CN111444467A - Method for local linear interpolation and prediction based on real-time positioning track data - Google Patents
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Abstract
The invention provides a method for local linear interpolation and prediction based on real-time positioning track data, which comprises the following steps: step 1, reading a piece of real-time track resolving data; step 2, if the calculation in the step 1 is invalid or interpolation prediction is needed and the number of historical calculation data is more than 5, turning to the step 3, otherwise, turning to the step 8; step 3, 6 newly solved historical track calculation data are taken out; step 4, resolving data of the 6 historical tracks in the step 3, resolving linear coefficients and obtaining a coefficient matrix; step 5, performing matrix multiplication on the last five data of the 6 pieces of data taken out in the step 3 and the coefficient matrix obtained in the step 4 to predict the next coordinate; step 6, optimizing the predicted data and the historical track calculation data; step 7, adding the newly predicted data into a historical track calculation data set after filtering; and 8, resolving the positioning data of the next round, and turning to the step 1.
Description
Technical Field
The invention relates to a method for processing related data of indoor positioning, in particular to a method for performing local linear interpolation and prediction based on real-time positioning track data.
Background
In the outdoor environment, the Global Positioning System (GPS) is widely used due to the advantages of high accuracy, high stability and low cost, but in the indoor environment, since satellite signals cannot penetrate buildings, the GPS is severely limited, and the indoor environment is more significantly affected by multipath effect and non-line-of-sight (N L OS) than the outdoor environment, and dynamic changes of the environment are also problematic, which all increase the challenge of accurate indoor positioning.
Among the TDOA positioning methods, Wade H.Foy is widely applied according to the method proposed by Taylor expansion (Taylor sequence method for short) with the advantages of simple form and high precision, and the method carries out Taylor expansion near the given initial coordinates and ignores more than two-order components, and then gradually optimizes the coordinates by iteration calculation of local least square solution of errors, however, because indoor positioning is interfered by various problems, such as packet loss during data transmission, and even serious data loss problem due to much noise interference, the original solution effect is poor, so that on the premise of the requirement of a real-time positioning system on accuracy and timeliness, how to carry out efficient and accurate data interpolation and prediction to complement track points is very important, in the documents of Foy W.position-L locations by Taylor-Series Estimation [ J ] IEEE transaction area & AES & 12, AES & 187-AES & 12) system 194.
Disclosure of Invention
The purpose of the invention is as follows: in the resolving process, if the current resolving fails or loses points, interpolation supplement is carried out on the lost points or subsequent track points are predicted on the premise of confirming the timeliness and the high efficiency according to the time sequence information and the priori knowledge of track coordinates, so that the smoothness and the continuity of the track are enhanced.
In order to solve the technical problems, the invention discloses a method for interpolating and predicting based on real-time positioning track data in a complex environment, which can be used for warehouse management, positioning navigation, robot tracking, port real-time positioning tracking and other applications and comprises the following steps:
step 1, reading a piece of real-time track resolving data;
step 2, if the resolving is invalid due to the problems of data abnormality and the like in the step 1, for example, a packet loss event occurs in the data transmission process or a correct resolving solution cannot be obtained in the resolving process, or interpolation prediction is required currently and the number of historical resolving data is not less than 6, turning to the step 3, otherwise, turning to the step 8;
step 3, 6 historical track calculation data which are calculated recently are taken out;
step 4, resolving the 6 th historical track in the step 3, linearly representing the 6 th historical track resolving data by using the previous 5 historical track resolving data, resolving a linear coefficient, normalizing the linear coefficient, optimizing the linear coefficient, minimizing the distance between a linear expression result and the 6 th data in the step 4 to obtain an optimal coefficient vector, and obtaining a coefficient matrix;
step 6, performing Kalman filtering optimization on the obtained predicted coordinate data and historical track resolving data as a whole;
step 7, adding the optimized predicted data into a historical track calculation data set;
and 8, resolving the positioning data of the next round, and turning to the step 1.
In step 1, reading positioning data in the form of:
data＝((x1，y1)，(x2，y2)，...，(xNtemp_after，yNtemp_after))，
wherein Ntemp _ after represents the number of historical track solution data in the historical track solution data set, xi，yiRespectively representing the abscissa and the ordinate corresponding to the ith solved positioning data, wherein i is more than or equal to 1 and less than or equal to Ntemp _ after.
The step 2 comprises the following steps: and (3) judging the number Ntemp _ after of the historical track calculation data, if the number Ntemp _ after is not more than 6, judging that enough historical track calculation data exist for carrying out filtering optimization, and executing the step 3, otherwise, executing the step 8.
The step 3 comprises the following steps: taking out 6 recently calculated historical track calculation data, and reading in the historical track calculation data in the form of vector history _ data, wherein the vector history _ data is in the form of:
Window＝((xi，yi)，(xi+1，yi+1)，(xi+2，yi+2)，(xi+3，yi+3)，(xi+4，yi+4)，(xi+5，yi+5))，xi，yirespectively representing the corresponding abscissa and ordinate of the ith calculated positioning data, and the window is window data of the historical track calculation needing to calculate the linear coefficient.
Step 4 comprises the following steps: solving data (x) for the 6 th historical tracki+5，yi+5) Abscissa xi+5Ordinate yi+5Linear coefficients were solved separately:
xi+5＝a1xi+a2xi+1+a3xi+2+a4xi+3+a5xi+4
yi+5＝b1yi+b2yi+1+b3yi+2+b4yi+3+b5yi+4
wherein, atFor the coefficient corresponding to the t-th abscissa to be solved, btThe coefficient corresponding to the t-th ordinate to be solved is obtained;
linear coefficient is solved to obtain coefficient matrix
R＝[A B]Wherein A, B is a coefficient matrix of 5 × 1 on the abscissa, a coefficient matrix of 5 × 1 on the ordinate, and R is a coefficient matrix of 5 × 2.
To obtain an optimal coefficient representation, the following objective function is set:
wherein the content of the first and second substances,
argmin represents minimizing the above objective function;
let the above-mentioned objective function
Wherein A isT＝(a1a2a3a4a5)，W＝(xi+5-xixi+5-xi+1xi+5-xi+2xi+5-xi+3xi+5-xi+4) Wherein W is a temporary variable, i.e. representing the sixth abscissa taken in step 3Interpolation of the values and the other five abscissas.
To minimize, the values of the linear coefficients a are solved using the lagrange multiplier method:
wherein
For Lagrangian function solution, λ is the coefficient in the Lagrangian multiplier method, ITIf (11111) is a full 1 vector and the length is 5, the above equation is solved further to obtain:
will be provided with
To ATAnd (3) calculating a partial derivative to obtain:
wherein C ═ WTW is a matrix obtained by transposing the vector W and performing matrix multiplication on W;
through calculation deduction:
AT＝λC-1I，
in addition have
Then:
ITλC-1I＝1，
therefore:
λ＝(ITC-1I)-1，
finally, the following is obtained:
the optimal coefficient matrix a is thus solved, and the optimal coefficient matrix B is solved in the same manner.
The step 5 comprises the following steps: and (3) setting the coordinates to be predicted as (x, y), the calculation method is as follows:
x＝data_xT×A，
y＝data_yT×B，
wherein the data _ x and the data _ y are respectively the abscissa and the ordinate of the last five pieces of data of the six pieces of data taken out in the step 3, and are expressed as follows:
data_xTis a transposed matrix of the data _ x matrix.
The step 6 comprises the following steps: the data1 that needs to be smoothed this time is expressed as follows:
Data1＝((xi，yi)，(xi+1，yi+1)，(xi+2，yi+2)，(xi+3，yi+3)，(xi+4，yi+4)，(xi+5，yi+5)，(x，y))
smoothing the data1 vector to obtain a new vector data':
data’＝((xi′，yi′)，(xi+1′，yi+1′)，(xi+2′，yi+2′)，(xi+3′，yi+3′)，(xi+4′，yi+4′)，(xi+5′，yi+5′)，(x′，y′))
wherein xi′，yi' are respectively the abscissa and ordinate of the ith solution data obtained after the smoothing process, and x ' and y ' respectively represent the abscissa and ordinate of the prediction obtained after the smoothing process.
And 7, updating the new data points obtained by filtering into a historical track calculation data set, wherein the new data points already contain the coordinates of the predicted interpolation points, and filtering the result to ensure the smoothness basis.
Has the advantages that: the invention has the obvious advantages that a brand new interpolation algorithm is provided, the problems of packet loss and solution failure in indoor positioning in a real-time environment are solved, when the real-time positioning data is interpolated and predicted, a good effect can be achieved only by little priori coordinate data knowledge, in addition, when interpolation operation is carried out each time, only the coordinate data of the nearest points are needed, the algorithm delay is very low, and under the equipment of 4HZ, the delay is about msThereby optimizing the performance of the overall positioning system. Compared with other interpolation methods, the method eliminates the requirement on data monotonicity when the main interpolation method such as a spherical interpolation method or a cubic spline interpolation method is used for interpolation, is suitable for processing real-time track tracking in the walking process of a person, can ensure the continuity and the real-time performance of the track, and obviously improves the performance and the effect of a positioning system.
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The foregoing and/or other advantages of the invention will become further apparent from the following detailed description of the invention when taken in conjunction with the accompanying drawings.
FIG. 1 is an overall flow chart of the present invention for interpolating and predicting real-time positioning trajectory data.
Fig. 2a is an original coordinate data image.
Fig. 2b is the result of a complete trajectory point prediction from the original coordinates.
Fig. 3a is a trace image of simulation data.
FIG. 3b is a comparative test of mean error and index for various interpolation methods.
Detailed Description
FIG. 1 is a flow chart of the invention, comprising 8 steps.
In a first step, positioning data is read in the form of:
data＝((x1，y1)，(x2，y2)，...，(xNtemp_after，yNtemp_after))，
wherein n represents the number of the historical track solution data in the historical track solution data set, xi，yiRespectively representing the abscissa and the ordinate corresponding to the ith solved positioning data, wherein i is more than or equal to 1 and less than or equal to Ntemp _ after.
In the second step, the number of the solved data needs to be judged to determine whether enough historical track solving data can be used for interpolation prediction:
if Ntemp _ after is more than or equal to 6, judging that enough historical track resolving data exist for carrying out filtering optimization;
ntemp _ after is the number of data currently solved.
In the third step, six latest historical track resolving data need to be taken out and read in a vector history _ data form, wherein the vector history _ data form is as follows:
Window＝((xi，yi)，(xi+1，yi+1)，(xi+2，yi+2)，(xi+3，yi+3)，(xi+4，yi+4)，(xi+5，yi+5))，xi，yirespectively representing the corresponding abscissa and ordinate of the ith calculated positioning data, and the window is window data of the historical track calculation needing to calculate the linear coefficient.
In the fourth step, six pieces of data taken out in the step need to be processed, specifically, the sixth piece of data needs to be linearly represented by the first five pieces of data, because of the independence between the horizontal and vertical coordinates of the trajectory data, and in order to enhance the stability of the algorithm, the horizontal and vertical coordinates are respectively solved with linear coefficients:
xi+5＝a1xi+a2xi+1+a3xi+2+a4xi+3+a5xi+4
yi+5＝b1yi+b2yi+1+b3yi+2+b4yi+3+b5yi+4
wherein xiFor the ith positioning data, yiFor the ith positioning data, atFor the coefficient corresponding to the t-th abscissa, b, to be solvedtFor the coefficient corresponding to the t-th ordinate to be solved. The linear coefficient can be solved based on the knowledge of linear algebra to obtain a coefficient matrix
R＝[A B]Wherein A, B are all matrices of 5 × 1, and R is a coefficient matrix of 5 × 2.
To obtain the above optimal coefficient representation, the following objective function is set:
wherein the content of the first and second substances,
argmin represents minimizing the above objective function.
Let the above-mentioned objective function
Wherein A isT＝(a1a2a3a4a5)，W＝(xi+5-xixi+5-xi+1xi+5-xi+2xi+5-xi+3xi+5-xi+4) For minimization, the values of the linear coefficients a are solved using the lagrangian multiplier method.
Where λ is the coefficient in the Lagrange multiplier method, ITWith (11111) being a full 1 vector and a length of 5.
Continuing to solve the above equation to obtain:
will be provided with
To ATAnd (3) calculating a partial derivative to obtain:
wherein C ═ WTW。
A can be deduced through calculationT＝λC-1I
In addition have
Then
ITλC-1I is 1, so that,
λ＝(ITC-1I)-1
in the end of this process,
the optimal coefficient matrix a is thus solved, and the coefficient matrix B can be solved in the same manner. The coefficient matrix calculated according to the above procedure can be guaranteed to be optimal.
In the fifth step, matrix multiplication is performed on the last five data of the taken 6 pieces of data and the coefficient matrix obtained in the step 4 to predict the next coordinate, and if the coordinate to be predicted is (x, y), the calculation method is as follows:
x＝data_xT×A
y＝data_yT×B
wherein the data _ x and the data _ y are respectively the abscissa and the ordinate of the last five pieces of data of the six pieces of data taken out in the step 3:
data_xTand A, B are respectively linear combination coefficients of horizontal and vertical coordinates calculated in step 4, which are the transpose matrix of the data _ x matrix.
In the sixth step, filtering optimization is carried out on the obtained predicted data and the historical track calculation data to ensure the smoothness of the track data, the method adopted here is Kalman filtering, and the data needing to be smoothed at this time is as follows:
data＝((xi，yi)，(xi+1，yi+1)，(xi+2，yi+2)，(xi+3，yi+3)，(xi+4，yi+4)，(xi+5，yi+5)，(x，y))
wherein x and y in the last coordinate are the coordinates of the point to be predicted solved in step 5, and x in the first six coordinatesiFor the abscissa, y, of the i-th positioning data taken in step 3iThe ordinate of the i-th positioning data taken out in step 3.
And smoothing the data vector to obtain a new vector data':
data’＝((xi′，yi′)，(xi+1′，yi+11)，(xi+2′，yi+2′)，(xi+3′，yi+3′)，(xi+4′，yi+4′)，(xi+5′，yi+5′)，(x′，y，))
wherein xi′，yi' are respectively the abscissa and ordinate of the i-th solution data obtained after the smoothing processing.
And in the seventh step, updating the new data points obtained by filtering into a historical track calculation data set, wherein the new data points already contain the coordinates of the predicted interpolation points, and filtering the results to ensure the smooth basis.
In the eighth step, the positioning data of the next round is resolved, and the procedure goes to step 1.
Examples
In order to verify the effectiveness of the algorithm, sites are deployed and tested in the actual environment. The test site is a room with the size of 5m by 7m, a piece of glass is arranged at the upper left corner of the room, and signals nearby can be obviously reflected. 8 base stations are arranged around the site, and the height of each base station is about 3 m. The tester walks for a plurality of weeks along the edge in the field, and the motion track is close to a rectangle. The coordinate data acquired by resolving the TDOA data is used as test data for track prediction in the invention, wherein the implementation and parameter details of each step are as follows:
in step 1, reading positioning coordinate data;
in step 2, the number of the solved data needs to be judged, whether enough historical track solving data can be used for interpolation prediction is determined, and 6 pieces of historical track solving data are needed to ensure timeliness;
in step 3, 6 recently calculated historical track calculation data are taken out for data preparation;
in step 4, resolving data of the six historical tracks in the step 3, linearly representing the 6 th data by using the first 5 data, resolving a linear coefficient, and simultaneously minimizing the distance between the linear coefficient and the predicted point and normalizing to obtain a coefficient matrix;
in step 5, performing matrix multiplication on the last five data of the 6 pieces of data taken out in the step 3 and the coefficient matrix obtained in the step 4 to predict the next coordinate or perform interpolation on a certain position point;
and 6, performing Kalman filtering optimization on the obtained prediction data and historical track calculation data to ensure smoothness.
In step 7, adding the newly predicted data into a historical track calculation data set after filtering;
in step 8, the positioning data of the next round is resolved, and the procedure goes to step 1.
In fig. 2a and fig. 2b, a comparison graph of intermediate results obtained by solving a set of coordinate data is shown, where fig. 2a is an image of original coordinate data, and fig. 2b is a result of completely predicting track points according to the original coordinates, and it can be seen that the track of the predicted point is substantially consistent with the original track.
In fig. 3a and 3b, average error evaluation of various methods after prediction is performed on partial coordinate data under simulation data is shown, wherein fig. 3a is a track image of simulation data, fig. 3b is a comparative test of average error and index for various interpolation methods, and LL I (L octally L initial interpolation) is used as the method of the present invention.
The above data shows that the continuity and the timeliness obtained on the trace of the invention show satisfactory results.
The present invention provides a method for local linear interpolation and prediction based on real-time positioning track data, and a plurality of methods and approaches for implementing the technical solution, and the above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, a plurality of improvements and modifications may be made without departing from the principle of the present invention, and these improvements and modifications should also be considered as the protection scope of the present invention. All the components not specified in the present embodiment can be realized by the prior art.
Claims (7)
1. The method for performing local linear interpolation and prediction based on real-time positioning track data is characterized by comprising the following steps of:
step 1, reading a piece of real-time track resolving data;
step 2, if the calculation is invalid due to data abnormality in the step 1, or interpolation prediction is needed currently and the number of historical calculation data is not less than 6, turning to the step 3, otherwise, turning to the step 8;
step 3, 6 historical track calculation data which are calculated recently are taken out;
step 4, resolving the 6 th historical track in the step 3, linearly representing the 6 th historical track resolving data by using the previous 5 historical track resolving data, resolving a linear coefficient, normalizing the linear coefficient, optimizing the linear coefficient, minimizing the distance between a linear expression result and the 6 th data in the step 4 to obtain an optimal coefficient vector, and obtaining a coefficient matrix;
step 5, performing matrix multiplication on the last 5 historical track calculation data of the 6 historical track calculation data extracted in the step 3 and the coefficient matrix obtained in the step 4 to predict the next coordinate;
step 6, performing Kalman filtering optimization on the obtained predicted coordinate data and historical track resolving data as a whole;
step 7, adding the optimized predicted data into a historical track calculation data set;
and 8, resolving the positioning data of the next round, and turning to the step 1.
2. Method according to claim 1, characterized in that in step 1 positioning data are read in the form of:
data＝((x1，y1)，(x2，y2)，...，(xNtemp_after，yNtemp_after))，
wherein Ntemp _ after represents the number of historical track solution data in the historical track solution data set, xi，yiRespectively representing the abscissa and the ordinate corresponding to the ith solved positioning data, wherein i is more than or equal to 1 and less than or equal to Ntemp _ after.
3. The method of claim 2, wherein step 2 comprises: and (3) judging the number Ntemp _ after of the historical track calculation data, if the number Ntemp _ after is not more than 6, judging that enough historical track calculation data exist for carrying out filtering optimization, and executing the step 3, otherwise, executing the step 8.
4. The method of claim 3, wherein step 3 comprises: taking out 6 recently calculated historical track calculation data, and reading in the historical track calculation data in the form of vector history _ data, wherein the vector history _ data is in the form of:
Window＝((xi，yi)，(xi+1，yi+1)，(xi+2，yi+2)，(xi+3，yi+3)，(xi+4，yi+4)，(xi+5，yi+5))，
xi，yirespectively representing the corresponding abscissa and ordinate of the ith calculated positioning data, and the window is window data of the historical track calculation needing to calculate the linear coefficient.
5. The method of claim 4, wherein step 4 comprises: solving data (x) for the 6 th historical tracki+5，yi+5) Abscissa xi+5Ordinate yi+5Linear coefficients were solved separately:
xi+5＝a1xi+a2xi+1+a3xi+2+a4xi+3+a5xi+4
yi+5＝b1yi+b2yi+1+b3yi+2+b4yi+3+b5yi+4
wherein, atFor the coefficient corresponding to the t-th abscissa to be solved, btThe coefficient corresponding to the t-th ordinate to be solved is obtained;
linear coefficient is solved to obtain coefficient matrix
R＝[A B]Wherein A, B is coefficient matrix of 5 × 1 on abscissa, coefficient matrix of 5 × 1 on ordinate, and R is coefficient matrix of 5 × 2;
to obtain an optimal coefficient representation, the following objective function is set:
wherein the content of the first and second substances,
argmin tableMinimizing the objective function;
let the above-mentioned objective function
Wherein A isT＝(a1a2a3a4a5)，W＝(xi+5-xixi+5-xi+1xi+5-xi+2xi+5-xi+3xi+5-xi+4) Wherein W is a temporary variable;
to minimize, the values of the linear coefficients a are solved using the lagrange multiplier method:
wherein
For Lagrangian function solution, λ is the coefficient in the Lagrangian multiplier method, ITIf (11111) is a full 1 vector and the length is 5, the above equation is solved further to obtain:
will be provided with
To ATAnd (3) calculating a partial derivative to obtain:
wherein C ═ WTW is the matrix obtained by transposing the vector W and matrix multiplying W；
Through calculation deduction:
AT＝λC-1I，
in addition have
Then:
ITλC-1I＝1，
therefore:
λ＝(ITC-1I)-1，
finally, the following is obtained:
the optimal coefficient matrix a is thus solved, and the optimal coefficient matrix B is solved in the same manner.
6. The method of claim 5, wherein step 5 comprises: and (3) setting the coordinates to be predicted as (x, y), the calculation method is as follows:
x＝data_xT×A，
y＝data_yT×B，
wherein the data _ x and the data _ y are respectively the abscissa and the ordinate of the last five pieces of data of the six pieces of data taken out in the step 3, and are expressed as follows:
data_xTis a transposed matrix of the data _ x matrix.
7. The method of claim 6, wherein step 6 comprises: the data1 that needs to be smoothed this time is expressed as follows:
Data1＝((xi，yi)，(xi+1，yi+1)，(xi+2，yi+2)，(xi+3，yi+3)，(xi+4，yi+4)，(xi+5，yi+5)，(x，y))
smoothing the data1 vector to obtain a new vector data':
data’＝((xi′，yi′)，(xi+1′，yi+1′)，(xi+2′，yi+2′)，(xi+3′，yi+3′)，(xi+4′，yi+4′)，(xi+5′，yi+5′)，(x′，y′))
wherein xi′，yi' are respectively the abscissa and ordinate of the ith solution data obtained after the smoothing process, and x ' and y ' respectively represent the abscissa and ordinate of the prediction obtained after the smoothing process.
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| CN113103241A (en) * | 2021-04-29 | 2021-07-13 | 哈尔滨工业大学 | Method, device and system for realizing G2 continuous robot double-NURBS track interpolation |
| CN114234984A (en) * | 2022-02-28 | 2022-03-25 | 湖南工商大学 | Indoor positioning track smoothing method, system and equipment based on difference matrix |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103136270A (en) * | 2011-12-01 | 2013-06-05 | 无锡物联网产业研究院 | Method and system for obtaining data interpolation |
| CN104064023A (en) * | 2014-06-18 | 2014-09-24 | 银江股份有限公司 | Dynamic traffic flow prediction method based on space-time correlation |
| CN109613477A (en) * | 2019-01-11 | 2019-04-12 | 南京大学 | A kind of TDOA location tracking method under complex environment |
| CN110631589A (en) * | 2019-09-29 | 2019-12-31 | 广东星舆科技有限公司 | Method for correcting positioning track in real time |
| CN110850363A (en) * | 2019-10-22 | 2020-02-28 | 南京大学 | Method for carrying out dynamic filtering optimization based on real-time positioning track data |
-
2020
- 2020-04-21 CN CN202010316990.5A patent/CN111444467B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103136270A (en) * | 2011-12-01 | 2013-06-05 | 无锡物联网产业研究院 | Method and system for obtaining data interpolation |
| CN104064023A (en) * | 2014-06-18 | 2014-09-24 | 银江股份有限公司 | Dynamic traffic flow prediction method based on space-time correlation |
| CN109613477A (en) * | 2019-01-11 | 2019-04-12 | 南京大学 | A kind of TDOA location tracking method under complex environment |
| CN110631589A (en) * | 2019-09-29 | 2019-12-31 | 广东星舆科技有限公司 | Method for correcting positioning track in real time |
| CN110850363A (en) * | 2019-10-22 | 2020-02-28 | 南京大学 | Method for carrying out dynamic filtering optimization based on real-time positioning track data |
Non-Patent Citations (2)
| Title |
|---|
| 毕京学: "智能手机Wi-Fi/PDR室内混合定位优化问题研究", 《中国优秀博硕士学位论文全文数据库(博士)信息科技辑》 * |
| 陈茂清: "飞行载体的导航数据处理与轨迹拟合方法研究及应用", 《中国优秀博硕士学位论文全文数据库(硕士)工程科技Ⅱ辑》 * |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113103241A (en) * | 2021-04-29 | 2021-07-13 | 哈尔滨工业大学 | Method, device and system for realizing G2 continuous robot double-NURBS track interpolation |
| CN114234984A (en) * | 2022-02-28 | 2022-03-25 | 湖南工商大学 | Indoor positioning track smoothing method, system and equipment based on difference matrix |
| CN114234984B (en) * | 2022-02-28 | 2022-05-20 | 湖南工商大学 | Indoor positioning track smoothing method, system and equipment based on difference matrix |
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