CN113884098A - Iterative Kalman filtering positioning method based on specific model - Google Patents

Iterative Kalman filtering positioning method based on specific model Download PDF

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CN113884098A
CN113884098A CN202111204542.7A CN202111204542A CN113884098A CN 113884098 A CN113884098 A CN 113884098A CN 202111204542 A CN202111204542 A CN 202111204542A CN 113884098 A CN113884098 A CN 113884098A
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CN113884098B (en
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李一染
危义坤
管西强
张云侠
安康
刘翔鹏
徐效农
宋亚庆
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Abstract

The invention relates to an iterative Kalman filtering positioning method based on a specific model, which comprises the following steps: step 1: initializing a map, namely setting initial values for variables of the map; step 2: establishing a system state equation of the robot, and initializing a motion model; and step 3: the pose estimation is carried out based on the iterative Kalman filtering algorithm of the materialized model so as to improve the precision of the pose estimation, solve the problems of SLAM real-time mapping and positioning and improve the precision of the pose estimation.

Description

Iterative Kalman filtering positioning method based on specific model
Technical Field
The invention relates to the technical field of positioning and map construction, in particular to an iterative Kalman filtering positioning method based on a specific model.
Background
The method comprises the Steps of (SLAM), namely, the robot moves from an unknown position in an unknown field, the robot is positioned according to position estimation and surrounding maps in the moving process, and incremental map updating is carried out on the basis of self positioning, so that autonomous positioning and navigation of the robot are realized.
In 1960, a New method for Linear Filtering and Prediction problem (A New Approach to Linear Filtering and Prediction) is proposed in a paper published by Kalman, a Kalman filter comes from, in 1988, Smith and Self et al adopt an Extended Kalman Filter (EKF) algorithm to expand a Kalman Filtering algorithm only suitable for a Linear system, so that the Kalman Filtering algorithm can be practically applied to SLAM under a nonlinear system, at present, besides the expanded Kalman algorithm is used for solving the SLAM problem, the Fast-SLAM algorithm, the PF-SLAM algorithm, the UKF-SLAM algorithm and the like are formed for SLAM research by using main methods such as Markov positioning, maximum likelihood estimation, unscented Kalman filter and particle filter.
In the SLAM system, the extended kalman filter algorithm is to perform first-order linear expansion on the nonlinear system, but the working point for first-order linearization is often not the optimal value of the input state, and only the first-order term is retained in the linearization process, and many high-order terms are discarded, which may cause the accuracy of the EKF algorithm to decrease or cause the filter to diverge.
Disclosure of Invention
The present invention aims to overcome the defects of the prior art, and provides an iterative kalman filtering positioning method based on a materialized model.
The purpose of the invention can be realized by the following technical scheme:
an iterative kalman filtering positioning method based on a materialization model, comprising the following steps:
step 1: initializing a map, namely setting initial values for variables of the map;
step 2: establishing a system state equation of the robot, and initializing a motion model;
and step 3: and performing pose estimation based on an iterative Kalman filtering algorithm of the materialization model to improve the precision of the pose estimation.
In the step 1, the variables of the map include the state of the landmark points and the origin of the map, the initial value of the state of the landmark points is set to 0, and the initial pose of the robot is set to the origin of the map.
In the step 2, initializing the motion model specifically includes:
and setting an initial value of the state of the robot at the initial moment and a corresponding initial value of the covariance.
The system state equation of the robot is as follows:
xt＝g(ut,xt-1)+εt
zt＝h(xt)+δt
wherein x istIs the state vector at time t, g (-) is the motion model, xt-1Is the state vector at time t-1, utFor control input of the system from t-1 to ttObeying a Gaussian distribution (0, Q) for the noise of the motion modelt)，ztIs an observation vector of a landmark point at the time t, h (-) is an observation model, deltatObeying a Gaussian distribution (0, R) to observe the noise of the modelt)。
In step 3, the pose estimation process based on the iterative kalman filtering algorithm of the materialized model includes the following steps:
step 31: predicting EKF;
step 32: updating the EKF;
step 33: the state is expanded.
In step 31, the EKF prediction process specifically includes:
predicting the system pose at the t moment according to the state estimation value at the t-1 moment and the control input at the t moment to obtain a priori state estimation value
Figure BDA0003306362090000021
And corresponding covariance matrix
Figure BDA0003306362090000022
The estimated value of the prior state
Figure BDA0003306362090000023
The expression of (a) is:
Figure BDA0003306362090000024
wherein the content of the first and second substances,
Figure BDA0003306362090000025
is the estimated value of the prior state at the time t, g (-) is a motion model, utFor control input of the system from time t-1 to time t, μt-1Is the state estimate at time t-1.
The covariance matrix
Figure BDA0003306362090000026
The expression of (a) is:
Figure BDA0003306362090000027
wherein the content of the first and second substances,
Figure BDA0003306362090000031
as a priori state estimate at time t
Figure BDA0003306362090000032
Corresponding covariance matrix, GtJacobian matrix, which is a motion model g (-) representing the motion model g (-) for the state estimate μtDerivation of the deviation, sigmat-1Is the state estimate mu at time t-1t-1Corresponding covariance matrix, RtCovariance matrix of noise for observation model。
In step 32, the EKF update process specifically includes:
obtaining a covariance corresponding to the prior state estimated value at the time t, a Jacobian matrix of an observation model and a covariance matrix corresponding to noise of a motion model through a sensor, and further calculating a Kalman gain KtAnd performing optimal pose estimation:
Figure BDA0003306362090000033
Figure BDA0003306362090000034
Figure BDA0003306362090000035
wherein, KtKalman gain at time t, HtTo observe the Jacobian matrix of model h (-),
Figure BDA00033063620900000311
as a priori state estimate at time t
Figure BDA0003306362090000036
Corresponding covariance matrix, QtCovariance matrix of noise, mu, for motion modeltFor the state estimate at time t,
Figure BDA0003306362090000037
is an estimate of the prior state at time t, ztH (-) is an observation model representing the nonlinear mapping of the state space to the measurement space for the observed value at the time t,
Figure BDA0003306362090000038
in order to observe the estimated value(s),
Figure BDA0003306362090000039
is the residual error r (t),
Figure BDA00033063620900000310
and the covariance matrix corresponding to the state estimation value at the time t.
In step 33, the process of state augmentation specifically includes:
when the observation model is reversible, state augmentation is carried out, namely when the robot finds unobserved landmark points, the newly found landmark points are initialized, the state of the newly found landmark points is added into the map through an observation equation, and then the size of the total state vector is increased, namely the filter in the EKF-SLAM is dynamically changed.
Compared with the prior art, the invention has the following advantages:
firstly, the EKF algorithm is improved, an iterative model-iterative extended Kalman filter (RIEKF) algorithm based on a specific model is provided for pose estimation, accumulated errors of a motion model can be effectively reduced, the pose estimation precision is improved, and the EKF algorithm has the characteristic of good robustness;
secondly, the method adopts a concrete model and carries out an algorithm experiment on a real trolley simplified model, the fitting degree of pose estimation and a real track is high, and the high accuracy, the high availability and the high robustness in a real environment are verified.
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FIG. 1 is a schematic flow chart of the present invention.
FIG. 2 is a diagram of simulation results on MATLAB platform according to the present invention.
FIG. 3 is a graph comparing error in the X and Y directions using the EKF algorithm and the present invention, respectively.
FIG. 4 is a graph of a two-norm error comparison using the EKF algorithm and using the present invention, respectively.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
Examples
The invention provides an iterative Kalman filtering positioning method based on a specific model, which comprises the following steps:
step 1: initializing a map, wherein no information of any landmark point exists before the robot starts to move, the map only has the state information of the robot, the initial pose of the robot is used as the origin of the map, and the initial covariance is set according to the actual situation;
step 2: initializing a motion model, solving the problems of SLAM real-time map building and positioning by using an iterative Kalman filtering algorithm based on a specific model, wherein the system state equation of the robot is as follows:
xt＝g(ut,xt-1)+et
zt＝h(xt)+δt
wherein x istIs the state vector at time t, g (-) is the motion model, xt-1Is the state vector at time t-1, utFor control input of the system from t-1 to ttObeying a Gaussian distribution (0, Q) for the noise of the motion modelt)，ztIs an observation vector of a landmark point at the time t, h (-) is an observation model, deltatObeying a Gaussian distribution (0, R) to observe the noise of the modelt)；
And step 3: EKF prediction, in the prediction stage, the estimation value of the system pose at the t moment is predicted according to the state estimation value at the t-1 moment and the control input at the t moment
Figure BDA0003306362090000041
And corresponding covariance matrix
Figure BDA0003306362090000042
Figure BDA0003306362090000043
Figure BDA0003306362090000044
Wherein the content of the first and second substances,
Figure BDA0003306362090000045
is the estimated value of the prior state at the time t, g (-) is a motion model, utFor control input of the system from time t-1 to time t, μt-1Is the state estimate at time t-1,
Figure BDA0003306362090000046
as a priori state estimate at time t
Figure BDA0003306362090000047
Corresponding covariance matrix, GtJacobian matrix, which is a motion model g (-) representing the motion model g (-) for the state estimate μtDerivation of the deviation, sigmat-1Is the state estimate mu at time t-1t-1Corresponding covariance matrix, RtA covariance matrix of noise for the observation model;
and 4, step 4: EKF updating, in the updating stage, Kalman gain K is calculated according to the numerical value obtained by the sensortAnd performing optimal pose estimation:
Figure BDA0003306362090000051
Figure BDA0003306362090000052
Figure BDA0003306362090000053
wherein, KtKalman gain at time t, HtTo observe the Jacobian matrix of model h (-),
Figure BDA0003306362090000054
as a priori state estimate at time t
Figure BDA0003306362090000055
Corresponding covariance matrix, QtCovariance matrix of noise, mu, for motion modeltFor the state estimate at time t,
Figure BDA0003306362090000056
is an estimate of the prior state at time t, ztH (-) is an observation model representing the nonlinear mapping of the state space to the measurement space for the observed value at the time t,
Figure BDA0003306362090000057
in order to observe the estimated value(s),
Figure BDA0003306362090000058
is the residual error r (t),
Figure BDA0003306362090000059
a covariance matrix corresponding to the state estimation value at the time t;
and 5: when the observation equation is reversible, the state is expanded, which means the initialization of newly discovered landmark points, and when the robot finds a landmark point which has not been observed once, the new landmark state is added into the map by using the observation equation, and the operation of the step can increase the size of the total state vector, so that the size of the filter in the EKF-SLAM is dynamically changed, that is, the motion model is dynamically changed.
In step 1, there is no information about any landmark point before the robot starts moving, so that only the state information of the robot itself is in the map at this time, n is 0, x is R, and the SLAM often uses the initial pose of the robot as the origin of the map, and its initial covariance may be set according to practical situations, for example:
Figure BDA00033063620900000510
wherein the content of the first and second substances,
Figure BDA00033063620900000511
for the initial pose of the robotAnd P is the initial covariance.
In order to verify the performance of the invention, the experiment is carried out on a real trolley, the model used for research experiment is an intelligent trolley, the intelligent trolley is equipped with a radium laser LS01G laser radar, the trolley model is provided with an outdoor cross-country chassis, the front wheel and the rear wheel are provided with differentials, the measurement range of the laser radar is 8 meters, the measurement frequency is 3600-4000 HZ, the scanning frequency is 3-11 HZ, the precision is in millimeter level within 1 meter, and the accuracy of the pose estimation is analyzed and compared on the experimental trolley by adopting the EKF algorithm and the IEKF algorithm respectively, as can be seen from the table 1, the pose estimation by adopting the IEKF (iterative Kalman filtering of the materialized model) algorithm after the materialized model is much smaller than the error of the EKF (extended Kalman filtering of the materialized model) algorithm after the materialized model is adopted in the X direction and the two norms, the accuracy of the position and orientation estimation of the improved materialized model by the iterative Kalman filtering is obviously superior to that of the original EKF algorithm:
table 1 method comparative experiment data table
Mean value of error in X direction Mean value of errors in Y direction Mean of two-norm errors
Embodied EKF 1.1072 0.5047 1.3247
Embodied IEKF 0.4341 0.5275 0.7430
While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and those skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope of the invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (10)

1. An iterative kalman filter positioning method based on a materialization model, characterized in that the method comprises the following steps:
step 1: initializing a map, namely setting initial values for variables of the map;
step 2: establishing a system state equation of the robot, and initializing a motion model;
and step 3: and performing pose estimation based on an iterative Kalman filtering algorithm of the materialization model to improve the precision of the pose estimation.
2. The materialized model-based iterative kalman filter positioning method according to claim 1, wherein in step 1, the variables of the map include a state of the landmark points and an origin of the map, and the initial value of the state of the landmark points is set to 0, and the initial pose of the robot is set to the origin of the map.
3. The method according to claim 2, wherein in the step 2, initializing the motion model specifically includes:
and setting an initial value of the state of the robot at the initial moment and a corresponding initial value of the covariance.
4. The materialized model-based iterative kalman filter positioning method according to claim 3, wherein the system state equation of the robot is as follows:
xt＝g(ut,xt-1)+εt
zt＝h(xt)+δt
wherein x istIs the state vector at time t, g (-) is the motion model, xt-1Is the state vector at time t-1, utFor control input of the system from t-1 to ttObeying a Gaussian distribution (0, Q) for the noise of the motion modelt)，ztIs an observation vector of a landmark point at the time t, h (-) is an observation model, deltatObeying a Gaussian distribution (0, R) to observe the noise of the modelt)。
5. The materialized model based iterative kalman filtering positioning method according to claim 4, wherein in the step 3, the pose estimation process by the materialized model based iterative kalman filtering algorithm includes the following steps:
step 31: predicting EKF;
step 32: updating the EKF;
step 33: the state is expanded.
6. The method according to claim 5, wherein in step 31, the EKF prediction process specifically comprises:
predicting the system pose at the t moment according to the state estimation value at the t-1 moment and the control input at the t moment to obtain a priori state estimation value
Figure FDA0003306362080000021
And corresponding covariance matrix
Figure FDA0003306362080000022
7. The materialized model based iterative Kalman filter positioning method according to claim 6, characterized in that the estimation value of the prior state
Figure FDA0003306362080000023
The expression of (a) is:
Figure FDA0003306362080000024
wherein the content of the first and second substances,
Figure FDA0003306362080000025
is the estimated value of the prior state at the time t, g (-) is a motion model, utFor control input of the system from time t-1 to time t, μt-1Is the state estimate at time t-1.
8. The materialized model based iterative kalman filter positioning method of claim 7, wherein the covariance matrix
Figure FDA0003306362080000026
The expression of (a) is:
Figure FDA0003306362080000027
wherein the content of the first and second substances,
Figure FDA0003306362080000028
as a priori state estimate at time t
Figure FDA0003306362080000029
Corresponding covariance matrix, GtJacobian matrix, which is a motion model g (-) representing pairs of motion models g (-)State estimate mutDerivation of the deviation, sigmat-1Is the state estimate mu at time t-1t-1Corresponding covariance matrix, RtIs the covariance matrix of the noise of the observation model.
9. The materialized model based iterative kalman filter positioning method according to claim 8, wherein in step 32, the EKF update process specifically comprises:
obtaining a covariance corresponding to the prior state estimated value at the time t, a Jacobian matrix of an observation model and a covariance matrix corresponding to noise of a motion model through a sensor, and further calculating a Kalman gain KtAnd performing optimal pose estimation:
Figure FDA00033063620800000210
Figure FDA00033063620800000211
Figure FDA00033063620800000212
wherein, KtKalman gain at time t, HtTo observe the Jacobian matrix of model h (-),
Figure FDA00033063620800000213
as a priori state estimate at time t
Figure FDA00033063620800000214
Corresponding covariance matrix, QtCovariance matrix of noise, mu, for motion modeltFor the state estimate at time t,
Figure FDA00033063620800000215
is an estimate of the prior state at time t, ztH (-) is an observation model representing the nonlinear mapping of the state space to the measurement space for the observed value at the time t,
Figure FDA00033063620800000216
in order to observe the estimated value(s),
Figure FDA00033063620800000217
is the residual error r (t),
Figure FDA00033063620800000218
and the covariance matrix corresponding to the state estimation value at the time t.
10. The method according to claim 9, wherein in step 33, the state augmentation process specifically includes:
when the observation model is reversible, state augmentation is carried out, namely when the robot finds unobserved landmark points, the newly found landmark points are initialized, the state of the newly found landmark points is added into the map through an observation equation, and then the size of the total state vector is increased, namely the filter in the EKF-SLAM is dynamically changed.
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CN117193020B (en) * 2023-10-12 2024-05-07 武汉科技大学 Target identification and path planning method based on full-automatic liquid sample processing workstation

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