CN117109593B - Submersible robot positioning method and system based on robust Kalman filtering - Google Patents
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Abstract
The invention belongs to the field of robot positioning, and provides a robust Kalman filtering-based submersible robot positioning method and a robust Kalman filtering-based submersible robot positioning system.
Description
Technical Field
The invention belongs to the field of robot positioning, and particularly relates to a robust Kalman filtering-based submersible robot positioning method and system.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
The safe operation of the petroleum storage tank is a primary target of crude oil storage, and the oil submersible robot detects the bottom of the storage tank in the environment of oil, so that the intrinsic safety of the storage tank and the long-period operation of the storage tank can be effectively ensured. However, due to the complexity (including closed space, oil environment, strong signal attenuation, numerous interference and the like) of the crude oil storage tank in a service state, the positioning signal of the oil submersible robot at the bottom of the petroleum storage tank contains stronger noise, and the positioning precision of the oil submersible robot is seriously affected.
The inventor finds that the existing oil submersible robot positioning method has the following defects:
1. the existing method for processing the outlier data adopts a 3 sigma criterion to remove the outlier, reduces the interference effect of the outlier through an adjusting coefficient and the like, and the complexity of the working environment of the submersible robot leads the method to inaccurate discrimination and filling of the outlier data, so that the accuracy is insufficient in the navigation positioning application of the submersible robot, and the operation effect of the robot is affected.
2. The existing positioning method needs to determine the structural parameters of the positioning object in advance and keep the structural parameters unchanged. However, after the different crude oil storage tanks are subjected to multiple overhauling and transformation, structural parameters are greatly changed, the unknown property is high, the structural dimensions of the different crude oil storage tanks and the quality of internal crude oil are different, and the change of the environment in the storage tanks can be influenced when the submersible robot works in the storage tanks, so that the parameters of the positioning algorithm of the submersible robot can change with time, and if the positioning parameters cannot be updated on line, the positioning precision of the submersible robot can be reduced along with the increase of the working time.
Disclosure of Invention
In order to solve at least one technical problem in the background art, the invention provides a submersible robot positioning method and a system based on robust Kalman filtering, firstly, aiming at the problem that outliers exist in coordinate data of a submersible robot, a robust Kalman filtering algorithm is provided for solving the signal processing task of positioning the submersible robot in a crude oil storage tank, parameters required by submersible robot positioning signal filtering are obtained by carrying out information mining on submersible robot positioning data containing outlier pollution, and secondly, aiming at the problem that algorithm parameters are changed due to the change of the working environment of the submersible robot, the invention provides a submersible robot positioning system capable of updating positioning parameters on line, which can update and correct the parameters of the robust Kalman filtering algorithm in real time by utilizing online data when the submersible robot works, thereby improving the positioning precision and guaranteeing the working quality when the submersible robot works.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
the first aspect of the invention provides a submersible robot positioning method based on robust Kalman filtering, which comprises the following steps:
acquiring a coordinate data sample set and control input of the oil submerged robot in a storage tank;
combining a coordinate data sample set and control input of the submersible robot in the storage tank, and training by using an expected maximization algorithm to obtain model parameters of a robust Kalman filtering algorithm; the training process of the robust Kalman filtering algorithm comprises the following steps:
determining the structure of a robust Kalman filtering algorithm model, learning posterior distribution expectations of hidden variables of the model in the step E under the structure of the robust Kalman filtering algorithm model, updating parameters of the model in the step M, and determining termination conditions of expected maximization algorithm iteration;
and predicting new coordinate data based on the trained robust Kalman filtering algorithm to obtain the position information of the oil submerged robot at the current moment in the storage tank.
Further, the method for acquiring the coordinate data sample set of the submersible robot in the storage tank comprises the following steps:
in order to determine the coordinate position and the posture of the submersible robot during operation, a group of positioning sensors are respectively arranged at the head and the tail of the robot, and s (s 1, s 2) is assumed to be the coordinate of the submersible robot, wherein s1 is a latitude coordinate value, and s2 is a longitude coordinate value.
Further, the structure of the robust Kalman filtering algorithm model is determined by the following steps:
determining a dynamic relation between state values and a relation between an observed value and the state values in a robust Kalman filtering algorithm model;
and according to the property of student t distribution, utilizing the student t distribution to replace Gaussian distribution, and rewriting the dynamic relationship between the state values and the relationship between the observed values and the state values.
Further, after the coordinate data sample and the control input of the oil submerged robot in the storage tank are obtained, dimensionless processing is carried out on the coordinate data sample set and the control input, and the variance of the data set is converted into unit variance.
Further, the posterior distribution expectation of the hidden variables of the E-step learning model specifically includes:
according to the structure of the robust Kalman filtering algorithm model, calculating to obtain a log-likelihood function of the complete data;
solving a posterior distribution of hidden variables for likelihood functions of the complete data;
unknown parameters in posterior distribution of the hidden variables are obtained through forward propagation learning and backward propagation learning, and relevant statistics of the hidden variables are obtained.
Further, the parameters of the model parameters of the robust kalman filter algorithm include: a state transition matrix, an output matrix, an accuracy matrix of the true value and the observed value and the degree of freedom of student t distribution.
Further, the method for updating the parameters of the model in the step M is as follows: and obtaining a corresponding parameter updating formula for updating by deriving posterior distribution of the likelihood function and enabling the result of the derivation to be equal to zero.
Further, likelihood functions of the observed data are used as judgment conditions for iterative convergence in the parameter learning process.
A second aspect of the present invention provides a robust kalman filter algorithm-based positioning system for a submersible robot, comprising:
the data acquisition module is used for acquiring a coordinate data sample set and control input of the oil submerged robot in the storage tank;
the model parameter determining module is used for combining a coordinate data sample set of the oil-submerged robot in the storage tank and control input, and training by using an expected maximization algorithm to obtain model parameters of a robust Kalman filtering algorithm; the training process of the robust Kalman filtering algorithm comprises the following steps:
determining the structure of a robust Kalman filtering algorithm model, learning posterior distribution expectations of hidden variables of the model in the step E under the structure of the robust Kalman filtering algorithm model, updating parameters of the model in the step M, and determining termination conditions of expected maximization algorithm iteration;
and the positioning module predicts the new coordinate data based on the trained robust Kalman filtering algorithm to obtain the position information of the submersible robot at the current moment in the storage tank.
Compared with the prior art, the invention has the beneficial effects that:
aiming at the problem that the accuracy of a Kalman filtering algorithm is reduced due to outlier pollution of coordinate data, the invention provides a positioning method of an oil-submerged robot based on a robust Kalman filtering algorithm, namely, long-tail distribution-student t distribution is used for replacing Gaussian distribution in a traditional Kalman filtering algorithm, and compared with the existing robust Kalman filtering algorithm, the method can more effectively treat the problem of outlier data pollution in navigation positioning of the oil-submerged robot; the capability of the Kalman filtering algorithm for processing outlier coordinate data is enhanced, the robustness of the Kalman filtering algorithm is ensured, and the positioning accuracy of the oil submerged robot in the crude oil storage tank is improved.
Aiming at the problem that parameters of a robust Kalman filtering algorithm change along with a working environment, the invention provides the positioning system of the submersible robot, which can update the parameters on line, and can ensure the positioning accuracy of the submersible robot by updating the parameters of the robust Kalman filtering on line through coordinate data collected by the submersible robot in real time.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention.
FIG. 1 is a flowchart of a positioning method of a submersible robot based on robust Kalman filtering provided by an embodiment of the invention;
FIG. 2 is an actual value of coordinate data provided by an embodiment of the present invention;
FIG. 3 is a coordinate data observation provided by an embodiment of the present invention;
FIG. 4 is a graph of coordinates after processing according to various methods provided by embodiments of the present invention.
Detailed Description
The invention will be further described with reference to the drawings and examples.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the invention. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present invention. As used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof.
The storage tank is very common storage equipment in the petrochemical industry, utilizes the oil-submerged robot to detect the inside storage tank in oily state and can reduce the time length of downtime, reduce detection cost. However, due to the specificity of the working environment, the robot works in a closed liquid environment, so that an accurate positioning method is needed to acquire the position of the submersible robot in real time, thereby assisting the working task of the machine at the tank bottom. Due to the structural design of the storage tank and the interference of oil medium in the storage tank, the robot coordinate directly acquired by the ultrasonic positioning system has serious noise interference, and in order to improve the positioning accuracy, a Kalman filtering algorithm is often adopted to perform noise reduction treatment on the coordinate data of the oil submerged robot.
The Kalman filtering is a positioning signal noise reduction method commonly used in navigation positioning, and the Kalman filtering reduces the influence of noise by utilizing dynamic information of coordinate signals to obtain a predicted position of a positioning coordinate. This estimate may be a filtering of the current submersible robot position, a prediction of future submersible robot positions, or an interpolation or smoothing of past submersible robot positions. The state of the commonly used Kalman filtering algorithm in a navigation positioning system is described as
(1)
Wherein,、/>and->Respectively representkStatus value, control input value and observation value of the positioning signal of the submersible robot at moment +.>、/>And->A state transition matrix, an input control matrix and an output mapping matrix, respectively, < >>Andthe gaussian distributions respectively representing the process noise and the observed noise, and the mean value of the two gaussian distributions is 0,/and->And->The mean value and the covariance matrix of the Gaussian distribution are respectively, and the covariance matrix changes along with the change of the working environment of the oil-submerged robot.
Because the complexity of the internal space of the crude oil storage tank causes that the coordinate information of the oil submerged robot contains outlier pollution, the traditional Kalman filtering algorithm has limited noise reduction degree on the positioning information of the oil submerged robot, and cannot provide accurate position, posture and speed information of the oil submerged robot, the Kalman filtering algorithm needs to be improved, and the capability of the Kalman filtering algorithm for processing noise interference of the oil submerged robot is enhanced.
Description of the preferred embodiments
As shown in fig. 1, the embodiment provides a positioning method of a submersible robot based on robust kalman filtering, which includes the following steps:
step 1: coordinate data collection
In step 1, in order to determine the coordinate position and posture of the submersible robot during operation, a group of positioning sensors are typically arranged at the head and tail of the robot, assuming thats(s 1 ,s 2 ) Is the coordinates of the oil-submersible robot, whereins 1 Is a coordinate value of latitude,s 2 is a longitude coordinate value.
Coordinate data collected by a navigational positioning system of an oil submerged robot form a dataset，/>Is shown inkThe coordinate information obtained at the moment in time,Kthe control input for the robust Kalman filter is +.>。
Step 2: robust Kalman filtering algorithm model structure
In the robust Kalman filtering algorithm model, the dynamic relationship between state values is that
(2)
The relationship between the observed value and the state value is that
(3)
Wherein,probability density function of student t distribution, +.>，/>Andvrespectively mean value, precision matrix and degree of freedom of student t distribution,>is a model parameter of a robust kalman filter algorithm.
In order to facilitate model training, the robust Kalman filter algorithm models (2) - (3) can be written as follows according to the nature of student t distribution
(4)
(5)
(6)
Wherein the method comprises the steps ofAs a probability density function of a gaussian distribution, +.>Is a probability density function of the gamma distribution. />For the state transition matrix>For controlling the input matrix>And->The precision matrices of the true and observed values respectively,vthe degree of freedom of the distribution of student t is thetaRandom variables introduced according to degrees of freedom during model transformation. />，/>And->Respectively iskThe true value, control input and observation of the moment,/->Is thatk-a true value at time 1.
Step 3: robust Kalman filtering algorithm parameter determination method
Positioning coordinate data of the submersible robot is obtained through a coordinate collection mode in the step 1, and a coordinate data set is obtained firstlyAnd the input control amount of the model is +.>And carrying out dimensionless treatment, and converting the data variance into unit variance.
Parameters of the robust kalman filter can be updated using a expectation maximization algorithm: the method comprises the following steps of learning posterior distribution expectations of hidden variables of a model, solving relevant statistics of the hidden variables, updating parameters of the model in M steps, and maximizing termination conditions of algorithm iteration, and specifically comprises the following steps:
according to the formulas (4) - (6), the log likelihood function of the complete data is calculated as
(7)
First, likelihood function for complete dataFinding posterior distribution of hidden variables, noted as
(8)
Wherein,to find the desired operation.
To determine parameters of the robust Kalman model, a state transition matrix needs to be determinedFOutput matrixUPrecision matrix phi sum of true and observed valuesDegree of freedomv。
The specific expression is as follows:
(1) For a switching matrixFBy deriving the posterior distribution of likelihood functions and making the result equal to zero, a switching matrix can be obtainedFIs used for updating the formula of the parameter of (a),
(9)
(2) Aiming at the precision matrix phi of the hidden variables, the parameter updating formula of the precision matrix phi can be obtained by deriving the posterior distribution of the likelihood function and making the derivation result equal to zero,
(10)
(3) Transmitting matrix for hidden variablesUBy deriving the posterior distribution of likelihood functions and making the result equal to zero, a transmission matrix can be obtainedUIs used for updating the formula of the parameter of (a),
(11)
(4) Precision matrix for observed variablesGeneral purpose medicineDeriving the posterior distribution of likelihood function, and making the result equal to zero to obtain accuracy matrix +.>Is used for updating the formula of the parameter of (a),
(12)
(5) For degrees of freedomvBy deriving the posterior distribution of likelihood functions and making the result of the derivation equal to zero, the degree of freedom can be obtainedvIs used for updating the formula of the parameter of (a),
(13)
wherein the statistics in parameter formulas (9) - (13)，/>，/> And->The posterior distribution of the hidden variables is required to be obtained, and the specific expression is as follows:
(14)
wherein,，/>and->Obtained from forward propagation and backward propagation learning:
(1) Solving by using forward propagation algorithmP(k)(P(k) For posterior distribution), forward propagation with online update formula of
(15)
(2) Solving hidden variables by using backward propagation algorithmPosterior distribution of (a), backward propagation learning formula is
(16)
(3) StatisticsAnd->From hidden variablesθPosterior distribution acquisition of->And->The expression of (2) is
(17)
Wherein,，/>the expression is
(18)
Wherein,Din order to view the dimensions of the quantity,from
(19)
Wherein,
(20)
in the iterative learning process of the expectation maximization algorithm, the likelihood function of the observed data monotonically increases, so that the likelihood function of the observed data is used as a judgment condition for iterative convergence in the parameter learning process and is subjected to the following steps ofnThe likelihood function of the observed data for the multiple iterations is:
(21)
the convergence condition is
(22)
Wherein,a convergence threshold is set for the consideration.
After training is completed by using the expectation maximization algorithm, parameters are obtained。
When the submersible robot performs tank bottom operation, the newly collected coordinate data is recorded asThe new data can be filtered by using a robust Kalman filtering algorithm:
the prediction process of the robust Kalman filtering algorithm comprises the following steps:
(23)
wherein,is according to->The system state at the current time obtained by prediction can be set to be any number of initial states, and the input matrix is controlled>Given by the control terminal.
(24)
Wherein,is according to->Predicting the obtained noise covariance matrix of the current moment.
The signal filtering process of the robust Kalman filtering algorithm comprises the following steps:
the filtering process is to use the state value obtained by the prediction processSum of covariance->The filtering process is carried out to realize the purpose of noise reduction, and a Kalman filtering gain matrix is firstly required to be constructed before the filtering process is carried out>
(25)
Using the Kalman gain matrix at the current timeThe state values of the prediction phases can be individually assigned>And covariance matrix->Filtering
(26)
Wherein,the filtered state values and the fluctuation matrix, respectively.
In order to utilize the coordinate position of the oil-submersible robot obtained by the robust Kalman filtering, the parameters of the robust Kalman filtering can be updated through the latest data when the oil-submersible robot works.
Then, the online coordinate data of the oil submerged robot during working is collected and used as a data set required for updating the parameters of the training robust Kalman filtering model.
In order to verify the performance of the robust Kalman filtering algorithm parameter determination method disclosed by the invention, simulation experiments are performed by utilizing MATLAB software. The experimental conditions and experimental results are as follows:
(1) Experimental conditions
Firstly, a movement track of the submersible robot in the closed oil tank is generated by sine function simulation, and 629 coordinate points are generated, as shown in fig. 2. In order to simulate noise interference in the ultrasonic positioning system signal collection process of the submersible robot, noise interference conforming to student t distribution is added, the coordinate distribution after noise addition is shown in fig. 3, and a plurality of outliers exist in the obtained coordinate data as can be seen from fig. 3.
The invention is compared with a Kalman filtering parameter determination method based on Gaussian distribution.
(2) Experimental results
Fig. 4 is a comparison of noise reduction effects of different methods on coordinate signals, wherein the midpoint is a true value without noise interference, the circle represents an observed value of a positioning system after noise interference, the asterisk is a filtered value after processing by the method of the present invention, and the square represents a filtered value obtained by a conventional kalman filter parameter determination method. It can be seen that the directly acquired observed value has a larger deviation compared with the true value, and the result processed by the robust kalman filter algorithm provided by the invention is closer to the true value compared with the traditional kalman filter. In order to verify the effectiveness of the present invention, the test results were quantified, and Root Mean Square Error (RMSE) was selected as an evaluation index, and the evaluation results are shown in table 1.
Table 1 quantization of the accuracy of the filtering results for different models
Compared with the traditional Kalman filtering method, the coordinate filtering precision of the method provided by the invention is improved by 66.87% through the table 1.
(27)
Wherein,and->Respectively represent the firstkThe actual values and the filtered values of the individual coordinate samples,Kthe smaller the RMSE, the closer the data sample number, representing the processed data to the true value; the larger the RMSE, the opposite.
Experimental results show that the robust Kalman filtering algorithm provided by the invention has stronger robustness when processing the positioning signal containing outlier noise, can effectively reduce noise interference of observed data, and improves navigation accuracy.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. The positioning method of the submersible robot based on the robust Kalman filtering is characterized by comprising the following steps of:
acquiring a coordinate data sample set and control input of the oil submerged robot in a storage tank;
combining a coordinate data sample set and control input of the submersible robot in the storage tank, and training by using an expected maximization algorithm to obtain model parameters of a robust Kalman filtering algorithm; the training process of the robust Kalman filtering algorithm comprises the following steps:
determining the structure of a robust Kalman filtering algorithm model, learning posterior distribution expectations of hidden variables of the model in the step E under the structure of the robust Kalman filtering algorithm model, updating parameters of the model in the step M, and determining termination conditions of expected maximization algorithm iteration;
predicting new coordinate data based on a trained robust Kalman filtering algorithm to obtain the position information of the oil submerged robot at the current moment in the storage tank;
the structure determination method of the robust Kalman filtering algorithm model comprises the following steps:
determining a dynamic relation between state values and a relation between an observed value and the state values in a robust Kalman filtering algorithm model;
according to the property of student t distribution, utilizing the student t distribution to replace Gaussian distribution, and rewriting the dynamic relationship between state values and the relationship between observed values and state values;
the posterior distribution expectation of the hidden variables of the E-step learning model specifically comprises the following steps:
according to the structure of the robust Kalman filtering algorithm model, calculating to obtain a log-likelihood function of the complete data;
solving a posterior distribution of hidden variables for likelihood functions of the complete data;
obtaining unknown parameters in posterior distribution of hidden variables through forward propagation learning and backward propagation learning, and solving relevant statistics of the hidden variables;
the parameters of the model parameters of the robust Kalman filtering algorithm comprise: the state conversion matrix, the output matrix, the precision matrix of the true value and the observed value and the degree of freedom of student t distribution;
the method for updating the parameters of the model in the step M is as follows: and obtaining a corresponding parameter updating formula for updating by deriving posterior distribution of the likelihood function and enabling the result of the derivation to be equal to zero.
2. The method for positioning the submersible robot based on the robust Kalman filtering according to claim 1, wherein the method for acquiring the coordinate data sample set of the submersible robot in the storage tank is as follows:
in order to determine the coordinate position and the posture of the submersible robot during operation, a group of positioning sensors are respectively arranged at the head and the tail of the robot, and s (s 1, s 2) is assumed to be the coordinate of the submersible robot, wherein s1 is a latitude coordinate value, and s2 is a longitude coordinate value.
3. The positioning method of the submersible robot based on the robust Kalman filtering, as set forth in claim 1, is characterized in that after the coordinate data sample set and the control input of the submersible robot in the storage tank are obtained, dimensionless processing is carried out on the coordinate data sample set and the control input, and the variance of the data set is converted into unit variance.
4. The submersible robot positioning method based on the robust Kalman filtering according to claim 1, wherein likelihood functions of observed data are used as judgment conditions for iterative convergence in a parameter learning process.
5. The submersible robot positioning method based on the robust kalman filter according to claim 1, wherein the predicting of the new coordinate data based on the trained robust kalman filter algorithm comprises:
constructing a Kalman filtering gain matrix according to the obtained model parameters;
and respectively carrying out filtering treatment on the state value and the covariance matrix of the prediction stage by using the Kalman gain matrix at the current moment to obtain a filtered state value and a fluctuation matrix, wherein the state value is the coordinate position of the oil-submerged robot.
6. An oil submerged robot positioning system based on robust kalman filtering, comprising:
the data acquisition module is used for acquiring a coordinate data sample set and control input of the oil submerged robot in the storage tank;
the model parameter determining module is used for combining a coordinate data sample set of the oil-submerged robot in the storage tank and control input, and training by using an expected maximization algorithm to obtain model parameters of a robust Kalman filtering algorithm; the training process of the robust Kalman filtering algorithm comprises the following steps:
determining the structure of a robust Kalman filtering algorithm model, learning posterior distribution expectations of hidden variables of the model in the step E under the structure of the robust Kalman filtering algorithm model, updating parameters of the model in the step M, and determining termination conditions of expected maximization algorithm iteration;
the positioning module predicts new coordinate data based on a trained robust Kalman filtering algorithm to obtain the position information of the submersible robot at the current moment in the storage tank;
the structure determination method of the robust Kalman filtering algorithm model comprises the following steps:
determining a dynamic relation between state values and a relation between an observed value and the state values in a robust Kalman filtering algorithm model;
according to the property of student t distribution, utilizing the student t distribution to replace Gaussian distribution, and rewriting the dynamic relationship between state values and the relationship between observed values and state values;
the posterior distribution expectation of the hidden variables of the E-step learning model specifically comprises the following steps:
according to the structure of the robust Kalman filtering algorithm model, calculating to obtain a log-likelihood function of the complete data;
solving a posterior distribution of hidden variables for likelihood functions of the complete data;
obtaining unknown parameters in posterior distribution of hidden variables through forward propagation learning and backward propagation learning, and solving relevant statistics of the hidden variables;
the parameters of the model parameters of the robust Kalman filtering algorithm comprise: the state conversion matrix, the output matrix, the precision matrix of the true value and the observed value and the degree of freedom of student t distribution;
the method for updating the parameters of the model in the step M is as follows: and obtaining a corresponding parameter updating formula for updating by deriving posterior distribution of the likelihood function and enabling the result of the derivation to be equal to zero.
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