A method for estimating the lower bound of error in a 5G indoor integrated positioning system

Abstract

The application discloses a 5G indoor combined positioning system error lower bound estimation method, comprising the following steps: establishing a TDOA observation quantity non-Gaussian mixed initial model, and giving an original estimated value; and extracting observation noise and positioning noise data sets from observation data, iteratively estimating model parameters by using an expectation maximization algorithm, and approximating the true distribution of the data set; introducing measurement constraint information, expanding the Fisher information matrix, and obtaining a close first error lower bound estimation value; deriving the ZZB boundary of the fingerprint positioning algorithm according to the propagation model of the CSI signal, introducing a Bayesian estimation framework and prior position information, and giving an effective second error lower bound estimation value; and combining the two estimation values to give a positioning error lower bound suitable for the 5G indoor combined positioning system, which serves as a basis for 5G indoor combined positioning system performance evaluation. The application can overcome the 5G PRS signal indoor scene non-linear and non-Gaussian noise problems, and realize accurate system error lower bound evaluation.

Description

Technical Field

[0001] This invention belongs to the field of indoor positioning service technology, and particularly relates to an error lower bound estimation method for a 5G indoor integrated positioning system. Background Technology

[0002] Indoor positioning services, as a crucial component of location-based services, have been widely applied in key areas such as autonomous navigation for intelligent robots, guidance for people with disabilities, and disaster emergency search and rescue positioning, greatly facilitating people's daily lives. At the theoretical level, analytical methods based on geometric error propagation models remain the core analytical approach, revealing the chain effect of observation signal errors on position estimation bias through mathematical statistical modeling. In recent years, with the development of artificial intelligence technology, performance analysis of nonlinear positioning models containing machine learning or deep learning algorithms has become a research hotspot. Traditional performance analysis metrics are represented by root mean square error (RMSE) and mean variance. RMSE, by calculating the root mean square deviation between the estimated position and the true position, comprehensively reflects the overall level of systematic and random errors; mean variance focuses on the fluctuation characteristics of position estimation. Furthermore, researchers have introduced a lower bound for positioning error as a theoretical benchmark for performance evaluation. The Cramero lower bound (CRLB), based on parameter estimation theory, provides a theoretical lower bound for the mean square error of the estimator under the unbiased estimation assumption by calculating the inverse matrix of the Fisher information matrix. In positioning scenarios, the derivation of the traditional CRLB requires consideration of signal propagation models, noise distribution characteristics, and observation geometry. For geometric positioning systems, researchers have established statistical models of signal arrival time and error distribution models of time difference of arrival, typically assuming that the error follows a Gaussian distribution. For fingerprint positioning systems, a common method is based on Fisher information theory, utilizing the relationship between the variable to be estimated and the random variable of the observed signal to find the negative reciprocal of the trace of the Fisher information matrix as the minimum of the theoretical variance between the estimated value and the true value of the unknown parameter.

[0003] However, existing methods have significant problems when applied to 5G indoor integrated positioning systems. First, the signal observation error distribution does not conform to the Gaussian assumption. In indoor environments, due to structural irregularities, signal reflection and diffraction, and dynamic changes in the environment (such as personnel movement and door opening and closing), the signal propagation path becomes complex, thus affecting signal delay and strength. These changes are reflected in the error distribution, manifesting as various statistical characteristics, such as mean, variance, and distribution shape, which are difficult to conform to the Gaussian distribution in conventional performance analysis models. Second, the location estimation method does not conform to the unbiased estimation assumption. Currently, fingerprint positioning algorithms mostly employ machine learning or deep learning methods, and these positioning models are not theoretically rigorous unbiased estimators. Furthermore, the non-uniformity of fingerprint collection density and distribution, as well as the uncertainty of the indoor signal propagation environment, all affect the location estimation results, causing the estimated values ​​to fail to meet the unbiased estimation assumption, rendering traditional error lower bound calculation methods unusable. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes an error lower bound estimation method for a 5G indoor integrated positioning system, thereby resolving the issues present in the prior art.

[0005] To achieve the above objectives, in a first aspect, the present invention provides a method for estimating the lower bound of the error in a 5G indoor integrated positioning system, comprising:

[0006] Based on the 5G PRS channel characteristics of the 5G indoor integrated positioning system, a non-Gaussian mixture initial model of TDOA observations is established, and the original estimated values ​​are given. Then, by extracting the observation noise and positioning noise data sets from the observation data, the model parameters are estimated iteratively using the expectation-maximization algorithm to approximate the true distribution of the dataset.

[0007] By introducing measurement constraint information and expanding the Fisher information matrix, a tight estimate of the first lower bound of error is obtained;

[0008] Based on the propagation model of CSI signals, the ZZB boundary of the fingerprint localization algorithm is derived. A Bayesian estimation framework and prior location information are introduced to give an effective estimate of the second lower bound of error.

[0009] The first lower bound estimate and the second lower bound estimate are combined to give a lower bound for the positioning error applicable to the 5G indoor integrated positioning system, which serves as the basis for performance evaluation of the 5G indoor integrated positioning system.

[0010] Preferably, the steps for establishing a non-Gaussian mixture initial model of TDOA observations based on the 5G PRS channel characteristics of the 5G indoor integrated positioning system include:

[0011] Define the location and base station coordinates, calculate the TDOA observation value based on the base station coordinates, and assume the measurement error distribution;

[0012] Define the probability density function of the mixture T distribution, introduce latent variables, and construct the likelihood function;

[0013] The posterior probability is calculated in the E-step of the expectation-maximization algorithm, and the parameters are updated in the M-step to obtain the k-value, mean, variance, and degrees of freedom based on the mixed T-distribution.

[0014] Preferably, in the non-Gaussian mixture initial model of the TDOA observation, the mixture T-distribution is used to model heavy-tailed noise by weighting multiple T-distributions, each component corresponding to a different error source, and the PDF of the T-distribution contains gamma function terms and polynomial terms.

[0015] Preferably, in the maximum expectation algorithm, when calculating the posterior probability in the E-step, according to Bayes' theorem, the posterior probability is proportional to the product of the prior weight and the likelihood term. The denominator is normalized, and the contribution of each observation is allocated to each mixture component according to probability.

[0016] Preferably, in the maximum expectation algorithm, when updating parameters in step M, the mixed weights are updated to the mean of the posterior probabilities of each component, and the degrees of freedom are solved numerically by maximizing the following formula, and optimized using the Newton-Raphson iteration method.

[0017] Preferably, the step of introducing measurement constraint information to expand the Fisher information matrix includes:

[0018] Based on FIM, measurement constraint information is introduced through additional FIM blocks, which are in the form of block diagonal matrices;

[0019] The constraint information matrix is ​​superimposed on the original FIM to obtain the constraint-aware FIM, and the constrained extended Fisher matrix is ​​obtained through block matrix operations.

[0020] Preferably, the step of deriving the ZZB boundary of the fingerprint localization algorithm based on the propagation model of the CSI signal includes:

[0021] In indoor positioning scenarios, deploy a wireless access point, each AP is equipped with N antennas to form a MIMO system, and pre-collect CSI fingerprint data of each reference point in the positioning area;

[0022] The location estimation is modeled as a Bayesian inference problem. Two competing hypotheses are constructed, assuming that each measurement is independent, to obtain the joint likelihood of the observation data.

[0023] The optimal decision rule is obtained through the joint likelihood, and the influence of all displacements is taken into account to obtain the LPEB suitable for CSI fingerprint localization.

[0024] Preferably, in the fingerprint positioning algorithm, if the actual positioning error exhibits directional anisotropy, the off-diagonal elements of the covariance matrix are adjusted in conjunction with the scene map to characterize the spatial correlation of the error.

[0025] Preferably, the step of combining two error lower bounds to provide a positioning error lower bound applicable to a 5G indoor integrated positioning system includes:

[0026] For the lower bound of the error in the geometric positioning part, the first information matrix is ​​obtained according to the formula, and the reciprocal of its trace is the lower bound of the error covariance.

[0027] For the fingerprint localization part, assuming that the lower bound given by ZZB is the isotropic error, the diagonal covariance matrix is ​​obtained, and the second information matrix is ​​obtained through the diagonal covariance matrix.

[0028] The first information matrix and the second information matrix are weighted and added together. The inverse of the joint information matrix gives the theoretical lower bound of the combined system error.

[0029] In a second aspect, the present invention also discloses a computer program product, including a computer program that, when executed by a processor, implements the steps of the method described in the first aspect.

[0030] Compared with the prior art, the present invention has the following advantages and technical effects:

[0031] This invention provides a method for estimating the lower bound of error in a 5G indoor integrated positioning system, comprising: First, establishing a non-Gaussian mixture initial model of TDOA observations based on the 5G PRS channel characteristics of the 5G indoor integrated positioning system, and providing the original estimated value; then, extracting the observation noise and positioning noise data sets from the observation data, and using the expectation-maximization algorithm to iteratively estimate the model parameters to approximate the true distribution of the dataset; second, introducing measurement constraint information to expand the Fisher information matrix and obtain a tight first lower bound estimate of error; next, deriving the ZZB boundary of the fingerprint positioning algorithm based on the propagation model of the CSI signal, introducing a Bayesian estimation framework and prior location information, and providing an effective second lower bound estimate of error; finally, combining the first lower bound estimate of error with the second lower bound estimate of error to provide a positioning error lower bound applicable to the 5G indoor integrated positioning system, which serves as the basis for performance evaluation of the 5G indoor integrated positioning system.

[0032] To address the issue of non-Gaussian distribution of observation errors caused by indoor multipath interference, this invention proposes a method for calculating the lower bound of errors in a combined positioning system that integrates observation constraint information. For the TDOA geometric positioning system, this invention proposes a TDOA error modeling method based on a mixed t-distribution and expands the information content of the original Fisher matrix by modeling the observation information as a diagonal matrix, thus obtaining an effective and tight lower bound estimate of the error. Furthermore, considering the dynamic time-varying characteristics of CSI fingerprint positioning, the Ziv-Zakai bound is adopted, utilizing a Bayesian estimation framework and scene prior knowledge to quantify the theoretical accuracy limit of channel feature matching when the error distribution of the observed signal is unknown. This invention is the first to achieve lower bound estimation of errors in a combined geometric positioning and fingerprint matching positioning system, providing a quantifiable performance boundary for multi-algorithm collaborative positioning. Attached Figure Description

[0033] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0034] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0035] Figure 2 This is a flowchart illustrating an example method of an embodiment of the present invention;

[0036] Figure 3 This is a schematic diagram of the experimental environment of an embodiment of the present invention. (a) is a partial site photo, and (b) is a trajectory diagram. Detailed Implementation

[0037] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0038] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0039] Example 1

[0040] like Figure 1 As shown, to address the issues of existing error lower bound calculation methods where the signal observation error distribution does not conform to the Gaussian assumption and the position estimation method does not conform to the unbiased estimation assumption, this embodiment provides an error lower bound estimation method for a 5G indoor integrated positioning system, enabling performance analysis for complex positioning systems. Specifically, it includes:

[0041] S1. Based on the 5G PRS channel characteristics of the 5G indoor integrated positioning system, establish a non-Gaussian mixture initial model of TDOA observations, give the original estimated value, and extract the observation noise and positioning noise data set through the observation data. Use the expectation-maximization algorithm to iteratively estimate the model parameters to approximate the true distribution of the dataset.

[0042] Specifically, the process of establishing the TDOA observation error model:

[0043] Let the position of the target in two-dimensional space be θ = [x, y]. T There are M base stations with coordinates as follows: For any two base stations i and j, their TDOA observations are as shown in formula (1):

[0044]

[0045] Where c is the signal propagation speed (e.g., the speed of light); ∈ ij The measurement error follows a K-component mixture T-distribution. The mixture T-distribution models heavy-tailed noise by weighting multiple T-distributions, with each component corresponding to a different error source (such as LOS / NLOS environments). The PDF of the T-distribution contains a gamma function term Γ(·) and a polynomial term, specifically in the form:

[0046]

[0047] In the formula, Γ(·) is the gamma function, ν controls the thickness of the distribution tail, and σ is the scale parameter. To apply the EM algorithm, a latent variable Z = {z} is introduced. ijk}, where z ijk =1 indicates that the TDOA error of the i,j-th base station is ∈ ij It belongs to the k-th component, otherwise it is 0. For all data, its likelihood function is:

[0048]

[0049] in The set of parameters to be estimated. The latent variable Z identifies the mixture component to which each observation belongs, and the joint likelihood is decomposed into a product of these components. This decomposition allows the posterior probability to be computed in the E-step, thus simplifying the parameter update in the M-step. E-step: Posterior probability computation. Given the current parameter estimate Φ... (t) The posterior expectation of the latent variables is:

[0050]

[0051] in

[0052]

[0053] According to Bayes' theorem, the posterior probability γ ijk Proportional to the prior weight w k Likelihood Term The product of the product. Normalizing the denominator ensures... This step essentially assigns the "contribution" of each observation to each mixture component according to probability. M-step: Parameter update. Mixture weight update:

[0054]

[0055] Where N is the total number of observations, i.e. Mixed weights w k The maximum likelihood estimate is the mean of the posterior probabilities of each component. Intuitively, if the posterior probability of a component is generally high, its weight will be increased to better fit the data distribution. Degrees of freedom ν k There is no closed-form solution; it needs to be solved numerically by maximizing the following expression:

[0056]

[0057] Using Newton's iteration method:

[0058]

[0059] Degrees of freedom νk Controlling the tail thickness of the T-distribution requires numerical methods for optimization. The first derivative... The function involved is ψ(·), and the second derivative involves the function ψ1(·). Iteration continues until convergence, typically requiring 3-5 iterations. Iteration stops when the parameter change is less than the threshold ∈ [a_0, b_0].

[0060]

[0061] The convergence criterion needs to balance accuracy and computational cost. Typical settings are ∈ = 10. -5 If convergence is not achieved after exceeding the maximum number of iterations, the initial value is changed and the iteration is restarted. Using the EM algorithm, this embodiment obtains the k-value, mean, variance, and degrees of freedom based on a mixed T-distribution. A TDOA observation distribution model in an indoor environment is established, providing an observation error model for deriving the calculation method of the lower bound of error in the next subsection.

[0062] S2. Introduce measurement constraint information to expand the Fisher information matrix and obtain more compact boundary estimates;

[0063] Calculation of the lower bound of the error in the geometric positioning algorithm:

[0064] Based on FIM, this invention proposes a method to fuse measurement constraints into the information matrix, expanding the information of the Fisher matrix and obtaining tighter lower bounds on the constraints. The original Fisher matrix is ​​for the complete parameter vector. (including user location x) u The propagation parameter k) can be re-expressed as:

[0065]

[0066] in A FIM block representing user location parameters; The cross FIM block representing the position and propagation parameters; J κ,κ The FIM block representing the propagation parameters is a block diagonal matrix (the parameters of different APs are independent of each other). Measurement constraint information is transmitted through an additional FIM block J. a (θ u Introduced. Its form is a block diagonal matrix:

[0067]

[0068] In the matrix, J a (x u () is the information matrix constrained by the user's location. If position x u The feasible region is rectangle A. L =[x L ,x U ]×[yL ,y U ],but:

[0069]

[0070] Where c m =4 is a constant. J a (κ k ) represents the propagation parameter constraint information matrix of the k-th AP. If parameter K k =[α k ,β k ,a k ,b k ] T The feasible regions are [α] L ,α U ], [β L ,β U ], [a L ,a U ],[b L ,b U ]but:

[0071]

[0072] The constraint information matrix J a (θ u Superimposed on the original FIM, we obtain the constraint-aware FIM:

[0073] I c (θ u )=J(θ u )+J a (θ u (14)

[0074] Through block matrix operations, the constrained extended Fisher matrix The calculation is as follows:

[0075]

[0076] This represents the cross FIM block between the user's location and the k-th AP parameter. The original FIM block for the k-th AP parameter. This represents the inverse FIM block for the k-th AP parameter under constraints. By modeling the constraint information as an additional FIM and utilizing block matrix operations, the extended FIM under constraints can be accurately derived.

[0077] S3. Based on the propagation model of CSI signal, derive the ZZB boundary of fingerprint positioning algorithm, introduce Bayesian estimation framework and prior location information, and give an effective lower bound estimate of error.

[0078] Specifically, the lower bound of fingerprint localization error is calculated based on CSI:

[0079] In indoor positioning scenarios, we deploy M wireless access points (APs), each equipped with N antennas, forming a MIMO system. Positioning area. CSI fingerprint data of L reference points (RPs) are pre-collected. in This represents the channel state information matrix measured at the l-th RP. The core of CSI fingerprint localization is to estimate the target location θ∈R by matching the real-time measured CSI with the fingerprint database. 3 At the target location θ, the CSI matrix received by the m-th AP can be represented as:

[0080]

[0081] Where d m The target represents the straight-line distance to the m-th AP; α represents the path loss exponent; a m ,b m : Array response vectors of AP and target; W m The noise matrix is ​​measured. The LOS component characterizes the signal attenuation effect along the direct path, and its intensity varies with distance d. m The power increases and decreases. The NLOS component, on the other hand, consists of K reflection paths, each with a power P. k With distance d m,k Correlation, phase φ m,k and angle θ m,k Random distribution.

[0082] The location estimation is modeled as a Bayesian inference problem, with the parameters to be estimated being θ~p(θ). The prior distribution p(θ) reflects prior knowledge of the possible areas where the target may appear. The observation data is the set of CSI matrices Y={H1,…,H1} obtained from T independent samplings. T The objective function is to minimize the mean squared error. Its lower bound is ZZB. Compared to classical estimation theory, the Bayesian framework explicitly utilizes prior information p(θ), making it suitable for localization scenarios in confined spaces. It improves the tightness of the lower bound through prior constraints. For any displacement Δ, two competing hypotheses are constructed:

[0083] H0: The true position is θ0;

[0084] H1: The true position is θ0 + Δ;

[0085] Assuming each measurement is independent, the joint likelihood of the observed data is:

[0086]

[0087] in, This represents the CSI mean at position θ in the fingerprint database. The composite covariance matrix representing multipath and noise is used, and the optimal decision rule is given by the likelihood ratio test (LRT):

[0088]

[0089] The corresponding minimum error probability is:

[0090]

[0091] The core idea is the probability of error. The algorithm's ability to distinguish between θ0 and θ0+Δ. This is relevant if the CSI distributions at two locations highly overlap. This indicates that the direction of displacement is difficult to distinguish, leading to a large positioning error.

[0092] Taking into account the effects of all displacements Δ, the LPEB expression is:

[0093]

[0094] Displacement weight |Δ| 2 The parameters emphasize the greater contribution of large displacements to the MSE. The prior product p(θ0)p(θ0+Δ): This displacement only makes a significant contribution to the integral when both θ0 and θ0+Δ are located in regions of high prior probability. Outer integration limit. The inner integral Δ must satisfy It reflects the limited space.

[0095] Based on the above simplifications, we obtain the LPEB suitable for CSI fingerprint localization:

[0096]

[0097] Based on the above derivation and analysis, this embodiment proposes an LPEB calculation method for CSI fingerprint positioning systems. It should be noted that in specific engineering practice, since the observation error distribution of CSI signals is unknown, the Monte Carlo integration method should be used in combination with specific data sampling values ​​to solve the integral in LPEB.

[0098] S4. Combining the two error lower bounds, a positioning error lower bound applicable to the 5G indoor integrated positioning system is given, which serves as the basis for performance evaluation of the 5G indoor integrated positioning system.

[0099] Specifically, for the lower bound of the error in the geometric positioning part, the Fisher information matrix J is obtained according to formula (15). TDOA The reciprocal of its matrix trace is the lower bound of the error covariance. For the fingerprint localization part, obtaining its information matrix is ​​relatively difficult, requiring LPEB... CSI Convert to information matrix form. The ZZB framework used for fingerprint localization derives the lower bound of the mean square error of parameter estimation through hypothesis testing error probability, and its output is usually a scalar value:

[0100]

[0101] Where L ZZB This represents a theoretical lower bound. In positioning scenarios, assuming the user's location is two-dimensional, ZZB might provide a lower bound for the overall position error's mean squared error (MSE), but it doesn't distinguish between error components in each direction. The information matrix, however, is a measure of the covariance matrix, reflecting the uncertainty in parameter estimation.

[0102]

[0103] To integrate the scalar lower bound of ZZB into the information fusion framework, it needs to be converted into a form compatible with the information matrix. Assume the lower bound L given by ZZB... ZZB To ensure isotropic error, construct the diagonal covariance matrix:

[0104]

[0105] Where d is the parameter dimension. The corresponding information matrix is:

[0106]

[0107] The lower bound of the mean squared error (LPEB) is calculated using the hypothesis testing error probability. CSI This needs to be converted into an equivalent covariance form. Assume LPEB CSI The equivalent covariance corresponding to the lower bound is C. CSI =LPEB CSI • If I (isotropy assumption) is true, then the equivalent information matrix is: The information matrices of the two branches are weighted and summed, where the weights can be allocated empirically or based on the weight values ​​of the Kalman filter:

[0108] J 融合 =αJ TDOA +βJ CSI (26)

[0109] Regarding the lower bound of the fusion error, geometric localization provides accurate information at high confidence levels, while fingerprint localization enhances robustness in ambiguous regions. The inverse of the joint information matrix gives the theoretical lower bound of the combined system error.

[0110]

[0111] In practice, positioning errors may exhibit anisotropic behavior, which introduces bias into the isotropic assumption. In such cases, adjusting the off-diagonal elements of the covariance matrix in conjunction with the scene map can characterize the spatial correlation of the error.

[0112]

[0113] Where ρ is the error correlation coefficient, which can be estimated using historical data. This invention derives the lower bound of the error for the integrated positioning system. By effectively fusing the lower bounds of the two errors, it is possible to effectively estimate the error boundary value of the indoor integrated positioning system, providing a theoretical basis for further system optimization.

[0114] Example:

[0115] The test environment consisted of a warehouse of approximately 1200 square meters, with reflective walls, including the warehouse walls and metal doors. The environment contained various metal objects, such as industrial-style vehicles or metal shelves. Figure 3 (a) shows an image of a portion of the warehouse. Eight base stations were placed on walls at varying heights in the environment. The transmitter equipment was carried by a person at a constant height of 1.05m, transmitting the received 5G signal at a fixed frequency. Data was recorded by a new 5G radio platform with a bandwidth of 100MHz and a center frequency of 3.75GHz. The transmitter's actual ground location was collected using a millimeter-level precision tracking system. Data was recorded and synchronized via an NTP server and preprocessed (removing corrupted data points and synchronizing RF and positioning reference data). Figure 3 (b) is the trajectory diagram.

[0116] This embodiment contains three data files: training data, test data, and specific test site data. Each row of data elements in the training and test data contains a timestamp in floating-point format and a JSON string representing the measurement data instance. Each row of measurement data contains the observation data to be located and the actual coordinates collected by the tracking system. Specifically, each data instance contains:

[0117] recTime: This data is floating-point data, in seconds. The timestamp received by the receiver node for CIR represents the global time index of the data received by the system and the observation data of the tracking system, used for data alignment and to distinguish positioning data from different epochs.

[0118] Window start time: Floating-point data in seconds. Represents the start time of the CIR window.

[0119] toa: This data is floating-point data in seconds. It represents the time when the receiver captured the first signal. The tap in the CIR (data at that time point will be identified as the first path) can be determined by subtracting the window start time from toa.

[0120] Burst ID: Integer data representing the receiver's time index. This can be used for synthesis. For each burst ID, the transmitter (i.e., the mobile node) transmits the pulse (i.e., the anchor) received by the receiver.

[0121] `csi_real` and `csi_imag`: Integer data, storing the real and imaginary parts of the CSI measurement in tuple format. The real part represents the amplitude data in the CSI measurement, and the imaginary part represents the phase data. The CSI is truncated with the first obvious peak point as the center, and each sample contains 128 sampling points at a sampling frequency of 184.32MHz.

[0122] anch_id: String data representing the anchor ID.

[0123] ref_x and ref_y: Floating-point data, corresponding to the reference position of the timestamp.

[0124] In summary, this dataset can simultaneously obtain TOA distance measurement information and CSI spatial distribution information, which is a good match for the patent implementation target—the 5G indoor combined positioning system.

[0125] like Figure 2 As shown, the implementation steps of the example are as follows:

[0126] (1) Establishing a non-Gaussian mixture model for TDOA observations: Based on the channel characteristics of 5G PRS, the propagation characteristics of signals in complex environments such as indoor multipath and obstruction are analyzed. The expectation-maximization algorithm is used to construct a t-distribution mixture model to describe the distribution of TDOA observation errors. By collecting raw observation data and combining it with the non-Gaussian mixture model, preliminary positioning estimates are generated, providing a basis for subsequent parameter estimation.

[0127] (2) Noise data extraction and model parameter estimation: The observation noise and location noise datasets are separated from the original observation data, and the parameters of the non-Gaussian mixture model are iteratively optimized again using the expectation-maximization algorithm. By alternately executing the expectation step (calculating the posterior probability of the latent variables in the noise data) and the maximization step (updating the model parameters), the true probability distribution of the noise data is gradually approximated, thereby improving the accuracy of the error model.

[0128] (3) Fisher Information Matrix Extension under Measurement Constraints: Known measurement constraints in the positioning system (such as geometric constraints, signal strength range, etc.) are transformed into mathematical constraint expressions, and the constraints are incorporated into the calculation process of the Fisher information matrix using the Lagrange multiplier method. The CRLB is re-derived using the extended matrix, eliminating the limitations of the traditional unbiased estimation assumption and obtaining a more robust error boundary estimation result.

[0129] (4) Fingerprint positioning EZZB boundary derivation: A channel state fingerprint database is established based on the propagation model of CSI signals, and prior distribution information of user location (such as indoor layout constraints) is introduced in combination with the Bayesian estimation framework. On this basis, the lower bound of ZZB error is derived, and the theoretical performance limit of the fingerprint positioning algorithm is quantified by the matching relationship between statistical signal features and location fingerprints.

[0130] (5) Fusion of lower bound of combined positioning error: The improved TDOA-CRLB and the ZZB result of fingerprint positioning are fused together. The two types of lower bounds of error are integrated by weighting factors or joint analysis methods (such as covariance cross fusion) to output the comprehensive lower bound index of the combined positioning system as the basis for evaluating the overall performance of the system.

[0131] Beneficial effects of this embodiment:

[0132] To address the issue of non-Gaussian distribution of observation errors caused by indoor multipath interference, this embodiment proposes a method for calculating the lower bound of errors in a combined positioning system that integrates observation constraint information. Specifically, for the TDOA geometric positioning system, a TDOA error modeling method based on a mixed t-distribution is proposed. By modeling the observation information as a diagonal matrix, the information content of the original Fisher matrix is ​​expanded, resulting in an effective and tight lower bound estimate of the error. Furthermore, considering the dynamic time-varying characteristics of CSI fingerprint positioning, the Ziv-Zakai bound is adopted. Utilizing a Bayesian estimation framework and scene prior knowledge, the theoretical accuracy limit of channel feature matching is quantified when the error distribution of the observed signal is unknown. This method achieves, for the first time, the lower bound estimation of errors in a combined geometric positioning and fingerprint matching positioning system, providing a quantifiable performance boundary for multi-algorithm collaborative positioning.

[0133] This embodiment can effectively overcome the nonlinearity and non-Gaussian noise problems in indoor 5G PRS signal scenarios, ensure the accuracy of error modeling, and achieve accurate evaluation of the lower bound of system error.

[0134] Example 2

[0135] This embodiment also discloses a computer program product, including a computer program that, when executed by a processor, implements the steps of the method described in Embodiment 1.

[0136] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for lower bound of error estimation of a 5G indoor integrated positioning system, characterized in that, The method comprises the following steps: According to the 5G PRS channel characteristics of the 5G indoor combined positioning system, an initial non-Gaussian mixed model of TDOA observation is established, and an original estimated value is given; and through observation data, observation noise and positioning noise data sets are extracted, model parameters are iteratively estimated by using the expectation maximization algorithm, and the true distribution of the data set is approximated; the initial non-Gaussian mixed model of TDOA observation is a mixed T distribution model; The measurement constraint information is introduced, and the Fisher information matrix is expanded to obtain a first error lower bound estimate value; The step of introducing the measurement constraint information and expanding the Fisher information matrix comprises: Based on the FIM, the measurement constraint information is introduced through an additional FIM block, and the form is a block diagonal matrix; The constraint information matrix is superimposed on the original FIM to obtain a constraint-aware FIM, and an extended Fisher matrix after the constraint is obtained through block matrix operation; According to the propagation model of the CSI signal, the ZZB boundary of the fingerprint positioning algorithm is derived, the Bayesian estimation framework and prior position information are introduced, and a second error lower bound estimate value is given; The step of deriving the ZZB boundary of the fingerprint positioning algorithm according to the propagation model of the CSI signal comprises: In an indoor positioning scene, a plurality of wireless access points are deployed, each AP is equipped with N antennas to form a MIMO system, and CSI fingerprint data of each reference point in the positioning area is pre-collected; The position estimation is modeled as a Bayesian inference problem, two competing hypotheses are constructed, the measurements are assumed to be independent, and the joint likelihood of the observation data is obtained; An optimal decision rule is obtained through the joint likelihood, the influence of all displacements is comprehensively considered, and an LPEB suitable for CSI fingerprint positioning is obtained; The first error lower bound estimate value and the second error lower bound estimate value are combined to give a positioning error lower bound suitable for the 5G indoor combined positioning system as a basis for performance evaluation of the 5G indoor combined positioning system.

2. The method of claim 1, wherein The step of establishing an initial non-Gaussian mixed model of TDOA observation according to the 5G PRS channel characteristics of the 5G indoor combined positioning system comprises: Defining the position and base station coordinates, calculating the TDOA observation value according to the base station coordinates, and assuming the measurement error distribution; Defining the probability density function of the mixed T distribution, introducing the latent variable, and constructing the likelihood function; The k value, mean value, variance and degree of freedom based on the mixed T distribution are obtained by calculating the posterior probability through the E step of the expectation maximization algorithm and updating the parameters through the M step.

3. The method of claim 2, wherein In the initial non-Gaussian mixed model of TDOA observation, the mixed T distribution models the heavy-tailed noise by weighting multiple T distributions, each component corresponds to a different error source, and the PDF of the T distribution contains a gamma function term and a polynomial term.

4. The method of claim 2, wherein In the expectation maximization algorithm, when calculating the posterior probability in the E step, according to the Bayes theorem, the posterior probability is proportional to the product of the prior weight and the likelihood term, and the denominator is normalized, and the contribution of each observation is distributed to each mixed component according to the probability.

5. The method of claim 2, wherein In the maximum likelihood algorithm, the mixing weight is updated as the mean of the posterior probabilities of each component, and the degrees of freedom are solved by maximizing the following formula, which is optimized using the Newton iteration method.

6. The method of claim 1, wherein, In the fingerprint positioning algorithm, if the actual positioning error presents direction anisotropy, the off-diagonal elements of the covariance matrix are adjusted in combination with the scene map to represent the spatial correlation of the error.

7. The method of claim 1, wherein, The steps of giving the lower bound of the positioning error suitable for the 5G indoor integrated positioning system in combination with the two error lower bounds include: For the error lower bound of the geometric positioning part, the first information matrix is obtained according to the formula, and the reciprocal of the matrix trace is the error covariance lower bound; For the fingerprint positioning part, assuming that the lower bound given by ZZB is isotropic error, a diagonal covariance matrix is obtained, and the second information matrix is obtained through the diagonal covariance matrix; The first information matrix and the second information matrix are weighted and added, and the inverse of the joint information matrix gives the theoretical error lower bound of the integrated system.

8. A computer program product comprising a computer program, characterized in that, The computer program is executed by the processor to realize the steps of the method of any one of claims 1-7.

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