Multi-source PNT observation data integration correction random model based on LS-VCE

Abstract

The specification describes a positioning technology for a global navigation satellite system (GNSS), aiming at improving the positioning accuracy in a complex environment. According to the technology, based on a corrected random model of least square variance component estimation (LS-VCE), the uncertainty of observation data is estimated more accurately, so that the positioning accuracy is remarkably improved. The technology comprises the following key steps: firstly, performing uncertainty modeling on GNSS observation data, and estimating variance and covariance components of the observation data by using an LS-VCE method; thirdly, defining a weight matrix to reflect the importance or reliability of different observation data, constructing an observation equation system, and associating the observation data with model parameters; and then, through iterative solution, optimal parameter estimation and variance component estimation are obtained by using a least square principle. And finally, verifying the effectiveness of the LS-VCE method through a simulation experiment, and optimizing the model according to an experiment result.

Description

Technical Field

[0001] This invention relates to positioning technology in Global Navigation Satellite Systems (GNSS), and in particular to improving positioning accuracy in complex environments, by providing a modified stochastic model based on least squares variance component estimation (LS-VCE). Background Technology

[0002] In traditional GNSS positioning, positioning accuracy is often limited due to issues such as signal propagation errors, multipath effects, and signal interference. Existing technologies typically employ simplified stochastic models, which may not accurately reflect the true statistical characteristics of the observation data, especially in complex environments. Summary of the Invention

[0003] The purpose of this invention is to provide a modified stochastic model that, through the least squares variance component estimation (LS-VCE) method, can more accurately estimate the uncertainty of observation data, thereby improving positioning accuracy.

[0004] The technical solution of this invention includes the following key steps:

[0005] 1. Uncertainty modeling of observation data

[0006] Modeling GNSS observation data involves including random noise from pseudorange and carrier phase. This noise typically has unknown variance and covariance characteristics, which need to be estimated using a model.

[0007] 2. Variance component estimation

[0008] The LS-VCE method is used to estimate the variance and covariance components of the observed data. LS-VCE is an iterative algorithm that uses the least squares principle to estimate the unknown variance components by optimizing the objective function.

[0009] 3. Definition of the weight matrix

[0010] In the LS-VCE method, users can define custom weight matrices to reflect the importance or reliability of different observations. The choice of weight matrix can be adjusted according to the needs of the specific application.

[0011] 4. Iterative solution

[0012] The least squares principle is used to iteratively solve the constructed observation equations to obtain the optimal parameter estimates and variance component estimates.

[0013] 5. Model Validation

[0014] The effectiveness of the LS-VCE method was verified through simulation experiments. Attached Figure Description

[0015] Figure 1 The flowchart of the stochastic correction model is shown.

[0016] Figure 2 The results after data preprocessing are shown.

[0017] Figure 3 The simulation experiment shows a performance comparison between the before and after improvements.

[0018] Figure 4 The iterative results of LS-VCE are shown. Specific implementation methods

[0019] The modified stochastic model of this invention mainly involves the following key steps in its implementation:

[0020] Step S101: Data Collection and Preprocessing

[0021] In complex scenarios such as chemical engineering, the accuracy and reliability of data are crucial. Therefore, it is first necessary to collect PNT (positioning, navigation, and timing) observation information, which may include pseudorange and carrier phase. Because this data is susceptible to electromagnetic interference and signal blockage, rigorous preprocessing is essential. Specific preprocessing methods include, but are not limited to, filtering, noise reduction, and data correction. Preprocessing can improve the accuracy of the data.

[0022] For example, in the simulation experiment, the observation information is TOA (Time of Arrival). A Kalman filter is used for data preprocessing to calculate the optimal predicted value of the current TOA. (See attached image.) Figure 1 As shown, the signal is closer to the true value after Kalman filtering.

[0023] Step S102: Construct a stochastic model

[0024] Based on data preprocessing, a comprehensive stochastic model is constructed, which needs to consider the uncertainty of observation information. This includes random noise in the pseudocode phase and carrier phase. The key points of model construction are the parameter vector and the (co)variance matrix. The model contains a parameter vector x, representing the unknown parameters that need to be estimated. The variance or weights of the observation information are evaluated by methods such as variance component estimation or determination based on actual deviations, in order to optimize the observation information.

[0025] For example, when developing a linear observation equation system for unknown (co)variance components, one can begin with a linear model.

[0026] E{y}=AxD{y}=Q yy

[0027]

[0028] Where E{.} and D{.} represent the mathematical expectation operator and the discrete operator, respectively. The above model contains two sets of unknowns: the parameter vector x and the (co)variance components σ_k, k = 1,…,p. The goal of VCE is to construct an estimation model for the unknown (co)variance components. Assume that the m×n matrix A is known and has full column rank. Similarly, the cofactor matrix Q... k k = 0, ..., p is also assumed to be known, and their weighted sum Q yy It is assumed to be positive definite. Matrix Q0 is the variance matrix Q. yy The known part. Then, a transformation of the corresponding observation vector y is introduced, so that the above equation takes a simplified form. Let B be the basis matrix of the null space of the transpose of A.

[0029] y and [x T ,t T ] T The following correspondence exists

[0030]

[0031] Q tt =B T Q yy B

[0032] Applying the above formula to equation (1), we can obtain...

[0033]

[0034] in This is the best linear unbiased estimate of x. t is a redundant vector, defined as b = mn. If y is normally distributed, then they are independent. From equations (2) and (4), since E{t} = 0 and D{t} = E{tt}... T}=B T Q yy B, therefore This equation can be viewed as a matrix observation equation for the unknown (covariance) components, and the matrix equation is given by b. 2 It consists of scalar observation equations. If E{tt T -B T The b b-dimensional column vectors of Q0B are stacked into a b 2 The observation vector *1 can transform the matrix observation equation into a familiar vector-matrix form of linear observation equation using vector operators.

[0035] However, due to the observation matrix ttT - BT Q 0B is symmetric, therefore we should only consider the diagonal and lower parts of the matrix. Otherwise, unnecessary data duplication will occur, which means that the vh operator should be used to transform the matrix observation equation into a linear observation equation.

[0036] E{y vh}=A vh σ

[0037] Where y vh =vh(tt) T -B T Q0B),A vh =[vh(B T Q1B),...,vh(B T Q p B)],σ=[σ1,...,σ p ] T The linear model in the above equation will form the basis for the least squares (covariance) component estimation.

[0038] Step S103: Least Squares Variance Component Estimation (LS-VCE)

[0039] The LS-VCE algorithm is implemented to estimate unknown (co)variance components. This involves constructing a system of linear observation equations, iterating using the principles of the least squares method, and allowing users to define custom weight matrices.

[0040] For example, the observation information is used to construct a custom weight matrix. In the simulation experiment, the preprocessed observation information still contains noise and interference. The weighted LS-VCE defined in 1 is... Right now

[0041]

[0042] The above formula can be simplified to

[0043]

[0044] The elements of matrix N and matrix r are respectively

[0045]

[0046] As attached Figure 4 As shown, the iterative process of the observation information and the comparison results between the final estimated variance and the actual variance are illustrated.

[0047] Step S104: Achieve positioning

[0048] Using the weight matrix obtained in step three, optimized observation information is applied to ultimately achieve high-precision positioning. The key to successful positioning lies in the design of the weight matrix, which optimizes the observation information to achieve high-precision positioning.

[0049] For example, such as Figure 2 As shown, the positioning error was reduced by 33% compared to the original algorithm, significantly improving the accuracy and reliability of positioning.

[0050] By implementing these steps, the modified stochastic model can effectively improve the accuracy and stability of positioning systems, especially in complex industrial environments.

Claims

1. A positioning method for a Global Navigation Satellite System (GNSS), characterized in that, The method includes the following steps: a. Model the GNSS observation data to estimate the random noise in the pseudorange and carrier phase; b. The least squares variance component estimation (LS-VCE) method is used to estimate the variance and covariance components of the observed data; c. Define a weight matrix to reflect the importance or reliability of different observation data; d. Construct a system of observation equations to link the observation data with the model parameters; e. The least squares principle is used to iteratively solve the constructed observation equations to obtain the optimal parameter estimates and variance component estimates; f. Verify the effectiveness of the LS-VCE method through simulation experiments, and optimize the model based on the experimental results.

2. The method as described in claim 1, characterized in that, The data preprocessing in step a includes filtering and denoising to reduce the impact of noise on subsequent processing.

3. The method as described in claim 1, characterized in that, The LS-VCE method in step b is an iterative algorithm that uses the least squares principle to estimate the unknown variance components by optimizing the objective function.

4. The method as described in claim 1, characterized in that, In step c, users can customize the weight matrix to suit different application needs.

5. The method as described in claim 1, characterized in that, The construction of the observation equations in step d is the foundation for implementing the LS-VCE method.

6. The method as described in claim 1, characterized in that, The iterative solution in step e allows users to evaluate the variance or weight of various types of observation information based on methods determined by the actual deviation.

7. The method as described in claim 1, characterized in that, The model validation and optimization in step f includes simulation experiments and reduction of positioning errors.

8. A Global Navigation Satellite System (GNSS) positioning device, characterized in that, The device is equipped with a processor that performs the method according to any one of claims 1 to 7.

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