: in, The standard deviation of user equipment speed, This represents the standard deviation of clock skew noise; The process of performing 5G channel simulation on the aforementioned indicator factors includes: The observation covariance of the Kalman filter is estimated based on the distance between the user equipment and the base station, the motion state of the user equipment, and the line-of-sight / non-line-of-sight conditions. The process of estimating the observation covariance of the Kalman filter based on the distance between the user equipment and the base station, the motion state of the user equipment, and line-of-sight / non-line-of-sight conditions includes, Based on centralized Kalman filtering, the prior state estimate of the nth epoch is obtained. and its covariance matrix , This represents the prior state estimate, which is obtained from observations but does not include... , This represents a posterior estimate, which is obtained from the observations and includes... ; in, yes Given the state transition matrix, yes The given state noise covariance matrix; In centralized Kalman filtering The formula for the posterior estimation process is: in, This represents the filter gain at the nth epoch. Denotes the covariance matrix of the posterior estimate. The covariance moment representing the observation noise; Assuming the initial state and the initial covariance matrix It is known that, based on a linear state transition model, directly applying Kalman filtering in the prediction stage... to Jacobi matrix in Being written is right The derivative of is further rewritten to include elements related to BS. , This represents the element in the i-th row and j-th column of the matrix.

2. The 5G adaptive filtering positioning method in a rapidly changing noise environment according to claim 1, characterized in that, After an observation at a certain time n-1, the process of updating the system state equation over time and predicting the mean and variance of the system state variables includes: Using the Bayesian criterion, the posterior distributions of the model parameters, system state, and 5G measurement noise variance are expressed as follows: in: For the formula The second to last item Assume the nth observation If it is unrelated to previous observations, then it is simplified to For a first-order Markov process, we also have: right and Integrating, we get: In the prediction step, the distribution of the parameters depends on n-1 observations. After time updates, the prior distribution of the parameters is obtained. After the nth observation update, the prior is corrected according to Bayes' criterion to obtain the posterior distribution. This provides input for the prediction steps up to time n+1.

3. The 5G adaptive filtering positioning method in a rapidly changing noise environment according to claim 2, characterized in that, For the time recursion of the observed noise variance distribution parameters, the process of obtaining the hyperparameters of the inverse gamma distribution according to the maximum entropy constraint theorem includes the following: Assumption The parameters in the system are independent of each other, and the variances of the system state and observation noise follow Gaussian and inverse gamma distributions, respectively. Where d represents the dimension of the observations, μ and P are two parameters of the Gaussian distribution, and α and β are two parameters of the inverse gamma distribution. Based on variational Bayesian learning, after the nth observation, a new distribution is used. replace .

4. The 5G adaptive filtering positioning method in a rapidly changing noise environment according to claim 2, characterized in that, After obtaining the observations at time n, the noise variance and system state are estimated. This iterative calculation process includes: The approximate distribution is considered to be factorably decomposable, i.e. = Parameters omitted and In the approximate distribution The dependency relationship is given by the logarithmic expression for calculating the distribution of each parameter: Where C represents the normalization factor, representing The expected value of the evidence is considered a constant and omitted in variational Bayesian learning; exist After taking the exponential expression on both sides of , Therefore, we have: Similarly, for variables have: Therefore, variance It still follows an inverse gamma distribution, that is: The parameters of the new distribution are: Considering: Expanding the second term of the above equation, we get: in yes Two parameters in the new Gaussian distribution; Due to the properties of the inverse gamma distribution, equation Each element in the matrix is ​​calculated separately: Finally, the convergence of the algorithm is judged, and the calculation of the lower bound function is expressed as follows: when < When the change in the lower bound value between two adjacent iterations is ignored, the algorithm is considered to have converged, and the process proceeds to the next filtering time.

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