CN112765548B - Covariance determination method, positioning method and device for sensor fusion positioning - Google Patents
Covariance determination method, positioning method and device for sensor fusion positioning Download PDFInfo
- Publication number
- CN112765548B CN112765548B CN202110042412.1A CN202110042412A CN112765548B CN 112765548 B CN112765548 B CN 112765548B CN 202110042412 A CN202110042412 A CN 202110042412A CN 112765548 B CN112765548 B CN 112765548B
- Authority
- CN
- China
- Prior art keywords
- matrix
- parameter
- covariance
- determining
- sensor
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 98
- 230000004927 fusion Effects 0.000 title claims abstract description 40
- 239000011159 matrix material Substances 0.000 claims abstract description 312
- 230000008569 process Effects 0.000 claims abstract description 28
- 238000004364 calculation method Methods 0.000 claims abstract description 17
- 230000008859 change Effects 0.000 claims abstract description 16
- 238000005259 measurement Methods 0.000 claims abstract description 12
- 238000000354 decomposition reaction Methods 0.000 claims description 6
- 230000004807 localization Effects 0.000 claims description 5
- 230000015654 memory Effects 0.000 description 11
- 238000005457 optimization Methods 0.000 description 9
- 238000004590 computer program Methods 0.000 description 7
- 238000012545 processing Methods 0.000 description 7
- 230000006870 function Effects 0.000 description 4
- 238000010586 diagram Methods 0.000 description 3
- 238000013459 approach Methods 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 2
- 238000004422 calculation algorithm Methods 0.000 description 2
- 238000013461 design Methods 0.000 description 2
- 239000002245 particle Substances 0.000 description 2
- 238000012216 screening Methods 0.000 description 2
- 230000009471 action Effects 0.000 description 1
- 230000004075 alteration Effects 0.000 description 1
- 230000005540 biological transmission Effects 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000003287 optical effect Effects 0.000 description 1
- 230000008707 rearrangement Effects 0.000 description 1
- 238000012546 transfer Methods 0.000 description 1
- 230000000007 visual effect Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/005—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 with correlation of navigation data from several sources, e.g. map or contour matching
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/20—Instruments for performing navigational calculations
Abstract
The disclosure discloses a covariance determination method, a positioning method and a device for sensor fusion positioning. The covariance determination method comprises the following steps: acquiring a sensor parameter of which the change step length is larger than a set step length threshold value, which is obtained by the current iteration in the positioning process, as a first parameter; updating a current Jacobian matrix according to the first parameter and a residual factor obtained by current iteration, wherein the residual factor is determined according to measurement data of a sensor and sensor parameters; updating the current hessian matrix according to the split dense submatrices in the updated Jacobian matrix, and returning to execute the step of acquiring the first parameters until the iteration ending condition is met, and outputting the final hessian matrix; decomposing the hessian matrix to obtain an upper triangular matrix; a covariance matrix characterizing the accuracy and relevance of the first parameter is determined recursively from the upper triangular matrix. The accuracy of the determined covariance can be ensured on the basis of reducing the calculation amount.
Description
Technical Field
The disclosure relates to the technical field of positioning, in particular to a covariance determination method, a positioning method and a device for sensor fusion positioning.
Background
The multi-sensor fusion positioning generally refers to a positioning system comprising a visual sensor (such as a camera), an inertial measurement unit (Inertial Measurement Unit, IMU, abbreviated as "inertial navigation") and a global navigation satellite system (Global Navigation Satellite System, GNSS) positioning, and the like, and the system has the advantages of high positioning precision and low cost, and becomes a positioning scheme mainly selected for application scenes requiring high-precision (centimeter-level) positioning results. In the process of obtaining a high-precision positioning result through sensor fusion positioning, parameters such as the position and the gesture of each sensor need to be determined, and covariance of the parameters needs to be determined, so that the positioning precision radius of the fusion positioning is estimated, the relevance is estimated, and the like.
In the prior art, covariance estimation is generally carried out by adopting a Hessen matrix inversion method, but the number of dimensions of parameters of multi-sensor fusion positioning is large, the calculation force consumption of direct matrix inversion is huge, the system cost is increased, and the accuracy of the estimated covariance can be influenced by performing approximation processing in order to reduce the cost. Therefore, there is a need to provide new covariance determination schemes to meet cost and accuracy requirements.
Disclosure of Invention
In view of the above, the present disclosure has been made in order to provide a covariance determination method, a positioning method, and an apparatus for sensor fusion positioning that overcome or at least partially solve the above problems.
In a first aspect, an embodiment of the present disclosure provides a covariance determination method for sensor fusion positioning, including:
a parameter programming step comprising: acquiring a sensor parameter of which the change step length is larger than a set step length threshold value, which is obtained by the current iteration in the positioning process, as a first parameter;
the Jacobian matrix calculation step comprises the following steps: updating a current Jacobian matrix according to a residual factor obtained by current iteration and a first parameter obtained by a parameter arrangement step, wherein the residual factor is determined according to measurement data of a sensor and sensor parameters;
the hessian matrix solving step comprises the following steps: updating the current hessian matrix according to the split dense submatrices in the updated Jacobian matrix, returning to the parameter arrangement step until the iteration ending condition is met, and outputting a final hessian matrix;
the decomposing step comprises the following steps: decomposing the hessian matrix to obtain an upper triangular matrix;
a covariance resolving step comprising: determining a covariance matrix representing the accuracy and the relevance of the first parameter in a recursive manner according to the upper triangular matrix.
In a second aspect, an embodiment of the present disclosure provides a sensor fusion positioning method, including:
determining the accuracy of the corresponding sensor parameters according to diagonal elements in the covariance matrix determined according to the method;
and taking the parameter with the accuracy larger than the set threshold value as an initial value of the corresponding parameter in the next step of sensor fusion positioning.
In a third aspect, an embodiment of the present disclosure provides a covariance determining apparatus for sensor fusion positioning, comprising:
the parameter programming module is used for acquiring the sensor parameter, which is obtained by the current iteration in the positioning process and is larger than the set step threshold, as a first parameter;
the Jacobian matrix calculating module is used for updating the current Jacobian matrix according to the residual factors obtained by the current iteration and the first parameters obtained by the parameter arrangement module, wherein the residual factors are determined according to the measurement data of the multiple sensors and the sensor parameters;
the Hessen matrix solving module is used for updating the current Hessen matrix according to the split dense submatrices in the updated Jacobian matrix obtained by the Jacobian matrix solving module; the parameter programming module, the Jacobi matrix solving module and the hessian matrix solving module work circularly until iteration is finished, and the hessian matrix solving module is also used for outputting a final hessian matrix;
The decomposition module is used for decomposing the hessian matrix output by the hessian matrix solving module to obtain an upper triangular matrix;
a covariance calculation module for recursively determining a covariance matrix representing the accuracy and correlation of the first parameter according to the upper triangular matrix obtained by the decomposition module
In a fourth aspect, embodiments of the present disclosure provide a computer program product comprising a computer program/instruction, wherein the computer program/instruction, when executed by a processor, implements the above-described covariance determination method for sensor fusion positioning, or implements the above-described sensor fusion positioning method.
The covariance determination method for sensor fusion positioning provided by the embodiment of the disclosure comprises the following steps: a parameter programming step, namely acquiring a sensor parameter, which is obtained in the current iteration in the positioning process and is larger than a set step threshold, as a first parameter; a Jacobian matrix calculating step, namely updating the current Jacobian matrix according to residual factors obtained by current iteration and first parameters obtained by a parameter arrangement step, wherein the residual factors are determined according to measurement data of multiple sensors and sensor parameters; a Hessen matrix solving step, namely updating the current Hessen matrix according to the split dense submatrices in the updated Jacobian matrix, and returning to a parameter programming step until iteration is finished to obtain a final Hessen matrix; decomposing the hessian matrix to obtain an upper triangular matrix; and a covariance calculation step of determining a covariance matrix representing the accuracy and the correlation of the first parameter in a recursive manner according to the upper triangular matrix. The beneficial effects of the technical scheme at least comprise:
(1) And screening parameters with the change step length larger than a set step length threshold as first parameters according to the change step length of the sensor parameters obtained by the current iteration, and updating the current Jacobian matrix according to the first parameters and residual factors obtained by the current iteration. After each iteration is finished, only elements corresponding to sensor parameters with larger change step length are updated by using the updating result of the Jacobian matrix after the last iteration is finished, so that the calculated amount is reduced; according to the method, the current hessian matrix is updated according to the split dense submatrices in the Jacobian matrix, so that the calculated amount of sparse blocks is saved, and compared with a mode of solving a second derivative of a residual factor, the calculated amount is further reduced by directly determining the hessian matrix according to the product of the Jacobian matrix and the transpose thereof; the method has the advantages that the Heisen matrix is decomposed to obtain the upper triangular matrix, each element in the covariance matrix is determined in sequence in a recursion mode, and calculated amount is reduced compared with a mode of directly utilizing the Heisen matrix to invert.
(2) According to the method, the Jacobian matrix and the hessian matrix are updated in an increment mode, each element in the covariance matrix is determined in a recursion mode, and the determining method is only converted, namely the covariance matrix of each sensor parameter is determined by adopting the increment recursion method, and approximation processing is not carried out in the determining process, so that the calculation amount is reduced, and meanwhile, the accuracy is ensured.
Additional features and advantages of the disclosure will be set forth in the description which follows, and in part will be apparent from the description, or may be learned by practice of the disclosure. The objectives and other advantages of the disclosure will be realized and attained by the structure particularly pointed out in the written description and claims thereof as well as the appended drawings.
The technical scheme of the present disclosure is described in further detail below through the accompanying drawings and examples.
Drawings
The accompanying drawings are included to provide a further understanding of the disclosure, and are incorporated in and constitute a part of this specification, illustrate embodiments of the disclosure and together with the description serve to explain the disclosure, without limitation to the disclosure. In the drawings:
FIG. 1 is a flow chart of a covariance determination method for sensor fusion localization in accordance with an embodiment of the disclosure;
FIG. 2 is a flowchart showing the implementation of step S12 in FIG. 1;
FIG. 3 is a flowchart showing a specific implementation of step S13 in FIG. 1;
fig. 4 is a flowchart of a specific implementation of a covariance determination method for sensor fusion positioning in a second embodiment of the disclosure;
FIG. 5 is an exemplary diagram of an arrangement of sensor parameter blocks in an embodiment of the present disclosure;
FIG. 6 is an exemplary diagram of determining a hessian matrix based on jacobian matrix delta in an embodiment of the disclosure;
Fig. 7 is a schematic structural diagram of a covariance determining apparatus for sensor fusion positioning in an embodiment of the disclosure.
Detailed Description
Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
In order to solve the problems of large calculation power consumption and low precision in the covariance determination process of the positioning parameters of the multi-sensor fusion positioning system in the prior art, the embodiment of the disclosure provides a covariance determination method, a positioning method and a device for sensor fusion positioning, which can accurately recover covariance and have relatively small calculation amount in the whole process.
The multi-sensor fusion positioning system in the following embodiments generally includes a vision sensor, an inertial navigation satellite system and a global navigation satellite system, and the multi-sensor positioning needs to determine sensor parameters according to measurement data of the multi-sensor in an iterative optimization manner, that is, positioning parameters related to the sensor, which need to be optimized in the positioning process, may also be simply referred to as positioning parameters. Specifically, the sensor parameters may be direct pose parameters, or may be other parameters to be optimized in the process of determining pose parameters, for example, the sensor parameters that are iteratively optimized during initialization include: the pose of the vision sensor (the position and pose of each frame relative to the first frame), the scale of the vision sensor, the speed of the vision sensor, the rotational external parameters between the camera coordinate system and the world coordinate system, the zero offset of the gyroscope, etc.; the sensor parameters for iterative optimization in the positioning process comprise: pose under relative world coordinate system, pose under absolute world coordinate system, rotation external parameter between relative world coordinate system and absolute world coordinate system, and relative position external parameter between antenna and inertial navigation of global positioning system, etc. In the iterative optimization process, a plurality of residual factors comprising measurement data of each sensor, namely observation data and sensor parameters to be optimized need to be established, and each residual factor can be a sensor parameter comprising part of the observation data and part of the sensor parameters.
Sensor parameter x= (X) 1 ,X 2 ,……，X n ) T When the covariance matrix is n-dimensional parameter, the covariance matrix is:
wherein, sigma ij The covariance between the ith sensor parameter and the jth sensor parameter is the element of the ith row and the jth column in the covariance matrix，i＝1,2……n，j＝1,2……n。
The covariance Matrix of the sensor parameters can be determined by firstly determining Jacobians Matrix according to the sensor parameters and residual factors, then determining Hessian Matrix according to the Jacobian Matrix, and finally determining the covariance Matrix according to the Hessian Matrix.
In vector calculus, a jacobian matrix is a matrix in which first partial derivatives are arranged in a certain manner, and its determinant is called jacobian. The importance of the jacobian matrix is that it represents a better linear approximation of a micro-equation to a given point.
Assume that there are m residual factors r 1 ,r 2 ,……，r m N sensor parameters X 1 ,X 2 ,……，X n The determined jacobian matrix J is:
wherein J is ti Representing the element of row t and column i in the Jacobian matrix, i.e. the t residual factor r t Regarding the ith sensor parameter x i T=1, 2 … … m, i=1, 2 … … n.
The hessian matrix is a square matrix of the second partial derivatives of a multivariate function, describing the local curvature of the function. Assuming that the target factor (i.e. the sum of the residual factors) constituted by the residual factors is r, n sensor parameters X 1 ,X 2 ,……，X n The determined hessian matrix H is:
wherein H is ij Representing the second partial derivatives of the target factor r with respect to the ith and jth sensor parameters, i=1, 2 … … n, j=1, 2 … … n.
The covariance determination method of the specific sensor parameters is described in detail in the following embodiments.
Example 1
An embodiment of the present disclosure provides a covariance determining method for sensor fusion positioning, the flow of which is shown in fig. 1, comprising the following steps:
step S11: and (5) parameter arrangement.
The method specifically comprises the following steps: and acquiring a sensor parameter of which the change step length obtained by the current iteration in the positioning process is larger than a set step length threshold as a first parameter.
In the positioning process, each sensor parameter needs to be subjected to iterative optimization, only a small part of the parameters possibly change in each iterative optimization process of the sensor parameter, which means that a lot of parameters do not need to be re-linearized, so that the sensor parameter with small step change in the iterative optimization does not need to be re-linearized with respect to the corresponding residual factor, the value of the corresponding element in the Jacobian matrix does not need to be updated, and the calculation force consumption can be greatly reduced.
Step S12: and solving the Jacobian matrix.
The method specifically comprises the following steps: updating the current Jacobian matrix according to the residual factor obtained by the current iteration and the first parameter obtained by the parameter arrangement step, wherein the residual factor is determined according to the measurement data of the sensor and the sensor parameter.
In one embodiment, referring to fig. 2, the updating of the jacobian matrix can include the steps of:
step S121: and for each residual factor obtained by the current iteration, determining the updated value of the corresponding element in the Jacobian matrix according to the first parameter contained in the residual factor.
Each residual factor may include one or more first parameters, and for each residual factor, according to the iteration result of each first parameter included in the residual factor at the current iteration, determining the first derivative of the residual factor with respect to each first parameter as the updated value of the residual factor and the corresponding element of each first parameter included in the residual factor in the jacobian matrix. Specifically, a residual factor and a first parameter contained in the residual factor correspond to an element in the jacobian matrix.
Step S122: and determining the position of the corresponding element of the residual factor in the Jacobian matrix according to the identification of the residual factor and the identification of the first parameter contained in the residual factor.
Step S123: the values of the elements of the location in the current jacobian matrix are replaced with corresponding updated values.
For example residual factor r 2 Comprising a first parameter x 1 And x 5 Then r can be determined 2 Concerning x 1 As residual factor r 2 And a first parameter x 1 Determining r in the Jacobian matrix corresponding to the updated value of element A 2 Concerning x 5 As residual factor r 2 And a first parameter x 5 The updated value of the corresponding element B in the jacobian matrix; according to the identification of the residual factor (subscript 2) and the first parameter x contained therein 1 Is determined to be the position of element a in the following jacobian matrix as row 2, column 1, based on the identity of the residual factor (subscript 2) and the first parameter x it contains 5 And (B) determines the position of element B in the jacobian matrix described below as row 2 and column 5. Replacing the value of the element in the 2 nd row and the 1 st column in the current Jacobian matrix with the updated value of the element A, and replacing the value of the element in the 2 nd row and the 5 th column with the updated value of the element B; because of residual factor r 2 No other residual factors are included, so that no change is made to other elements in row 2 of the jacobian matrix.
Wherein J is ti Representing the element of row t and column i in the Jacobian matrix, i.e. the t residual factor r t Regarding the ith sensor parameter x i T=1, 2 … … m, i=1, 2 … … n.
Step S13: and solving a hessian matrix.
The method specifically comprises the following steps: and updating the current hessian matrix according to the split dense submatrices in the updated Jacobian matrix.
Can be used forThe product of the jacobian matrix and the transpose matrix of the jacobian matrix is used as the hessian matrix, but the complexity of this approach is high, for example, the m-dimensional residual factor, and the overall complexity is (mn) when the n-dimensional sensor parameters are 2 . Since each residual factor often contains only few sensor parameters, many elements in the jacobian matrix are 0, i.e., the jacobian matrix is sparse, so that a fast hessian matrix update can be performed in an incremental manner.
Specifically, the dense submatrix refers to a matrix with more non-0 elements.
In one embodiment, referring to fig. 3, updating the current hessian matrix based on the split dense submatrices in the updated jacobian matrix may include the steps of:
step S131: for each row in the updated jacobian matrix, starting from the first non-zero element, splitting the continuous at least two non-zero elements into a dense sub-matrix, and determining the value of the updated sub-element according to the dense sub-matrix.
Specifically, for each row in the jacobian matrix, one dense submatrix may be split, or multiple dense submatrices may be split, for example, starting from a first non-zero element, at intervals of zero elements, at least two consecutive non-zero elements are split into one dense submatrix, and if a next element of one non-zero element is a zero element, the non-zero element and a subsequent consecutive non-zero element are split into one dense submatrix.
The value of the updated sub-element is determined from the dense sub-matrix, which may be by first determining the product of the dense sub-matrix and the transpose of the dense sub-matrix, and determining that the non-zero element therein is the value of the updated sub-element.
Step S132: and determining the position of the corresponding element of the updated subelement in the hessian matrix according to the identification of the first parameter corresponding to the updated subelement.
Specifically, the value of each updated subelement is obtained according to the values of two elements in the Jacobian matrix, and can be two identical elements in the Jacobian matrix or two different elements; the elements in the Jacobian matrix are corresponding to the unique identifiers of the first parameters, and the positions of the corresponding elements of the updated sub-elements in the Heisen matrix are determined according to the identifiers of the two first parameters.
For example, dense submatrix A isAA T Is->The dense submatrix a may determine 4 second updated subelements +.>And->The positions of the corresponding elements in the hessian matrix are respectively 1 st row and 1 st column, 1 st row and 5 th column, 5 th row and 1 st column and 5 th row and 5 th column.
Step S133: and replacing the value of the element at the position in the current hessian matrix with the sum of the values of the corresponding updated subelements.
Disassembling elements in the jacobian matrix corresponding to each residual factor into a plurality of dense increment blocks, and updating a plurality of increment type dense submatrices on the sparse hessian matrix; and combining the stable parameters in the step S11, namely, corresponding elements of the first parameters with small step change in the jacobian matrix are not updated, the jacobian matrix and the hessian matrix are updated in an incremental mode, and the covariance determination efficiency is improved.
The fusion positioning is to determine the sensor parameters by an iterative optimization method, update the current jacobian matrix and the hessian matrix after each iteration of one optimization, and recover the covariance matrix according to the final hessian matrix after the iteration is finished. Therefore, after the step S13 is performed, it is determined whether the iteration end condition is satisfied, if yes, the step S14 is performed; if not, returning to the step S11 until the iteration ending condition is met.
Step S14: and outputting the final hessian matrix.
Step S15: and decomposing the hessian matrix.
The method specifically comprises the following steps: and decomposing the hessian matrix to obtain an upper triangular matrix.
In one embodiment, the hessian matrix is decomposed by Cholesky to obtain an upper triangular matrix. And decomposing the Heisen matrix into products of an upper triangular matrix and a lower triangular matrix to obtain the upper triangular matrix.
Step S16: covariance solution.
Specifically, a covariance matrix characterizing the accuracy and the relevance of the first parameter is determined in a recursive manner according to the upper triangular matrix.
The covariance matrix is determined by utilizing the inverse mode of the hessian matrix, and the values of the elements in the covariance matrix can be determined step by step in a recursive mode because the larger number of dimensions of the first parameter can cause great calculation power consumption.
In one embodiment, the values of the elements with undetermined values in the covariance matrix are determined according to the values of the corresponding elements in the upper triangular matrix and the values of the corresponding elements with determined values in the covariance matrix in turn in a recursive manner according to the order of the row-column numbers from large to small and diagonal elements first and then non-diagonal elements. The total number of rows and total columns of elements in the covariance matrix are respectively consistent with the total number of rows and total columns of elements in the upper triangular matrix.
Specifically, firstly, according to the value of the diagonal element with the largest row and column number in the upper triangular matrix, determining the value of the element at the corresponding position in the covariance matrix, namely, firstly, according to the value of the diagonal element with the largest row and column number in the upper triangular matrix, determining the value of the element at the corresponding position in the covariance matrix for the first time; and determining the values of the elements which are not determined to be valued in the covariance matrix according to the values of the corresponding elements in the upper triangular matrix and the values of the corresponding elements in the covariance matrix in turn in a recursive manner according to the sequence of the diagonal elements and the off-diagonal elements from large to small in row and column numbers. And finally, determining the value of each element in the covariance matrix, and finishing updating the covariance matrix.
Specifically, the above covariance matrix, whose diagonal elements represent the accuracy of the first parameter, that is, the accuracy radius of the first element, so that the accuracy of the corresponding sensor parameter can be determined according to the diagonal elements in the covariance matrix; each element in the covariance matrix characterizes the correlation of the corresponding two sensor parameters, so that the correlation of the sensor parameters can be determined pairwise according to the elements in the covariance matrix.
The technical scheme in the first embodiment at least has the following beneficial effects:
(1) And screening the sensor parameters with the change step length larger than the set step length threshold as the first parameters according to the change step length of the sensor parameters obtained by the current iteration, and updating the current Jacobian matrix according to the first parameters and residual factors obtained by the current iteration. After each iteration is finished, only elements corresponding to sensor parameters with larger change step length are updated by using the updating result of the Jacobian matrix after the last iteration is finished, so that the calculated amount is reduced.
(2) According to the method, the current hessian matrix is updated according to the split dense submatrices in the Jacobian matrix, so that the calculated amount of sparse blocks is saved, and compared with a mode of solving a second derivative of a residual factor, or a mode of directly determining the hessian matrix according to the product of the Jacobian matrix and the transpose thereof, the calculated amount is further reduced.
(3) The method has the advantages that the Heisen matrix is decomposed to obtain the upper triangular matrix, each element in the covariance matrix is determined in sequence in a recursion mode, and calculated amount is reduced compared with a mode of directly utilizing the Heisen matrix to invert.
(4) According to the method, the Jacobian matrix and the hessian matrix are updated in an increment mode, each element in the covariance matrix is determined in a recursion mode, and the determining method is only converted, namely the covariance matrix of each sensor parameter is determined by adopting the increment recursion method, and approximation processing is not carried out in the determining process, so that the calculation amount is reduced, and meanwhile, the accuracy is ensured.
Example two
The second embodiment of the disclosure provides a specific implementation of a covariance determination method for sensor fusion positioning, and the flow is shown in fig. 4, and includes the following steps:
step S41: and determining target parameters from the sensor parameters to be optimized according to the set rules.
In the iterative optimization process of the sensor parameters, covariance matrixes (used for representing the accuracy and the relevance of the sensor parameters) which are required to be recovered are only a part of the whole covariance matrix, and the covariance matrixes which are required to be recovered specifically are different for different application scenes, so that a real-time positioning system is realized, and the pose covariance matrix of the latest frame is required to be recovered; for lossless information transfer of the crowdsourcing high-precision map, only covariance matrixes of the last few key frames with strong correlation are required to be recovered; for the data association problem, only covariance matrices of some feature points need to be recovered.
The sensor parameters of covariance to be determined can be determined according to specific application scenes and used as target parameters; referring to FIG. 5, with the overall covariance matrix, first a rearrangement of sensor parameter blocks, e.g., sensor parameters for which covariance needs to be determined are xi, xj, and xk; and (3) centralizing the sensor parameters (target parameters) of the covariance to be restored in the corresponding elements in the covariance matrix to form an edge covariance block to be restored, and determining each element to be determined according to the determined edge covariance block.
The determination of the target parameters enables the steps to be executed on the basis of the screened target parameters, and the calculated amount is reduced.
Step S42: and acquiring a target parameter, which is obtained by the current iteration in the positioning process and is larger than a set step threshold, as a first parameter.
Step S43: and updating the current Jacobian matrix according to the residual factor obtained by the current iteration and the first parameter obtained by the parameter arrangement step.
Step S44: and updating the current hessian matrix according to the split dense submatrices in the updated Jacobian matrix.
Referring to fig. 6, each row in the jacobian matrix J has a correspondence with one of the residual factors Res, and each column in J has a correspondence with one of the first parameters, specifically, each row is a first derivative of one of the residual factors with respect to each of the first parameters.
Splitting elements in J according to a row, for example, splitting J_i corresponding to residual factor Res_i and J_j … … corresponding to residual factor Res_k corresponding to residual factor Res_j; then, for each row to be split, the dense blocks (i.e. dense submatrices) are split, for example, J_i splits the dense blocks X_i, X_j … … X_k; and updating the current hessian matrix H according to the split dense blocks in the Jacobian matrix.
After the step S44 is executed, it is determined whether the iteration end condition is satisfied, if yes, the step S45 is executed; if not, returning to the step S42 until the iteration end condition is satisfied.
Step S45: and outputting the final hessian matrix.
Step S46: and (5) performing Cholesky decomposition on the Heisen matrix to obtain an upper triangular matrix.
Step S47: and determining the value of the element at the corresponding position in the covariance matrix according to the value of the diagonal element with the largest row and column number in the upper triangular matrix.
Step S48: according to the sequence of the diagonal line elements and the off-diagonal line elements from large to small in row and column numbers, determining the values of the elements which are not determined to be valued in the covariance matrix in sequence in a recursion mode according to the values of the corresponding elements in the upper triangular matrix and the values of the corresponding elements in the covariance matrix.
In order of row number from large to small and diagonal elements first followed by non-diagonal elements, in particular, in covariance matrix (Σ) ij ) nn For example, the diagonal element Σ of the lower right corner of the covariance matrix is first determined nn The method comprises the steps of carrying out a first treatment on the surface of the Then determining other elements in the nth row according to the sequence from the big column number to the small column number, and determining other elements in the nth column according to the sequence from the big column number to the small column number; determining the diagonal element sigma (n-1)(n-1) The method comprises the steps of carrying out a first treatment on the surface of the Then determining other elements in the n-1 th row according to the sequence from the large column number to the small column number, and determining other elements in the n-1 th column according to the sequence from the large column number to the small column number; determining the diagonal element sigma (n-2)(n-2) … … until the values of all elements in the covariance matrix are determined.
To determine the complete diagonal element sigma ii The latter is exemplified by specifically determining the same in the ith rowThe other elements in the ith column or the other elements determined first can be performed simultaneously.
Specifically, the method for determining the element in the covariance may include:
when an element which is not determined to be valued in the covariance matrix is a diagonal element, determining a first row number and a first column number of the element, and determining the value of the element which is not determined to be valued according to the value of the element with the same row number as the first row number in the upper triangular matrix and the value of the element with the row number larger than the first row number and the column number as the first column number in the covariance matrix;
when the element with the undetermined value in the covariance matrix is a non-corner line element, determining a second row number and a second column number of the element, and determining the value of the element with the undetermined value according to the value of the element with the same row number as the second row number in the upper triangular matrix, wherein the row number in the covariance matrix is larger than the value of the element with the same row number as the second column number, and the value of the element with the same column number as the second column number and the larger row number than the second row number in the covariance matrix.
Specifically, diagonal and off-diagonal elements in covariance can be determined separately by the following formulas:
wherein U is ik Or other subscripts representing an element of the upper triangular cross matrix, the subscripts representing its row and column numbers.
Specifically, in the above-mentioned covariance matrix determining process, for each type of matrix in the intermediate buffer, only the dense submatrices in the matrix and the position correspondence between the elements in the dense submatrices and the elements in the original matrix may be stored, so that the storage space requirement may be reduced, and the space complexity of the matrix may be reduced.
Based on the inventive concept of the present disclosure, an embodiment of the present disclosure further provides a sensor fusion positioning method, including:
determining the accuracy of the corresponding sensor parameters according to diagonal elements in the covariance matrix determined according to the method;
and taking the parameter with the accuracy larger than the set threshold value as an initial value of the corresponding parameter in the next step of sensor fusion positioning.
Based on the inventive concept of the present disclosure, an embodiment of the present disclosure further provides a covariance determining apparatus for sensor fusion positioning, with a structure as shown in fig. 7, including:
the parameter programming module 71 is configured to obtain, as a first parameter, a sensor parameter having a variation step length greater than a set step length threshold value obtained by a current iteration in the positioning process;
A jacobian matrix calculation module 72, configured to update a current jacobian matrix according to a residual factor obtained by a current iteration and a first parameter obtained by the parameter arrangement module 71, where the residual factor is determined according to measurement data of multiple sensors and sensor parameters;
a hessian matrix solving module 73, configured to update a current hessian matrix according to the split dense submatrices in the updated jacobian matrix obtained by the jacobian matrix solving module 72; the parameter programming module 71, the jacobian matrix solving module 72 and the hessian matrix solving module 73 work circularly until the iteration is finished, and the hessian matrix solving module 73 is also used for outputting a final hessian matrix;
the decomposition module 74 is configured to decompose the hessian matrix output by the hessian matrix solution module 73 to obtain an upper triangular matrix;
a covariance calculation module 75, configured to determine, in a recursive manner, a covariance matrix that characterizes the accuracy and the correlation of the first parameter according to the upper triangular matrix obtained by the decomposition module 74.
In one embodiment, the jacobian matrix calculation module 72 is specifically configured to:
for each residual factor obtained by the current iteration, determining an updated value of a corresponding element in the Jacobian matrix according to a first parameter contained in the residual factor; determining the position of a corresponding element of the residual factor in the Jacobian matrix according to the identification of the residual factor and the identification of the first parameter contained in the residual factor; the values of the elements of the location in the current jacobian matrix are replaced with corresponding updated values.
In one embodiment, the hessian matrix solution module 73 is specifically configured to:
for each row in the updated jacobian matrix, starting from a first non-zero element, splitting at least two continuous non-zero elements into a dense sub-matrix, and determining values of updated sub-elements according to the dense sub-matrix; determining the position of a corresponding element of the updated subelement in the hessian matrix according to the identification of the first parameter corresponding to the updated subelement; and replacing the value of the element of the position in the current hessian matrix with the sum of the values of the corresponding updated subelements.
In one embodiment, the covariance resolving module 75 is specifically configured to:
determining the value of the element at the corresponding position in the covariance matrix according to the value of the diagonal element with the maximum row and column number in the upper triangular matrix, wherein the total row number and the total column number of the element in the covariance matrix are respectively consistent with the total row number and the total column number of the element in the upper triangular matrix; according to the sequence of the diagonal line elements and the off-diagonal line elements from large to small in row and column numbers, determining the values of the elements which are not determined to be valued in the covariance matrix in sequence in a recursion mode according to the values of the corresponding elements in the upper triangular matrix and the values of the corresponding elements in the covariance matrix.
In one embodiment, the covariance resolving module 75 is specifically configured to:
when an element which is not determined to be valued in the covariance matrix is a diagonal element, determining a first row number and a first column number of the element, and determining the value of the element which is not determined to be valued according to the value of the element with the same row number as the first row number in the upper triangular matrix and the value of the element with the row number larger than the first row number and the column number as the first column number in the covariance matrix; when the element which is not determined to be valued in the covariance matrix is a non-corner line element, a second row number and a second column number of the element are determined, and according to the value of the element with the same row number as the second row number in the upper triangular matrix, the value of the element with the same row number as the second column number in the covariance matrix is larger than the value of the element with the same row number as the second row number, and the value of the element with the same column number as the second column number and with the larger row number than the second row number in the covariance matrix, the value of the element which is not determined to be valued is determined.
In one embodiment, the apparatus further comprises: a target parameter determination module 76 for:
determining target parameters from sensor parameters to be optimized according to set rules;
correspondingly, the parameter programming module 71 is specifically configured to:
The target parameter, which is obtained from the target parameter determined by the target parameter determining module 76 and is obtained by the current iteration in the positioning process and has a change step length greater than the set step length threshold, is the first parameter.
In one embodiment, the apparatus further comprises: a determining module 77 for:
determining the accuracy of the corresponding sensor parameters from diagonal elements in the covariance matrix obtained by covariance calculation module 75; and/or, determining the correlation of the sensor parameters by two according to the elements in the covariance matrix obtained by the covariance calculation module 75.
The specific manner in which the various modules perform the operations in the apparatus of the above embodiments have been described in detail in connection with the embodiments of the method, and will not be described in detail herein.
Based on the inventive concept of the present disclosure, the embodiments of the present disclosure further provide a computer program product, including a computer program/instruction, where the computer program/instruction, when executed by a processor, implements the above covariance determination method for sensor fusion positioning, or implements the above sensor fusion positioning method.
Based on the inventive concepts of the present disclosure, embodiments of the present disclosure also provide a computer-readable storage medium having stored thereon computer instructions that, when executed by a processor, implement the above-described covariance determination method for sensor fusion localization, or implement the above-described sensor fusion localization method.
Based on the inventive concept of the present disclosure, an embodiment of the present disclosure further provides a server, including: the system comprises a memory, a processor and a computer program stored in the memory and capable of running on the processor, wherein the processor realizes the covariance determination method for sensor fusion positioning or the sensor fusion positioning method when executing the program.
Unless specifically stated otherwise, terms such as processing, computing, calculating, determining, displaying, or the like, may refer to an action and/or process of one or more processing or computing systems, or similar devices, that manipulates and transforms data represented as physical (e.g., electronic) quantities within the processing system's registers or memories into other data similarly represented as physical quantities within the processing system's memories, registers or other such information storage, transmission or display devices. Information and signals may be represented using any of a variety of different technologies and techniques. For example, data, instructions, commands, information, signals, bits, symbols, and chips that may be referenced throughout the above description may be represented by voltages, currents, electromagnetic waves, magnetic fields or particles, optical fields or particles, or any combination thereof.
It should be understood that the specific order or hierarchy of steps in the processes disclosed are examples of exemplary approaches. Based on design preferences, it is understood that the specific order or hierarchy of steps in the processes may be rearranged without departing from the scope of the present disclosure. The accompanying method claims present elements of the various steps in a sample order, and are not meant to be limited to the specific order or hierarchy presented.
In the foregoing detailed description, various features are grouped together in a single embodiment for the purpose of streamlining the disclosure. This method of disclosure is not to be interpreted as reflecting an intention that the claimed embodiments of the subject matter require more features than are expressly recited in each claim. Rather, as the following claims reflect, the present disclosure is directed to less than all of the features of a single disclosed embodiment. Thus, the following claims are hereby expressly incorporated into this detailed description, with each claim standing on its own as a separate preferred embodiment of this disclosure.
Those of skill would further appreciate that the various illustrative logical blocks, modules, circuits, and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both. To clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, modules, circuits, and steps have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the overall system. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present disclosure.
The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module may reside in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor such the processor can read information from, and write information to, the storage medium. In the alternative, the storage medium may be integral to the processor. The processor and the storage medium may reside in an ASIC. The ASIC may reside in a user terminal. The processor and the storage medium may reside as discrete components in a user terminal.
For a software implementation, the techniques described herein may be implemented with modules (e.g., procedures, functions, and so on) that perform the functions described herein. These software codes may be stored in memory units and executed by processors. The memory unit may be implemented within the processor or external to the processor, in which case it can be communicatively coupled to the processor via various means as is known in the art.
The foregoing description includes examples of one or more embodiments. It is, of course, not possible to describe every conceivable combination of components or methodologies for purposes of describing the aforementioned embodiments, but one of ordinary skill in the art may recognize that many further combinations and permutations of various embodiments are possible. Accordingly, the embodiments described herein are intended to embrace all such alterations, modifications and variations that fall within the scope of the appended claims. Furthermore, as used in the specification or claims, the term "comprising" is intended to be inclusive in a manner similar to the term "comprising," as interpreted when employed as a transitional word in a claim. Furthermore, any use of the term "or" in the specification of the claims is intended to mean "non-exclusive or". The terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
Claims (10)
1. A covariance determination method for sensor fusion localization, comprising:
a parameter programming step comprising: acquiring a sensor parameter of which the change step length is larger than a set step length threshold value, which is obtained by the current iteration in the positioning process, as a first parameter;
The Jacobian matrix calculation step comprises the following steps: updating a current Jacobian matrix according to a residual factor obtained by current iteration and a first parameter obtained by a parameter arrangement step, wherein the residual factor is determined according to measurement data of a sensor and sensor parameters;
the hessian matrix solving step comprises the following steps: updating the current hessian matrix according to the split dense submatrices in the updated Jacobian matrix, returning to the parameter arrangement step until the iteration ending condition is met, and outputting a final hessian matrix;
the decomposing step comprises the following steps: decomposing the hessian matrix to obtain an upper triangular matrix;
a covariance resolving step comprising: determining a covariance matrix representing the accuracy and the relevance of the first parameter in a recursive manner according to the upper triangular matrix.
2. The method of claim 1, wherein the updating the current jacobian matrix according to the residual factor obtained in the current iteration and the first parameter obtained in the parameter arrangement step specifically comprises:
for each residual factor obtained by the current iteration, determining an updated value of a corresponding element in the Jacobian matrix according to a first parameter contained in the residual factor;
determining the position of a corresponding element of the residual factor in the Jacobian matrix according to the identification of the residual factor and the identification of the first parameter contained in the residual factor;
The values of the elements of the location in the current jacobian matrix are replaced with corresponding updated values.
3. The method according to claim 1, wherein the updating the current hessian matrix according to the split dense submatrices in the updated jacobian matrix specifically comprises:
for each row in the updated jacobian matrix, starting from a first non-zero element, splitting at least two continuous non-zero elements into a dense sub-matrix, and determining values of updated sub-elements according to the dense sub-matrix;
determining the position of a corresponding element of the updated subelement in the hessian matrix according to the identification of the first parameter corresponding to the updated subelement;
and replacing the value of the element of the position in the current hessian matrix with the sum of the values of the corresponding updated subelements.
4. The method according to claim 1, wherein said determining a covariance matrix characterizing the accuracy and the relevance of the first parameter from the upper triangular matrix in a recursive manner comprises:
determining the value of the element at the corresponding position in the covariance matrix according to the value of the diagonal element with the maximum row and column number in the upper triangular matrix, wherein the total row number and the total column number of the element in the covariance matrix are respectively consistent with the total row number and the total column number of the element in the upper triangular matrix;
According to the sequence of the diagonal line elements and the off-diagonal line elements from large to small in row and column numbers, determining the values of the elements which are not determined to be valued in the covariance matrix in sequence in a recursion mode according to the values of the corresponding elements in the upper triangular matrix and the values of the corresponding elements in the covariance matrix.
5. The method according to claim 4, wherein the determining the value of the element in the covariance matrix which is not determined to be valued sequentially according to the value of the corresponding element in the upper triangular matrix and the value of the corresponding element in the covariance matrix in a recursive manner specifically comprises:
when an element which is not determined to be valued in the covariance matrix is a diagonal element, determining a first row number and a first column number of the element, and determining the value of the element which is not determined to be valued according to the value of the element with the same row number as the first row number in the upper triangular matrix and the value of the element with the row number larger than the first row number and the column number as the first column number in the covariance matrix;
when the element which is not determined to be valued in the covariance matrix is a non-corner line element, a second row number and a second column number of the element are determined, and according to the value of the element with the same row number as the second row number in the upper triangular matrix, the value of the element with the same row number as the second column number in the covariance matrix is larger than the value of the element with the same row number as the second row number, and the value of the element with the same column number as the second column number and with the larger row number than the second row number in the covariance matrix, the value of the element which is not determined to be valued is determined.
6. The method of any one of claims 1-5, further comprising:
determining target parameters from sensor parameters to be optimized according to set rules; in a corresponding manner,
the sensor parameters, of which the variation step length obtained by the current iteration in the positioning process is larger than the set step length threshold, are first parameters, and specifically include:
and acquiring a target parameter, which is obtained in the current iteration in the positioning process and has a change step length greater than a set step length threshold, from the target parameter as a first parameter.
7. The method of any one of claims 1-5, further comprising, after performing the covariance resolving step:
determining the accuracy of the corresponding sensor parameters according to diagonal elements in the covariance matrix; and/or the number of the groups of groups,
and determining the correlation of the sensor parameters in pairs according to the elements in the covariance matrix.
8. A sensor fusion positioning method comprises the following steps:
determining the accuracy of the corresponding sensor parameter from diagonal elements in the covariance matrix determined according to the method of any one of claims 1-7;
and taking the parameter with the accuracy larger than the set threshold value as an initial value of the corresponding parameter in the next step of sensor fusion positioning.
9. A covariance determination apparatus for sensor fusion localization, comprising:
The parameter programming module is used for acquiring the sensor parameter, which is obtained by the current iteration in the positioning process and is larger than the set step threshold, as a first parameter;
the Jacobian matrix calculating module is used for updating the current Jacobian matrix according to the residual factors obtained by the current iteration and the first parameters obtained by the parameter arrangement module, wherein the residual factors are determined according to the measurement data of the multiple sensors and the sensor parameters;
the Hessen matrix solving module is used for updating the current Hessen matrix according to the split dense submatrices in the updated Jacobian matrix obtained by the Jacobian matrix solving module; the parameter programming module, the Jacobi matrix solving module and the hessian matrix solving module work circularly until iteration is finished, and the hessian matrix solving module is also used for outputting a final hessian matrix;
the decomposition module is used for decomposing the hessian matrix output by the hessian matrix solving module to obtain an upper triangular matrix;
and the covariance resolving module is used for determining a covariance matrix representing the accuracy and the relevance of the first parameter in a recursive manner according to the upper triangular matrix obtained by the decomposing module.
10. A computer readable storage medium having stored thereon computer instructions, wherein the computer instructions, when executed by a processor, implement the covariance determination method for sensor fusion positioning of any one of claims 1-7, or the sensor fusion positioning method of claim 8.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110042412.1A CN112765548B (en) | 2021-01-13 | 2021-01-13 | Covariance determination method, positioning method and device for sensor fusion positioning |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110042412.1A CN112765548B (en) | 2021-01-13 | 2021-01-13 | Covariance determination method, positioning method and device for sensor fusion positioning |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN112765548A CN112765548A (en) | 2021-05-07 |
| CN112765548B true CN112765548B (en) | 2024-01-09 |
Family
ID=75700098
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110042412.1A Active CN112765548B (en) | 2021-01-13 | 2021-01-13 | Covariance determination method, positioning method and device for sensor fusion positioning |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN112765548B (en) |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20230008651A1 (en) * | 2021-07-07 | 2023-01-12 | Rohde & Schwarz Gmbh & Co. Kg | Jitter determination method and measurement instrument |
| CN114881124B (en) * | 2022-04-21 | 2023-07-25 | 北京百度网讯科技有限公司 | Causal relation graph construction method and device, electronic equipment and medium |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109993113A (en) * | 2019-03-29 | 2019-07-09 | 东北大学 | A kind of position and orientation estimation method based on the fusion of RGB-D and IMU information |
| WO2019136613A1 (en) * | 2018-01-09 | 2019-07-18 | 深圳市沃特沃德股份有限公司 | Indoor locating method and device for robot |
| WO2020107930A1 (en) * | 2018-11-29 | 2020-06-04 | 南京人工智能高等研究院有限公司 | Camera pose determination method and apparatus, and electronic device |
| CN111678515A (en) * | 2020-04-28 | 2020-09-18 | 北京三快在线科技有限公司 | Device state estimation method and device, electronic device and storage medium |
-
2021
- 2021-01-13 CN CN202110042412.1A patent/CN112765548B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2019136613A1 (en) * | 2018-01-09 | 2019-07-18 | 深圳市沃特沃德股份有限公司 | Indoor locating method and device for robot |
| WO2020107930A1 (en) * | 2018-11-29 | 2020-06-04 | 南京人工智能高等研究院有限公司 | Camera pose determination method and apparatus, and electronic device |
| CN109993113A (en) * | 2019-03-29 | 2019-07-09 | 东北大学 | A kind of position and orientation estimation method based on the fusion of RGB-D and IMU information |
| CN111678515A (en) * | 2020-04-28 | 2020-09-18 | 北京三快在线科技有限公司 | Device state estimation method and device, electronic device and storage medium |
Non-Patent Citations (2)
| Title |
|---|
| 基于预测-校正原对偶内点法的无功优化新模型;余娟, 颜伟, 徐国禹, 杜鹏, 刘方;中国电机工程学报(第11期);全文 * |
| 非线性优化同时定位与地图创建问题;季晨;宋燕燕;秦军;敖甜甜;;软件工程(第09期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN112765548A (en) | 2021-05-07 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN112765548B (en) | Covariance determination method, positioning method and device for sensor fusion positioning | |
| CN112559784B (en) | Image classification method and system based on incremental learning | |
| Peherstorfer et al. | Dynamic data-driven reduced-order models | |
| US11796686B2 (en) | Positioning data processing method and processing apparatus, computing device, and storage medium | |
| CN111461106A (en) | Object detection method and device based on reconfigurable network | |
| CN110263832B (en) | AUV navigation system fault diagnosis method based on multi-scale analysis | |
| CN115147598B (en) | Target detection segmentation method and device, intelligent terminal and storage medium | |
| CN111596329A (en) | Vehicle positioning method, device and equipment and vehicle | |
| CN111078639A (en) | Data standardization method and device and electronic equipment | |
| Farrell | Carrier phase processing without integers | |
| CN112711032A (en) | Radar target detection method and system based on graph data and GCN | |
| CN109583487A (en) | A kind of SAR image change detection and device | |
| Liu et al. | Data-driven spatially dependent PDE identification | |
| CN114549945A (en) | Remote sensing image change detection method and related device | |
| Cao et al. | Sparse representation denoising framework for 3-D building reconstruction from airborne LiDAR data | |
| CN112230194A (en) | Translation array-based ambiguity resolution method, equipment and storage medium | |
| CN115861428B (en) | Pose measurement method and device, terminal equipment and storage medium | |
| Han et al. | Modeling nonlinearity in multi-dimensional dependent data | |
| CN112050735B (en) | Method for recursion refinement of ground position of optical remote sensing satellite big data and storage medium | |
| US11409988B2 (en) | Method, recording medium, and device for utilizing feature quantities of augmented training data | |
| WO2004038642A2 (en) | Method and apparatus for adaptive pixel estimation | |
| WO2022219686A1 (en) | Density ratio estimation device, density ratio estimation method, and density ratio estimation program | |
| CN112567203B (en) | Method and apparatus for assisting in the navigation of a fleet of vehicles using a invariant Kalman filter | |
| Wang et al. | Robust AUV Localization Based on Switchable Constraints | |
| CN116304550A (en) | Waveform curve matching method and device |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |