CN113932815A - Robustness optimized Kalman filtering method and device, electronic equipment and storage medium - Google Patents

Robustness optimized Kalman filtering method and device, electronic equipment and storage medium Download PDF

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CN113932815A
CN113932815A CN202111217468.2A CN202111217468A CN113932815A CN 113932815 A CN113932815 A CN 113932815A CN 202111217468 A CN202111217468 A CN 202111217468A CN 113932815 A CN113932815 A CN 113932815A
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kalman filtering
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CN113932815B (en
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王础
陈浩
李娜
张彤
张依漪
王佳佳
侯健
马静
王凤敏
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Beijing Jinghang Computing Communication Research Institute
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    • 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
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/10—Internal combustion engine [ICE] based vehicles
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Abstract

The invention relates to a robustness optimized Kalman filtering method, a robustness optimized Kalman filtering device, electronic equipment and a storage medium; the method comprises the following steps: determining a Kalman filtering state sequence and an observation sequence; establishing a Kalman filtering model corresponding to the state sequence and the observation sequence; filtering by adopting the established Kalman filtering model; in the Kalman filtering process, a Kalman gain matrix is adopted
Figure DDA0003311237190000011
Figure DDA0003311237190000012
The robustness of Kalman filtering is improved; wherein the content of the first and second substances,
Figure DDA0003311237190000013
a covariance matrix of a posteriori prediction errors estimated for the Kalman filtering of the kth time point; i is an identity matrix; hkTransferring the matrix for observation; vkFor observing noise matrix；λ1Is a first robustness parameter, λ2Is a second robustness parameter. Compared with the traditional Kalman filtering algorithm, the method improves the robustness of the measured data error and reduces the deviation of the calculation result and the true value.

Description

Robustness optimized Kalman filtering method and device, electronic equipment and storage medium
Technical Field
The present invention relates to the field of Kalman filtering and navigation technologies, and in particular, to a Kalman filtering method and apparatus, an electronic device, and a storage medium with optimized robustness.
Background
Kalman is an algorithm that uses a linear system state equation to optimally estimate the state of the system from system observations. At present, a robustness improving method of a Kalman filtering model is mainly based on links of processing sensed data and information fusion.
In the aspect of sensing data processing, the model output accuracy is improved mainly by detecting abnormal values of sensing data. And mining and identifying data with significant difference or change in other sensing data based on the prior information of the sensor and the distribution characteristics of the sensing data.
In the aspect of information fusion, the accuracy of the output result of the model is improved through data acquired by different sensors. Currently common data fusion methods include centralized fusion, distributed fusion, and hybrid fusion. The centralized fusion aims to directly input raw data of each sensor into a filtering model in parallel for processing. The distributed fusion preprocesses the data of each sensor to form intermediate information and then inputs the intermediate information into a filtering model for processing. The hybrid fusion is to input the original data and the preprocessed data into a filter model for processing.
In the existing robustness improving method, a mechanism for optimizing a filtering algorithm step is lacked, and the problem that the difference between a Kalman filtering model and an actual scene generates an unmodeled error, so that the calculation result of the filtering model has larger deviation from a true value is not solved.
Disclosure of Invention
In view of the above analysis, the present invention aims to provide a robustness-optimized Kalman filtering method, apparatus, electronic device, and storage medium, which solve the problem of the deviation of the computation result of the Kalman filtering model.
The technical scheme provided by the invention is as follows:
the invention discloses a Kalman filtering method with optimized robustness, which comprises the following steps:
determining a Kalman filtering state sequence and an observation sequence;
establishing a Kalman filtering model corresponding to the state sequence and the observation sequence;
filtering by adopting the established Kalman filtering model;
in the course of the Kalman filtering process,
using a Kalman gain matrix
Figure BDA0003311237170000021
The robustness of Kalman filtering is improved; wherein the content of the first and second substances,
Figure BDA0003311237170000022
a covariance matrix of a posteriori prediction errors estimated for the Kalman filtering of the kth time point; i is an identity matrix; hkTransferring the matrix for observation; vkTo observe the noise matrix; lambda [ alpha ]1Is a first robustness parameter, λ2Is a second robustness parameter.
Further, the state sequence is
Figure BDA0003311237170000023
The observation sequence is
Figure BDA0003311237170000024
The Kalman filtering model is:
Xk+1＝AkXk+GkWk；
Yk＝HkXk+Vk；
wherein N represents the total length of the sequence, AkIs a state transition matrix, HkTransferring the matrix for observation; gkIs a system noise coefficient matrix; system noise matrix WkSatisfying Gaussian distribution N (0, I); observing the noise matrix VkSatisfies the Gaussian distribution N (0, Sigma)k)；∑kIs a covariance matrix.
Further, the Kalman filtering process includes:
initial value X of the initialization state vector0And the variance initial value sigma of the observation noise0；
Prediction
Figure BDA0003311237170000025
And
Figure BDA0003311237170000026
computing a Kalman gain matrix
Figure BDA0003311237170000027
Estimated of
Figure BDA0003311237170000028
Wherein the content of the first and second substances,
Figure BDA0003311237170000029
is a prior state estimated value at the moment k;
Figure BDA00033112371700000210
is an estimated value of the posterior state at the moment k;
Figure BDA0003311237170000031
the error covariance matrix is predicted a posteriori.
Further, the air conditioner is provided with a fan,a first robustness parameter λ1The calculating step of (2):
computing a residual vector xk：
Figure BDA0003311237170000032
Based on residual vector xkCalculating { xkThe covariance matrix sigma of0：
Figure BDA0003311237170000033
Wherein;
Figure BDA0003311237170000034
computing a residual matrix Rk：
Figure BDA0003311237170000035
Definition of rkIs RkA vector of diagonal elements;
calculating a first robustness parameter lambda1：
Figure BDA0003311237170000036
Further, a second robustness parameter λ2The calculating step of (2):
calculate residual vector x'k：
Figure BDA0003311237170000037
Based on residual vector x'kCalculating { x'kCovariance matrix of }'0：
Figure BDA0003311237170000038
Wherein
Figure BDA0003311237170000039
Calculate residual matrix R'k：R′k＝∑′0-Vk(ii) a Definition of r'kIs R'kA vector of diagonal elements;
calculating a second robustness parameter λ2：
Figure BDA00033112371700000310
Further, when the relative navigation filtering of multiple unmanned aerial vehicles is carried out, the state sequence in the Kalman filtering model
Figure BDA00033112371700000311
State value X ofkA 12-dimensional state value vector representing a time point of a third order, comprising relative heading angular velocities of drone a and drone B, relative heading angular accelerations of drone a and drone C, relative position vectors of drone a and drone B, relative position vectors of drone a and drone C, and velocity vectors of drones A, B and C.
Further, when the relative navigation filtering of multiple unmanned aerial vehicles is carried out, an observation sequence in a Kalman filtering model
Figure BDA00033112371700000312
Y in (1)kThe 6-dimensional observation value vector representing the time point of the second order comprises the relative distance length of an unmanned aerial vehicle A and an unmanned aerial vehicle B, the relative distance length of the unmanned aerial vehicle B and the unmanned aerial vehicle C, the relative distance length of the unmanned aerial vehicle A and the unmanned aerial vehicle C, the difference value of the speed sizes of the unmanned aerial vehicle A and the unmanned aerial vehicle B, the difference value of the speed sizes of the unmanned aerial vehicle B and the unmanned aerial vehicle C and the difference value of the speed sizes of the unmanned aerial vehicle A and the unmanned aerial vehicle C.
The invention also discloses a Kalman filtering device with optimized robustness, which comprises a filtering interface module and a Kalman filtering module;
the filtering interface module is used for acquiring Kalman filtering input data and outputting a filtering result;
the Kalman filtering module performs filtering by using the robustness optimized Kalman filtering method described above.
The invention also discloses an electronic device, comprising:
one or more processors;
storage means for storing one or more programs;
when the one or more programs are executed by the one or more processors, the one or more processors are caused to implement a robustness optimized Kalman filtering method as described above.
The invention also discloses a computer readable medium on which a computer program is stored which, when executed by a processor, implements the robustness optimized Kalman filtering method described above.
The invention has the beneficial effects that:
compared with the traditional Kalman filtering algorithm, the method has the advantages that robustness optimization is performed on the gain matrix in the Kalman filtering algorithm step, robustness of measured data errors is improved, unmodeled errors caused by differences between a Kalman filtering model and an actual scene are solved, and deviation of a calculation result and a true value is reduced.
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, wherein like reference numerals are used to designate like parts throughout.
FIG. 1 is a flow chart of a Kalman filtering method in an embodiment of the present invention;
FIG. 2 is a flow chart of a Kalman filtering process in an embodiment of the present invention;
FIG. 3 is a flowchart of a method for calculating a first robustness parameter in an embodiment of the present invention;
fig. 4 is a flowchart of a second robustness parameter calculation method in the embodiment of the present invention.
Detailed Description
The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form a part hereof, and which together with the embodiments of the invention serve to explain the principles of the invention.
The embodiment discloses a robustness optimized Kalman filtering method, as shown in fig. 1, including the following steps:
step S101, determining a Kalman filtering state sequence and an observation sequence;
step S102, establishing a Kalman filtering model corresponding to the state sequence and the observation sequence;
s103, filtering by adopting the established Kalman filtering model;
in the conventional Kalman filtering process,
kalman gain matrix
Figure BDA0003311237170000051
In order to improve the robustness of the Kalman filtering, the conventional Kalman gain matrix is improved in the present embodiment,
using a Kalman gain matrix
Figure BDA0003311237170000052
Wherein the content of the first and second substances,
Figure BDA0003311237170000053
kalman filtering estimation for the first order time point; i is an identity matrix; hkTransferring the matrix for observation; vkTo observe the noise matrix; lambda [ alpha ]1Is a first robustness parameter, λ2Is a second robustness parameter. By determining a first robustness parameter lambda1And a second robustness parameter lambda2Carry-in gain matrix KkAnd the difference of an actual scene is eliminated in a Kalman filtering model, and the robustness of Kalman filtering is improved.
Specifically, the state sequence of Kalman filtering is
Figure BDA0003311237170000054
The observation sequence is
Figure BDA0003311237170000061
The Kalman filtering model is:
Xk+1＝AkXk+GkWk；
Yk＝HkXk+Vk；
wherein N represents the total length of the sequence, AkIs a state transition matrix, HkTransferring the matrix for observation; gkIs a system noise coefficient matrix; system noise matrix WkSatisfying Gaussian distribution N (0, I); observing the noise matrix VkSatisfies the Gaussian distribution N (0, Sigma)k)；∑kIs a covariance matrix.
More specifically, the Kalman filtering process is shown in fig. 2, and includes:
step S201, initializing initial value X of state vector0And the variance initial value sigma of the observation noise0；
Step S202, prediction
Figure BDA0003311237170000062
And
Figure BDA0003311237170000063
Figure BDA0003311237170000064
step S203, calculating a Kalman gain matrix;
in the step, for the calculation error caused by the modeling difference between the original Kalman filtering and the actual application scene, the method adopts
Figure BDA0003311237170000065
For system noise matrix WkAnd observing the noise matrix VkThe covariance matrix of (a) is modeled and corrected.
Step S204, estimation
Figure BDA0003311237170000066
And
Figure BDA0003311237170000067
Figure BDA0003311237170000068
wherein the content of the first and second substances,
Figure BDA0003311237170000069
is a prior state estimated value at the moment k;
Figure BDA00033112371700000610
is an estimated value of the posterior state at the moment k;
Figure BDA00033112371700000611
the error covariance matrix is predicted a posteriori.
In particular, a first robustness parameter λ1As shown in fig. 3, includes:
step S301, calculating a residual vector xk：
Figure BDA00033112371700000612
Step S302, based on the residual vector xkCalculating { xkThe covariance matrix sigma of0：
Figure BDA00033112371700000613
Wherein;
Figure BDA0003311237170000071
step S303, calculating a residual matrix Rk：
Figure BDA0003311237170000072
Definition of rkIs RkA vector of diagonal elements;
step S304, calculating a first robustness parameter lambda1：
Figure BDA0003311237170000073
In particular, the second robustness parameter λ2As shown in fig. 4, the calculating step includes:
step S401, calculating residual vector x'k：
Figure BDA0003311237170000074
Step S402, based on residual vector x'kCalculating { x'kCovariance matrix of }'0：
Figure BDA0003311237170000075
Wherein
Figure BDA0003311237170000076
Step S403, calculating residual matrix R'k：R′k＝∑′0-Vk(ii) a Definition of r'kIs R'kA vector of diagonal elements;
step S404, calculating a second robustness parameter lambda2：
Figure BDA0003311237170000077
A specific embodiment of the present invention is to perform kalman filtering on the relative navigation task of the unmanned aerial vehicle, so that the navigation result meets the requirement of the relative navigation precision.
Specifically, when performing the relative navigation filtering of multiple drones, it is determined in step S101 of this embodiment that the state sequence and the observation sequence of Kalman filtering are specifically:
state sequences in Kalman filtering models
Figure BDA0003311237170000078
State value X ofkA 12-dimensional state value vector representing a second order time point; the 12-dimensional state value vector comprises the relative course angular velocity of the unmanned aerial vehicle A and the unmanned aerial vehicle B in the 1 dimension, the relative course angular acceleration of the unmanned aerial vehicle A and the unmanned aerial vehicle C in the 1 dimension, the relative position vector of the unmanned aerial vehicle A and the unmanned aerial vehicle B in the 2 dimension, and the relative position vector of the unmanned aerial vehicle A and the unmanned aerial vehicle C in the 2 dimensionPosition vector, velocity vector of drone A, B and C in 2 dimensions;
observation sequence in Kalman filtering model
Figure BDA0003311237170000079
Y in (1)kThe 6-dimensional observation value vector representing the time point of the second order comprises the relative distance length of an unmanned aerial vehicle A and an unmanned aerial vehicle B, the relative distance length of the unmanned aerial vehicle B and the unmanned aerial vehicle C, the relative distance length of the unmanned aerial vehicle A and the unmanned aerial vehicle C, the difference value of the speed sizes of the unmanned aerial vehicle A and the unmanned aerial vehicle B, the difference value of the speed sizes of the unmanned aerial vehicle B and the unmanned aerial vehicle C and the difference value of the speed sizes of the unmanned aerial vehicle A and the unmanned aerial vehicle C.
Through the Kalman filtering algorithm of the embodiment, the system noise matrix W is paired in the gain matrixkAnd observing the noise matrix VkThe covariance matrix is modeled and corrected, robustness optimization is achieved, robustness of measured data errors is improved, unmodeled errors caused by differences between a Kalman filtering model and an actual scene are solved, and deviation of a calculation result and a true value is reduced.
In order to further solve the problem that in the relative navigation task of the unmanned aerial vehicle, the measured data is influenced by natural random errors and anti-noise interference, so that the calculated result of the state quantity has errors with the true value. The embodiment also identifies the measurement data with larger noise interference so as to reduce the influence of the measurement data error on the Kalman filtering model result.
Specifically, the patent mainly calculates an observed value vector YkRegarding the confidence of the Kalman filtering model, when the confidence is lower than a set confidence threshold, the noise of the measured data is judged to be large, and the current calculation result of the Kalman filtering model is invalid. Therefore, the measurement data with larger noise interference is identified, and the influence of the measurement data error on the Kalman filtering model result is reduced.
More specifically, the present embodiment combines the observation vector YkConfidence of (p)kIs defined as:
Figure BDA0003311237170000081
the vector of measurement values YkThe confidence ρ k of (1) is:
Figure BDA0003311237170000082
wherein, a is a weight; p (Y)k|Yk-1，...，Y1) For given vector of prior measurements Yk-1，...，Y1With respect to the vector Y of measurement valueskThe probability density function value of the Kalman filter;
Figure BDA0003311237170000083
indicating when the state value vector X of the second orderkAnd taking the value as a conditional probability density function value of the Kalman filtering estimated value.
Preferably, the probability density function value p (Y) of the present embodimentk) The calculation method comprises the following steps: due to p (Y)k|Yk-1，...，Y1) Having the following representation:
Figure BDA0003311237170000084
the embodiment adopts a sampling method to approximately calculate p (Y)k|Yk-1，...，Y1). According to the Kalman filtering estimation method of the embodiment, the method can be obtained
The p (Y)k|Yk-1，...，Y1) The expectation of the probability density function is
Figure BDA0003311237170000091
Variance is Pk；
Wherein;
Figure BDA0003311237170000092
is an estimated value of the posterior state at the moment k;
Pkby the formula
Figure BDA0003311237170000093
Carrying out estimation; wherein Q is a process excitation noise covariance;
to normal distribution
Figure BDA0003311237170000094
Sampling to obtain M samples
Figure BDA0003311237170000095
Then p (Y)k|Yk-1，...，Y1) By the formula
Figure BDA0003311237170000096
Calculating to obtain; wherein the content of the first and second substances,
Figure BDA0003311237170000097
is normally distributed
Figure BDA0003311237170000098
In the present embodiment, by adding the pair observation vector YkAnd performing confidence calculation based on the Kalman filtering model, identifying and mining the measured data lower than a given threshold value, and reducing the influence of the error of the measured data on the Kalman filtering model result.
In a specific aspect of this embodiment, a Kalman filtering apparatus with optimized robustness is further disclosed, which includes a filtering interface module and a Kalman filtering module;
the filtering interface module is used for acquiring Kalman filtering input data and outputting a filtering result;
the Kalman filtering module adopts the Kalman filtering method of robustness optimization as above to carry out filtering.
The specific technical details and effects in this embodiment are the same as those in the previous embodiment, and thus are not repeated herein.
In a specific aspect of this embodiment, an electronic device is further disclosed, including:
one or more processors;
storage means for storing one or more programs;
when executed by the one or more processors, cause the one or more processors to implement a Kalman filtering method for robustness optimization as described above.
The specific technical details and effects in this embodiment are the same as those in the previous embodiment, and thus are not repeated herein.
In a particular aspect of this embodiment, a computer-readable medium is also disclosed, on which a computer program is stored, which when executed by a processor implements the robustness optimized Kalman filtering method described above.
The specific technical details and effects in this embodiment are the same as those in the previous embodiment, and thus are not repeated herein.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.

Claims (10)

1. A Kalman filtering method for optimizing robustness is characterized by comprising the following steps:
determining a Kalman filtering state sequence and an observation sequence;
establishing a Kalman filtering model corresponding to the state sequence and the observation sequence;
filtering by adopting the established Kalman filtering model;
in the course of the Kalman filtering process,
using a Kalman gain matrix
Figure FDA0003311237160000011
The robustness of Kalman filtering is improved; wherein the content of the first and second substances,
Figure FDA0003311237160000012
a posteriori prediction error coordination for Kalman filter estimation of the k-th time pointA variance matrix; i is an identity matrix; hkTransferring the matrix for observation; vkTo observe the noise matrix; lambda [ alpha ]1Is a first robustness parameter, λ2Is a second robustness parameter.
2. The Kalman filtering method of claim 1,
the state sequence is
Figure FDA0003311237160000013
The observation sequence is
Figure FDA0003311237160000014
The Kalman filtering model is:
Xk+1＝AkXk+GkWk；
Yk＝HkXk+Vk；
wherein N represents the total length of the sequence, AkIs a state transition matrix, HkTransferring the matrix for observation; gkIs a system noise coefficient matrix; system noise matrix WkSatisfying Gaussian distribution N (0, I); observing the noise matrix VkSatisfies the Gaussian distribution N (0, Sigma)k)；∑kIs a covariance matrix.
3. The Kalman filtering method of claim 2,
the Kalman filtering process comprises:
initial value X of the initialization state vector0And the initial value of covariance of observed noise ∑0；
Prediction
Figure FDA0003311237160000015
And
Figure FDA0003311237160000016
computing a Kalman gain matrix
Figure FDA0003311237160000017
Estimated of
Figure FDA0003311237160000018
And
Figure FDA0003311237160000019
wherein the content of the first and second substances,
Figure FDA0003311237160000021
is a prior state estimated value at the moment k;
Figure FDA0003311237160000022
is an estimate of the posterior state at time k.
4. The Kalman filtering method of claim 3,
a first robustness parameter λ1The calculating step of (2):
computing a residual vector xk：
Figure FDA0003311237160000023
Based on residual vector xkCalculating { xkThe covariance matrix sigma of0：
Figure FDA0003311237160000024
Wherein;
Figure FDA0003311237160000025
computing a residual matrix Rk：
Figure FDA0003311237160000026
Definition of rkIs RkA vector of diagonal elements;
calculating a first robustness parameter lambda1：
Figure FDA0003311237160000027
5. The Kalman filtering method of claim 3,
second robustness parameter λ2The calculating step of (2):
calculate residual vector x'k：
Figure FDA0003311237160000028
Based on residual vector x'kCalculating { x'kCovariance matrix of }'0：
Figure FDA0003311237160000029
Wherein
Figure FDA00033112371600000210
Calculate residual matrix R'k：R′k＝∑′0-Vk(ii) a Definition of r'kIs R'kA vector of diagonal elements;
calculating a second robustness parameter λ2：
Figure FDA00033112371600000211
6. The Kalman filtering method of claim 3,
state sequence in Kalman filtering model when multi-UAV relative navigation filtering is carried out
Figure FDA00033112371600000212
State value X ofkThe 12-dimensional state value vector representing the kth time point includes the relative heading angular velocities of drone a and drone B, the relative heading angular accelerations of drone a and drone C, the relative position vectors of drone a and drone B, the relative position vectors of drone a and drone C, and the velocity vectors of drones A, B and C.
7. The Kalman filtering method of claim 3,
observation sequence in Kalman filtering model when multi-unmanned aerial vehicle relative navigation filtering is carried out
Figure FDA0003311237160000031
Y in (1)kThe 6-dimensional observation value vector representing the kth time point comprises the relative distance length of an unmanned aerial vehicle A and an unmanned aerial vehicle B, the relative distance length of the unmanned aerial vehicle B and the unmanned aerial vehicle C, the relative distance length of the unmanned aerial vehicle A and the unmanned aerial vehicle C, the difference value of the speed sizes of the unmanned aerial vehicle A and the unmanned aerial vehicle B, the difference value of the speed sizes of the unmanned aerial vehicle B and the unmanned aerial vehicle C, and the difference value of the speed sizes of the unmanned aerial vehicle A and the unmanned aerial vehicle C.
8. A Kalman filtering device with optimized robustness is characterized by comprising a filtering interface module and a Kalman filtering module;
the filtering interface module is used for acquiring Kalman filtering input data and outputting a filtering result;
filtering in the Kalman filtering module by adopting the robustness optimized Kalman filtering method of any one of claims 1-7.
9. An electronic device, comprising:
one or more processors;
storage means for storing one or more programs;
when executed by the one or more processors, cause the one or more processors to implement the robustness optimized Kalman filtering method of any of claims 1-7.
10. A computer-readable medium, on which a computer program is stored which, when being executed by a processor, carries out the robustness optimized Kalman filtering method of any one of claims 1 to 7.
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