CN114814727A - Ultra-wideband three-dimensional positioning algorithm with high positioning precision and anti-interference capability - Google Patents
Ultra-wideband three-dimensional positioning algorithm with high positioning precision and anti-interference capability Download PDFInfo
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Abstract
An ultra-wideband three-dimensional positioning algorithm with high positioning precision and anti-interference capability comprises the following steps: the method comprises the following steps: obtaining the distance between the base station and the label by using an ADS-TWR ranging method; step two: the ADS-TWR ranging data is filtered once through a KF algorithm, and more accurate measurement information is provided for an EPF positioning algorithm
Filtering the once filtered ranging value
As an aspect of extended particle filteringCarrying out 'secondary' filtering algorithm positioning on the measured signal; step three: updating the particles and weights using an EKF algorithm for subsequent accurate positioning; according to the invention, through a positioning algorithm (namely KF-EPF algorithm) combining Kalman filtering and an extended particle filtering algorithm, Kalman filtering is utilized to carry out 'one-time' filtering on distance data to process abnormal distance measurement data under the NLOS condition, and then the processed distance data is used as observation data of the extended Kalman filtering to carry out position settlement, so that the positioning accuracy is improved.
Description
Technical Field
The invention belongs to the field of server maintenance, and particularly relates to an ultra wide band three-dimensional positioning algorithm with high positioning precision and anti-interference capability.
Background
The existing Ultra Wide Band (UWB) three-dimensional positioning algorithm comprises a traditional trilateral positioning algorithm, an EKF algorithm, an UKF algorithm and an EPF algorithm, wherein compared with the UKF algorithm, the EKF algorithm and the trilateral positioning algorithm, the EPF positioning algorithm has the minimum root mean square error in three dimensions, and the positioning accuracy of an X axis and a Z axis is obviously improved. Due to the common defects of the particle filter algorithm, although the positioning accuracy of the EPF positioning algorithm is greatly improved, the real-time performance of the EPF positioning algorithm is poor, so that certain problems exist in the practical use.
Disclosure of Invention
The invention provides an ultra wide band three-dimensional positioning algorithm with high positioning precision and anti-interference capability, which is used for solving the defects in the prior art.
The invention is realized by the following technical scheme:
an ultra-wideband three-dimensional positioning algorithm with high positioning precision and anti-interference capability comprises the following steps:
the method comprises the following steps: obtaining the distance between the base station and the label by using an ADS-TWR ranging method;
taking the distance value measured by the ADS-TWR method as measurement information, and the measurement equation of the distance model is as follows:
in the formula: c ═ 10]，v d,k The variance of the ranging noise at time k is R d . Measuring the noise variance R d By multiple timesVariance R between distance measurement data obtained by ranging experiment and real distance c Represents;
in the formula:
formula (II)
ΔT k For the base station data sampling time interval, w d,k System noise at time k, with variance Q d ；
Step two: carry out "once" filtering to ADS-TWR range finding data through the KF algorithm, can filter the range finding data through this step to reduce the range finding information fluctuation that NLOS phenomenon and noise caused, get rid of unusual data, provide comparatively accurate measurement information for EPF positioning algorithm
Filtering the once filtered ranging value
Performing 'secondary' filter algorithm positioning as an observation signal of the extended particle filter;
the "quadratic" filtered distance measurement model is as follows:
in the formula:
in order to predict the state vector(s),
to predict the state covariance matrix, M k In order to be a matrix of gains, the gain matrix,
and
the state estimation vectors at time k-1 and k, respectively,
and
estimated state covariance matrices at time k-1 and time k, respectively, I being an identity matrix, filtered
Merging base station-to-tag ranging data filtering results into matrix
The following equation is used as the equation of state:
the following equation is taken as the nonlinear observation equation:
step three: updating the particles and weights using an EKF algorithm;
(1) when i is 0: from the prior distribution p (x) 0 ) Sampling point of middle structure
That is to say
Specifically, the formula is shown as follows:
(2) when i > 0, the particles are updated using the EKF algorithm:
where Q is the process noise variance and R is the measurement noise variance. Obtaining sampling points from importance functions
And (3) updating the weight:
normalization weight:
using EKF algorithm at time k-1, and up-to-date observation information D k To calculate the mean and variance of the ith particle, and to sample and update the particle with the mean and variance, the variance of the process noise and the measurement noise of the EKF needs to be re-given to ensure the positioning accuracy.
According to the ultra-wideband three-dimensional positioning algorithm with high positioning accuracy and anti-interference capability, in the first step, the base station communicates with the tag and the base stations communicate with each other, so that distance data between any two base stations can be acquired, when the tag coordinate is in a static state, the coordinate of the base station can be measured and calculated by using the tag coordinate, and the static tag is used as the base station to prevent the influence of abnormal movement of the base station on positioning data.
According to the ultra-wideband three-dimensional positioning algorithm with high positioning accuracy and anti-interference capability, when the coordinates of the tag jump within an error range, the tag can be considered to be in a static state.
In the ultra-wideband three-dimensional positioning algorithm with high positioning accuracy and high anti-interference capability, no matter in the actual indoor or outdoor application, the position of the base station in the positioning system is inevitably subjected to the action of external force to cause displacement, such as pets, wind in the nature, birds and the like. This may cause deviation of the base station coordinate matrix represented by RNt in the base station coordinate system from the true value, and may naturally cause deviation of the non-linear observation equation in the non-linear observation equation, thereby generating a chain reaction and greatly reducing the final label positioning accuracy. In order to avoid the large influence of the movement of the base station on the positioning precision of the label, the automatic updating algorithm of the position of the base station is substituted into the iteration of the KF-EPF positioning algorithm, and the accurate position information of the base station can be obtained through multiple iterations.
By utilizing the characteristic of two-way communication of ADS-TWR ranging algorithm, the base station communicates with the tag and communicates with each other, so that distance data D between the base station and the base station can be acquired a0,1 ,D a0,2 ,D a0,3 ,D a1,2 ,D a1,3 ,D a2,3 ，D a0,1 Is the measured distance between base station A0 and base station A1, D a0,2 Is the measured distance between base station A0 and base station A2, D a0,3 Is the measured distance between base station A0 and base station A3, D a1,2 Is the measured distance between base station A1 and base station A2, D a1,3 Is the measured distance between base station A1 and base station A3, D a2,3 Is the measured distance between base station a2 and base station A3. When the tag is stationary (when the tag coordinate is out of tolerance, the tag can be considered to be in a stationary state, and the coordinate is xstatic ═ xstatic temporal ztatic when the tag coordinate is assumed to be xstatic ═ xstatic]) The coordinates of the base station can be measured and calculated by using the coordinates of the label (the base station a0 No. 1 is a basic base station, and the east and north coordinates are always (0,0)), and the static label is used as the base station to prevent the positioning data from being influenced by the abnormal movement of the base station.
To the outputted positioning result X k Real-time monitoring is carried out, and if the coordinate change of the label is within the error rangeConsidering that the tag is in a static state, when measuring and calculating the base station coordinate No. 2 in fig. 3, the tag coordinate needs to be brought into the RN k In, replace label coordinate No. 2, i.e. RN k Instead, the method comprises the following steps:
at the same time, will
Updating the distance from the tag to the other three base stations to the base station No. 2, namely:
when measuring and calculating the coordinate of base station No. 3 in FIG. 3, the coordinate of the tag needs to be brought into RN k In, replace label coordinate No. 3, i.e. RN k Instead, the method comprises the following steps:
will be provided with
Updating the distance from the tag to the other three base stations to the base station No. 3, namely:
when measuring and calculating the coordinate of base station No. 4 in fig. 3, the coordinate of the tag needs to be brought into the RN k In, replace label coordinate No. 4, i.e. RN k Instead, the method comprises the following steps:
will be provided with
Updating the distance from the tag to the other three base stations to the base station No. 4, namely:
the particle groups are initialized to the coordinates before the movement of the base stations No. 2, No. 3 and No. 4 respectively, so that the number of iterations can be reduced. Experiments prove that the displacement base station can be accurately positioned after 30 iterations, and the positioning system adopted in the experiment can complete one-time positioning after 28ms, namely the repositioning of one base station can be completed only within 1 second. And taking the average value of 50 groups of data after 1 second as the final coordinate of the base station positioning.
The invention has the advantages that: according to the invention, through a positioning algorithm (namely KF-EPF algorithm) combining Kalman filtering and an extended particle filtering algorithm, Kalman filtering is utilized to carry out 'one-time' filtering on distance data to process abnormal distance measurement data under the NLOS condition, and then the processed distance data is used as observation data of extended Kalman filtering to carry out position settlement, so that the positioning accuracy is improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings described below are some embodiments of the present invention, and those skilled in the art can also obtain other drawings according to the drawings without creative efforts.
FIG. 1 is a flow chart of the KF-EPF algorithm of the present invention;
FIG. 2 is a trace diagram of the KF-EPF algorithm of the present invention;
FIG. 3 is a diagram of a laboratory test arrangement of the present invention;
FIG. 4 is a plot of the KF-EPF algorithm positioning trace of the invention;
fig. 5 is a three-dimensional SLAM laser scanning positioning track diagram of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
Indoor positioning system experiment
The setup of the indoor positioning system experiment is shown in fig. 3, and the instruments and functions represented by the numbers marked in the figure are:
firstly, the location base station is No. 0, the location surface position of the label is the origin of a coordinate system, and the location base station is communicated with other three base stations and labels through a data line and is also communicated with a computer.
And the No. 1, 2 and 3 positioning base stations are responsible for distance measurement communication with the labels and the base stations.
Fifthly, the positioning label is fixed on the mobile robot, and the label is ensured to be placed at the center of the top view of the robot.
And sixthly, the device is real-time positioning and 3D scanning equipment, and can output the six-degree-of-freedom position and the environment 3D point cloud of the equipment in real time without external auxiliary positioning such as GNSS (global navigation satellite system) and the like based on an advanced 3D laser SLAM (SLAM algorithm).
And the battery is a 12v DC lithium battery which supplies power for real-time positioning and 3D scanning equipment.
And the chassis of the double-wheel differential mobile robot can control the moving speed, the steering and the like of the robot through the flat control software.
Ninthly, the computer is responsible for running the software of the upper computer and communicating with the No. 0 base station.
And the third part is a positioning base station support for adjusting the height of the positioning label.
Static state experiment
In static experiments, four base stations are located at the vertices of a 2.4m by 7.2m rectangle. The labels are all placed at the top points of the floor tiles (600mm x 600mm) and are still, the coordinates of the top points of the floor tiles are used as the coordinates of the labels, no error is assumed, and in order to enable the experiment to be closer to the actual use condition, disturbance is artificially added in the experiment. The concrete mode is as follows: during the experiment, a plurality of people randomly move around the experimental field.
To show the KF-EPF advancement, three sets of comparative experiments were set up. The existing known UKF and UPF algorithm has the advantages of unobvious positioning accuracy under the condition that the state equation of a system model is linear, and the algorithm is complex, so that a physical experiment is not performed any more. And a KF-EPF, EKF and EPF three groups of comparison tests are set to verify the advantage of the KF-EPF algorithm in positioning precision.
And respectively placing the labels at different positions, and outputting coordinate data of the labels after the position of the labels on the upper computer is stably displayed. Each algorithm static experiment performed three sets of experiments, each set of experiments placing the tags in different positions. Labels were placed on (1.2,4.2,1.75), (1.2,3.0,0.45), (1.2,1.8, 0.15) coordinates, respectively, and 150 sets of label position data were collected for each position and their root mean square error was calculated using MATLAB, with the results shown in table one.
Watch 1
As can be seen from the table I, the data measured by the KF-EPF positioning algorithm in the static test is closest to the true value and the root mean square error is minimum, so that the KF-EPF positioning algorithm has the highest positioning precision on the static label. The minimum error of the EPF algorithm is 15.57cm, the maximum error is 18.93cm, the average error of the KF-EPF algorithm is about 12cm, and the maximum error is not more than 15 cm. Compared with an EPF algorithm, the positioning precision is improved by about 3cm, and the design requirements of the text are met.
Dynamic experiments
In order to verify the automatic updating function of the base station position of the KF-EPF algorithm, the No. 2 and the No. 3 base stations are respectively moved to the coordinates of (2.4,6.6,1.87) and (0,6.6,1.87), the simulation positioning system is shifted due to the action of external force in practical application, the updating data of the algorithm are respectively output after the coordinates of the base stations jump in a fixed range, 50 groups of data are output by each base station coordinate, the average value and the root mean square error are respectively made, and the result is shown in a table two.
Watch two
As can be seen from the second table, the automatic base station position updating function of the KF-EPF algorithm can accurately measure and calculate the position of the base station, the average positioning error of the base station is within 15cm, the root mean square error is small, and the practical application requirements are met.
In the dynamic experiment, the base station positions are as follows: base station 0(0,0,1.87), base station 1(2.4,0,1.87), base station 2(2.4,7.2,1.87), and base station 3(0,7.2, 1.87). The motion track of the label is shown as a red broken line in fig. 4, the motion height is 1.55m, the motion mode is that the positioning label is placed on a mobile robot, and the center of the robot moves at a constant speed along a ceramic tile gap according to a fixed track. The label motion track is accurately tracked by using three-dimensional laser positioning to obtain a more accurate positioning track, and the positioning track is shown in fig. 5. Meanwhile, label position information obtained by three-dimensional laser positioning is used as coordinate real position information, no error is assumed, and the coordinate real position information is used for comparing the positioning precision of the KF-EPF positioning algorithm and calculating the root mean square error of the KF-EPF positioning algorithm. The UWB localization trace using the KF-EPF localization algorithm is shown in fig. 3. Obviously, the KF-EPF positioning algorithm has good positioning precision, the label track estimated by the algorithm is very close to the real track, and only few road sections have slight deviation.
And (4) performing root mean square error on the output data of the upper computer and the real coordinate point obtained by three-dimensional SLAM laser scanning positioning, wherein the root mean square error of the X, Y, Z axis is shown in the third table. The dynamic positioning of the KF-EPF positioning algorithm has the minimum mean square root error of each axis and the highest positioning precision.
Watch III
The invention adopts a positioning algorithm combining Kalman filtering and an extended particle filtering algorithm. And performing primary filtering on the distance data by using Kalman filtering to process the distance measurement abnormal data under the NLOS condition, and performing position settlement by using the processed distance data as observation data of the extended Kalman filtering. Through experimental comparison of a KF-EPF algorithm, an EKF algorithm and an EPF algorithm, the KF-EPF algorithm is found to have the highest positioning precision. In order to verify the correctness of simulation, a physical experiment is carried out, and a dynamic experiment result shows that the KF-EPF algorithm has obvious superiority compared with other three positioning algorithms, the positioning precision is within 15cm, and the dynamic positioning error is greatly improved compared with the dynamic positioning error of 17cm of the EPF algorithm.
Finally, it should be noted that: the above examples are only used to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (3)
1. An ultra wide band three-dimensional positioning algorithm with high positioning precision and anti-interference capability is characterized in that: the method comprises the following steps:
the method comprises the following steps: obtaining the distance between the base station and the label by using an ADS-TWR ranging method;
taking the distance value measured by the ADS-TWR method as measurement information, and the measurement equation of the distance model is as follows:
in the formula: c ═ 10]，v d,k The variance of the ranging noise at time k is R d . Measuring the noise variance R d Variance R between distance measurement data obtained by multiple distance measurement experiments and real distance c Represents;
in the formula:
formula (II)
ΔT k For the base station data sampling time interval, w d,k System noise at time k, with variance Q d ；
Step two: carry out "once" filtering to ADS-TWR range finding data through the KF algorithm, can filter the range finding data through this step to reduce the range finding information fluctuation that NLOS phenomenon and noise caused, get rid of unusual data, provide comparatively accurate measurement information for EPF positioning algorithm
Filtering the once filtered ranging value
Performing 'secondary' filter algorithm positioning as an observation signal of the extended particle filter;
the "quadratic" filtered distance measurement model is as follows:
in the formula:
in order to predict the state vector(s),
to predict the state covariance matrix, M k In order to be a matrix of gains, the gain matrix,
and
the state estimation vectors at time k-1 and k, respectively,
and
estimated state covariance matrices at time k-1 and time k, respectively, I being an identity matrix, filtered
Merging base station-to-tag ranging data filtering results into matrix
The following equation is used as the equation of state:
the following equation is taken as the nonlinear observation equation:
step three: updating the particles and weights using an EKF algorithm;
(1) when i is 0: from the prior distribution p (x) 0 ) Sampling point of middle structure
That is to say
Specifically, the formula is shown as follows:
(2) when i > 0, the particles are updated using the EKF algorithm:
where Q is the process noise variance and R is the measurement noise variance. Obtaining sampling points from importance functions
And (3) updating the weight:
normalization weight:
using EKF algorithm at time k-1, and up-to-date observation information D k To calculate the mean and variance of the ith particle, and to sample and update the particle with the mean and variance, the variance of the process noise and the measurement noise of the EKF needs to be re-given, so as to ensure the positioning accuracy of the subsequent calculation。
2. The ultra-wideband three-dimensional positioning algorithm with high positioning accuracy and high interference rejection according to claim 1, wherein: in the first step, the base station communicates with the tag and communicates with each other, so that distance data between any two base stations can be acquired, when the tag coordinate is in a static state, the tag coordinate can be used for measuring and calculating the base station coordinate, and the static tag is used as the base station to prevent the influence of abnormal movement of the base station on positioning data.
3. The ultra-wideband three-dimensional positioning algorithm with high positioning accuracy and high interference rejection according to claim 2, wherein: when the label coordinate is jumped within the error range, the label can be considered to be in a static state.
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