Ppp / uwb tight combination positioning method and system, and storage medium

Abstract

The application discloses a PPP / UWB tight combination positioning method and system and a storage medium, wherein a third-order spherical radial volume criterion is used to realize nonlinear propagation of a measurement equation, and the influence of linearization errors of a traditional method is effectively weakened; by introducing variance component estimation, a GNSS and UWB measurement variance and covariance matrix is adaptively adjusted according to residual statistical characteristics, and adaptive adjustment of the measurement variance and covariance matrix is realized; meanwhile, in combination with a robust weight function, observation data containing gross errors and outliers are weighted and suppressed, and the robustness and anti-interference ability of a filtering system are improved. Compared with a traditional PPP / UWB combination method, the application can adaptively adjust the variance and covariance matrix according to environmental changes, and the influence of inaccurate empirical values and observation abnormalities on positioning results is significantly reduced; through volume Kalman filtering, linearization errors caused by the removal of high-order terms in Taylor first-order expansion are avoided.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation technology, and in particular to a PPP / UWB tightly coupled positioning method, system and storage medium. Background Technology

[0002] Global Navigation Satellite System (GNSS) technology, as a crucial means of acquiring the three-dimensional coordinates of targets, has been widely applied in scenarios requiring continuous high-precision positioning, such as pedestrian navigation, autonomous driving, and UAV mapping. However, in complex environments such as urban canyons, forest areas, and indoor-outdoor boundary areas, GNSS observation signals are highly susceptible to interference from obstruction, multipath propagation, and non-line-of-sight errors, leading to a significant decrease in the number of visible satellites and a deterioration in satellite geometry. Consequently, the accuracy and reliability of Precise Point Positioning (PPP) are noticeably reduced. To improve positioning performance in weak satellite environments, Ultra-Wideband (UWB) technology, due to its strong anti-interference capabilities, low cost, and high ranging accuracy, has been widely introduced into PPP systems for enhanced positioning.

[0003] However, existing PPP / UWB integrated positioning technologies still have shortcomings in terms of nonlinear processing capabilities and noise adaptability. For example, the linearization error of the traditional extended Kalman filter (EKF) is difficult to avoid in highly nonlinear UWB ranging models; the traditional capacitive Kalman filter (CKF) does not consider the time-varying characteristics of noise in complex environments, and is prone to causing a decrease in filtering accuracy in strong interference scenarios; the accuracy and reliability of PPP / UWB integrated positioning in complex environments are difficult to guarantee. Summary of the Invention

[0004] The technical problem to be solved by this invention is to provide a PPP / UWB compact combination positioning method, system, and storage medium to address the shortcomings of existing technologies and improve the robustness and anti-interference capability of filtering systems. To solve the above technical problem, the technical solution adopted by this invention is: a PPP / UWB compact combination positioning method, comprising the following steps:

[0005] S1. Unify the spatiotemporal reference of GNSS and UWB data, and establish the measurement equations for PPP / UWB; initialize the state vector and parameter variance-covariance matrix based on empirical values;

[0006] S2. Using the state vector and parameter variance covariance matrix, calculate the volume point based on the third-order spherical radial volume Kalman filter criterion, and perform nonlinear propagation on the volume point to obtain the predicted state and the predicted state covariance matrix. The measurement variance covariance matrix is ​​given based on the empirical model.

[0007] S3. Calculate the unit weighted variance using the predicted state combined with the variance component estimation method, adjust the variance scaling factor of GNSS and UWB based on the unit weighted variance, and update the measurement variance covariance matrix.

[0008] S4. Introduce the IGG3 robust weight function to suppress gross errors and outlier observations, obtain the variance inflation factor, and update the measurement variance covariance matrix again.

[0009] S5. Repeat steps S3 and S4, iteratively calculating until the unit weight variances of different types of observations are equal.

[0010] S6. After the iteration is completed, the measurement is updated using the final updated measurement variance covariance matrix and measurement equation to achieve the positioning solution.

[0011] The process of unifying the spatiotemporal reference of GNSS and UWB data includes:

[0012] Using the GNSS timestamp as a reference, the UWB timestamp is converted to GPST. When the UWB sampling frequency is greater than the GNSS sampling frequency, a linear interpolation method is used to establish a mapping between the UWB timestamp and the GPS timestamp to unify the time reference. For the spatial reference, the GNSS measurement center and the UWB measurement center are set on a vertical line. The height difference between the GNSS measurement center and the UWB measurement center is measured in advance. The distance correction factor projected onto the direction from the satellite to the GNSS measurement center is calculated. This correction factor is used to correct the original GNSS observation value and unify the measurement center to the position of the UWB measurement center.

[0013] The measurement equation for PPP / UWB is expressed as follows: ;in, Era numbering, For state vectors, For measurement vectors, For measurement functions, For measuring noise;

[0014] The state vector of the k-th epoch is represented as: ;

[0015] in, The three-dimensional coordinate components of the UWB measurement center in the Earth-centered Earth-fixed coordinate system. For receiver clock bias, To account for the deviation between different GNSS systems, For tropospheric delay, To eliminate ionospheric ambiguity.

[0016] In step S2, the volume point expression is: ; For parameter variance and covariance matrix Cholesky decomposition matrix, For weighted sigma points, =1,2…2 , State vector Dimension; , It is a diagonal matrix. Representing position and state respectively , , variance The variance representing the receiver clock error, The variance representing the deviation between different GNSS systems. The variance representing tropospheric delay, The variance represents the combined ambiguity of the deionization layer.

[0017] In step S2, predict the state. Covariance matrix of predicted state Represented as:

[0018]

[0019]

[0020] in, For process noise array, , () represents the state function.

[0021] In step S3, using the variance component estimation method, the formula for calculating the unit weight variance is:

[0022] ;

[0023] ;

[0024] ;

[0025] ;

[0026] in, and These are the unit weighted variances for GNSS and UWB, respectively. and These represent the number of GNSS satellites and the number of UWB base stations, respectively. For the prior residuals, derived from the prior residuals of GNSS Prior residuals of UWB composition, For the measurement matrix, The covariance matrix of the prior residuals; the measurement variance covariance matrix. , and These are the variance-covariance matrix of GNSS measurements and the variance-covariance matrix of UWB measurements, respectively.

[0027] The formulas for calculating the variance scaling factor of GNSS and UWB are as follows: ;

[0028] For fixed constants, m=1,2, where m=1 represents GNSS and m=2 represents UWB. This is the variance scaling factor from the previous iteration, with an initial value of 1; This is the variance scaling factor for the current iteration.

[0029] In step S4, the updated measurement variance covariance matrix Represented as: Variance inflation factor The expression is: In the formula, and It is an empirical constant. To standardize the residuals, the updated measurement variance matrix .

[0030] In step S6, the formula for the location solution is: ;in, For the posterior estimate of the state vector, , , and These are the mutual covariance and innovation covariance matrices, respectively. , , , , The volume point is calculated using the predicted state and the predicted state covariance matrix.

[0031] As an inventive concept, the present invention also provides a PPP / UWB tightly coupled positioning system, including a memory, a processor, and a computer program stored in the memory; the processor executes the computer program to implement the steps of the above method.

[0032] As an inventive concept, the present invention also provides a computer-readable storage medium having a computer program / instructions stored thereon; when the computer program / instructions are executed by a processor, they implement the steps of the above-described method.

[0033] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention utilizes the third-order spherical radial volume criterion to achieve nonlinear propagation of the measurement equation, effectively reducing the impact of linearization errors in traditional methods; by introducing variance component estimation, it adaptively adjusts the GNSS and UWB measurement variance covariance matrices based on residual statistical characteristics, achieving adaptive adjustment of the measurement variance covariance matrix; simultaneously, by combining robust weighting functions, it weights and suppresses observation data containing outliers, improving the robustness and anti-interference capability of the filtering system. Compared with traditional PPP / UWB combination methods, this invention can adaptively adjust the variance covariance matrix according to environmental changes, significantly reducing the impact of inaccurate empirical values ​​and observation anomalies on positioning results; through capacitive Kalman filtering, it avoids linearization errors caused by discarding higher-order terms in Taylor first-order expansion; combined with the above improvements, this invention enhances the accuracy and reliability of PPP / UWB tight combination positioning in complex environments such as indoor-outdoor transition zones and urban canyons, providing a reliable solution for high-precision positioning in complex environments. Attached Figure Description

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

[0035] Figure 2 This is a schematic diagram of the PPP / UWB compact combination localization result based on adaptive robust capacitive Kalman filtering in an embodiment of the present invention. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0037] Example 1

[0038] like Figure 1 As shown, this embodiment provides a PPP / UWB compact combination localization method based on adaptive robust commutative Kalman filtering, including the following steps:

[0039] S1. Unify the spatiotemporal references for GNSS and UWB data, and establish PPP / UWB measurement equations. Initialize the state vector and parameter variance-covariance matrix based on empirical values; specifically:

[0040] Using the GNSS timestamp as a reference, the UWB timestamp is converted to GPS timestamp. When the UWB sampling frequency is higher than the GNSS sampling frequency, a linear interpolation method is used to establish a mapping between the UWB timestamp and the GPS timestamp, thereby unifying the time reference. For the spatial reference, during equipment installation, the GNSS measurement center and the UWB measurement center are on the same vertical line, and the positional deviation between the two in the horizontal direction can be ignored. Therefore, only the deviation between the GNSS measurement center and the UWB measurement center in the elevation direction needs to be corrected. The specific process is as follows: the height difference between the GNSS measurement center and the UWB measurement center is measured in advance, and then the distance correction factor projected onto the direction from the satellite to the GNSS measurement center is calculated.

[0041] (1)

[0042] in Here is the distance correction, and ⋅ represents the dot product. The elevation difference between the GNSS measurement center and the UWB measurement center. For the satellite elevation angle, This is the satellite azimuth angle. Later, when establishing the PPP / UWB compact combination measurement equations, the obtained distance corrections are used to correct the original GNSS distance observations, thereby unifying the measurement center to the location of the UWB measurement center.

[0043] A location method based on ionospheric desmolysis combined with PPP and UWB time of arrival, and applying distance correction numbers. Establish PPP / UWB compact combination measurement equations

[0044] (2)

[0045] (3)

[0046] in, Era numbering, For state vectors, For measurement vectors, For measurement functions, To measure noise, and These represent the deionization combined pseudorange and the deionization combined carrier, respectively. For UWB distance observations. The state vector for epoch k is:

[0047] (4)

[0048] in The three-dimensional coordinate components of the UWB measurement center in the Earth-centered Earth-fixed coordinate system. At the speed of light, For receiver clock bias, To account for the deviation between different GNSS systems, For tropospheric delay, To eliminate ionospheric ambiguity.

[0049] Initialize the parameter variance and covariance matrix based on empirical values. :

[0050] (5)

[0051] in, Representing position and state respectively , ,and variance The variance representing the receiver clock error, The variance representing the deviation between different GNSS systems. The variance representing tropospheric delay, The variance represents the combined ambiguity of the deionization layer.

[0052] S2. Using the state vector and parameter variance-covariance matrix, calculate the volume point based on the third-order spherical radial volume Kalman filter criterion, and perform nonlinear propagation on the volume point to obtain the predicted state and the predicted state covariance matrix. The measurement variance-covariance matrix is ​​given based on an empirical model. Specifically:

[0053] Based on the state vector of step S2 Dimension Based on the third-order spherical radial volume criterion, combined with the state vector, 2 One volume point,

[0054] (6)

[0055] In the formula, For the parameter variance covariance matrix Cholesky decomposition matrix, For weighted sigma points, =1,2…2 .

[0056] Nonlinear propagation of the volume point is performed using formula (7):

[0057] (7)

[0058] In the formula, This is the state function.

[0059] Calculate the predicted state and the predicted state covariance matrix.

[0060] (8)

[0061] (9)

[0062] In the formula, and These are the predicted state and the predicted state covariance matrix, respectively. This is the process noise array.

[0063] Given a measurement variance-covariance matrix based on an empirical model.

[0064] (10)

[0065] In the formula, Represents a diagonal matrix. To measure the variance-covariance matrix, and These are the GNSS measurement variance covariance matrix and the UWB measurement variance covariance matrix, respectively.

[0066] S3. Calculate the unit weighted variance using the predicted state combined with the variance component estimation method, adjust the variance scaling factors of GNSS and UWB based on the unit weighted variance, and update the measurement variance covariance matrix; specifically:

[0067] The prior residuals are calculated using formula (11):

[0068] (11)

[0069] In the formula, For the measurement matrix, For the prior residuals, derived from the prior residuals of GNSS Prior residuals of UWB composition.

[0070] The unit weighted variances of GNSS and UWB are obtained based on variance component estimation. and

[0071] (12)

[0072] (13)

[0073] (14)

[0074] in, For the measurement matrix, and These are the unit weighted variances for GNSS and UWB, respectively. and These represent the number of GNSS satellites and the number of UWB base stations, respectively. Let be the covariance matrix of the prior residuals;

[0075] Determine the variance scaling factors for GNSS and UWB based on the unit weight variance. :

[0076] ;

[0077] Where m = 1, 2, m = 1 represents GNSS, m = 2 represents UWB. It is a fixed constant. This is the variance scaling factor from the previous iteration, with an initial value of 1; This is the variance scaling factor for the current iteration.

[0078] The obtained variance scaling factor was used to update the measurement variance covariance matrix: (15)

[0079] S4. Introduce the IGG3 robust weight function to suppress gross errors and outliers, obtain the variance inflation factor, and update the measurement variance covariance matrix; specifically:

[0080] Introducing IGG3, we obtain the variance inflation factor. :

[0081] (16)

[0082] in, and It is an empirical constant. For standardized residuals.

[0083] Using the variance inflation factor, update the covariance matrix of the measurement equation again: (17)

[0084] S5. Repeat steps S3 and S4, iteratively calculating until the unit weight variances of different types of observations are equal.

[0085] S6. After iteration, the measurement is updated using the final updated measurement variance-covariance matrix and the measurement equation to achieve the positioning solution. The volume point is then calculated using the predicted state and the predicted state covariance matrix. Then calculate the measured predicted value:

[0086] (18)

[0087] (19)

[0088] in, To measure the predicted value.

[0089] Based on the predicted state in step S2, calculate the cross-covariance matrix:

[0090] (20)

[0091] Calculate the innovation covariance matrix by combining the updated measurement variance covariance matrix from S4.

[0092] (twenty one)

[0093] In the formula, and These are the mutual covariance and innovation covariance matrices, respectively.

[0094] Finally, the Kalman gain, state vector estimate, and corresponding variance-covariance matrix are calculated.

[0095] (twenty two)

[0096] (twenty three)

[0097] (twenty four)

[0098] In the formula, The posterior estimate of the state vector is given by the first three terms, which are coordinate estimates, thus enabling the localization solution.

[0099] An experiment was conducted on the PPP / UWB compact combination positioning method based on adaptive robust capacitive Kalman filtering provided in this embodiment of the invention. GNSS and UWB observation data were synchronously acquired using a GNSS receiver and UWB tags, and a dynamic experiment lasting approximately 30 minutes was carried out. The experimental route covered open areas and indoor / outdoor boundary areas. UWB base stations were pre-deployed at the indoor / outdoor boundary to enhance GNSS positioning performance.

[0100] PPP / UWB compact combination positioning was performed using both the traditional extended Kalman filter-based processing method and the adaptive robust capacitive Kalman filter processing method provided in this embodiment of the invention. The positioning results obtained by the two methods were statistically compared for reference. Figure 2 In the diagram, red represents the traditional method, and blue represents the method proposed in the embodiments of the present invention. Figure 2 As can be seen, the positioning error curve of the traditional method fluctuates significantly, with jump points appearing at some epochs. In contrast, the method of this invention has higher positioning accuracy.

[0101] The root mean square error of the positioning results for both methods is shown in Table 1. The positioning accuracy of the method in this embodiment of the invention in the east, north, and elevation directions in complex areas is 0.41m, 0.12m, and 0.49m, respectively. Compared with the traditional method, the positioning accuracy in the east, north, and elevation directions is improved by approximately 40%, 61%, and 43%, respectively.

[0102] Table 1 shows the root mean square error of the positioning results for the two methods.

[0103]

[0104] Example 2

[0105] Embodiment 2 of the present invention provides a terminal device corresponding to Embodiment 1 above. The terminal device can be a processing device for a client, such as a mobile phone, a laptop, a tablet computer, a desktop computer, etc., to execute the method of the above embodiments.

[0106] The terminal device in this embodiment includes a memory, a processor, and a computer program stored in the memory; the processor executes the computer program in the memory to implement the steps of the method in Embodiment 1 described above.

[0107] In some implementations, the memory may be high-speed random access memory (RAM), and may also include non-volatile memory, such as at least one disk storage device.

[0108] In other implementations, the processor can be any type of general-purpose processor, such as a central processing unit (CPU) or a digital signal processor (DSP), and there is no limitation here.

[0109] Example 3

[0110] Embodiment 3 of the present invention provides a computer-readable storage medium corresponding to Embodiment 1 above, on which a computer program / instructions are stored. When the computer program / instructions are executed by a processor, they implement the steps of the method of Embodiment 1 above.

[0111] A computer-readable storage medium can be a tangible device that holds and stores instructions for use by an instruction execution device. A computer-readable storage medium can be, for example, but not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any combination thereof.

[0112] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of this application can be implemented in various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0113] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0114] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0115] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0116] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A PPP / UWB compact combination positioning method, characterized in that, Includes the following steps: S1. Unify the spatiotemporal reference of GNSS and UWB data, and establish the PPP / UWB measurement equation; based on empirical values, initialize the state vector and parameter variance-covariance matrix; the PPP / UWB measurement equation is expressed as: ;in, Era numbering, For state vectors, For measurement vectors, For measurement functions, For measuring noise; The state vector of the k-th epoch is represented as: ； in, The three-dimensional coordinate components of the UWB measurement center in the Earth-centered Earth-fixed coordinate system. For receiver clock bias, To account for the deviation between different GNSS systems, For tropospheric delay, To eliminate ionospheric ambiguity; S2. Using the state vector and parameter variance-covariance matrix, calculate the volume point based on the third-order spherical radial volume Kalman filter criterion, and perform nonlinear propagation on the volume point to obtain the predicted state and the predicted state covariance matrix. The measurement variance-covariance matrix is ​​given based on an empirical model. The expression for the volume point is: ; For parameter variance and covariance matrix The Cholesky decomposition matrix, For weighted sigma points, =1,2…2 , State vector Dimension; , It is a diagonal matrix. Representing position and state respectively , , variance The variance representing the receiver clock error, The variance representing the deviation between different GNSS systems. The variance representing tropospheric delay, The variance representing the combined ambiguity of the deionization layer; Predicted state Covariance matrix of predicted state Represented as: in, For process noise array, , () represents the state function; S3. Calculate the unit weighted variance using the predicted state combined with the variance component estimation method, adjust the variance scaling factor of GNSS and UWB based on the unit weighted variance, and update the measurement variance covariance matrix. The formula for calculating the unit weighted variance is: ； ； ； ； in, and These are the unit weighted variances for GNSS and UWB, respectively. and These represent the number of GNSS satellites and the number of UWB base stations, respectively. For the prior residuals, derived from the prior residuals of GNSS Prior residuals of UWB composition, For the measurement matrix, The covariance matrix of the prior residuals; the measurement variance covariance matrix. , and These are the variance-covariance matrix of GNSS measurements and the variance-covariance matrix of UWB measurements, respectively. The formulas for calculating the variance scaling factor of GNSS and UWB are as follows: ； For fixed constants, m=1,2, where m=1 represents GNSS and m=2 represents UWB. This is the variance scaling factor from the previous iteration, with an initial value of 1; This is the variance scaling factor for the current iteration; S4. Introduce the IGG3 robust weight function to suppress gross errors and outlier observations, obtain the variance inflation factor, and update the measurement variance covariance matrix again. Updated measurement variance covariance matrix Represented as: Variance inflation factor The expression is: ; In the formula, and It is an empirical constant. To standardize the residuals, the updated measurement variance matrix ; S5. Repeat steps S3 and S4, iteratively calculating until the unit weight variances of different types of observations are equal. S6. After the iteration is completed, the measurement is updated using the final updated measurement variance covariance matrix and measurement equation to achieve the positioning solution.

2. The PPP / UWB compact positioning method according to claim 1, characterized in that, The process of unifying the spatiotemporal reference of GNSS and UWB data includes: Using the GNSS timestamp as a reference, the UWB timestamp is converted to GPST. When the UWB sampling frequency is greater than the GNSS sampling frequency, a linear interpolation method is used to establish a mapping between the UWB timestamp and the GPS timestamp to unify the time reference. For the spatial reference, the GNSS measurement center and the UWB measurement center are set on a vertical line. The height difference between the GNSS measurement center and the UWB measurement center is measured in advance. The distance correction factor projected onto the direction from the satellite to the GNSS measurement center is calculated. This correction factor is used to correct the original GNSS observation value and unify the measurement center to the position of the UWB measurement center.

3. The PPP / UWB compact positioning method according to claim 1, characterized in that, In step S6, the formula for the location solution is: ;in, For the posterior estimate of the state vector, , , and These are the mutual covariance and innovation covariance matrices, respectively. , , , , The volume point is calculated using the predicted state and the predicted state covariance matrix.

4. A PPP / UWB compact positioning system, comprising a memory, a processor, and a computer program stored in the memory; characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 3.

5. A computer-readable storage medium having a computer program / instructions stored thereon; characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1 to 3.

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