CN113884098B - Iterative Kalman filtering positioning method based on materialization model - Google Patents

Iterative Kalman filtering positioning method based on materialization model Download PDF

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CN113884098B
CN113884098B CN202111204542.7A CN202111204542A CN113884098B CN 113884098 B CN113884098 B CN 113884098B CN 202111204542 A CN202111204542 A CN 202111204542A CN 113884098 B CN113884098 B CN 113884098B
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time
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covariance matrix
observation
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CN113884098A (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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Shanghai Normal University
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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

Abstract

The invention relates to an iterative Kalman filtering positioning method based on a concrete model, which comprises the following steps: step 1: initializing a map, namely setting an initial value for a variable of the map; step 2: establishing a system state equation of the robot, and initializing a motion model; step 3: the iterative Kalman filtering algorithm based on the materialized model is used for estimating the pose so as to improve the precision of pose estimation, solve the problems of SLAM real-time mapping and positioning, improve the precision of pose estimation, and compared with the prior art, the invention has the characteristics of effectively reducing the accumulated error of a motion model, improving the precision and the robustness of pose estimation and the like.

Description

Iterative Kalman filtering positioning method based on materialization 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 concrete model.
Background
And (5) performing instant positioning and map construction (simultaneous localization and mapping, SLAM), namely moving the robot from an unknown position in an unknown field, positioning the robot according to position estimation and a surrounding map in the moving process, and performing incremental map updating on the basis of self positioning, so as to realize autonomous positioning and navigation of the robot.
In 1960, the paper published by Kalman proposed a new method (A New Approach to Linear Filtering and Prediction) for linear filtering and prediction problems, and Kalman filters were derived therefrom, in 1988, smith and Self et al adopted an extended Kalman filter (extended Kalman filter, EKF) algorithm to extend a Kalman filter algorithm applicable only to a linear system, so that the Kalman filter algorithm can be practically applied to SLAM under a nonlinear system, and at present, besides the extended Kalman algorithm for solving the SLAM problem, there are main methods such as Markov positioning, maximum likelihood estimation, unscented Kalman filter and particle filter, and the formed Fast-SLAM algorithm, PF-SLAM algorithm and kf-SLAM algorithm are used for SLAM research.
In the SLAM system, the extended kalman filtering algorithm performs first-order linear expansion on the nonlinear system, but the working point for performing first-order linearization is often not the optimal value of the input state, only the first-order term is reserved in the linearization process, and many high-order terms are abandoned, which can cause the precision of the EKF algorithm to be reduced or cause the filter to diverge.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide an iterative Kalman filtering positioning method based on a materialized model.
The aim of the invention can be achieved by the following technical scheme:
an iterative kalman filter positioning method based on a materialized model, the method comprising the steps of:
step 1: initializing a map, namely setting an initial value for a variable of the map;
step 2: establishing a system state equation of the robot, and initializing a motion model;
step 3: and carrying out pose estimation by using an iterative Kalman filtering algorithm based on the concrete model so as to improve the precision of pose estimation.
In the step 1, the variables of the map include the state of the road mark point and the origin of the map, the initial value of the state of the road mark point is set to 0, and the initial pose of the robot is set to the origin of the map.
In the step 2, the motion model is initialized specifically as follows:
setting an initial value of the state of the robot at the initial moment and an initial value of the corresponding covariance.
The system state equation of the robot is as follows:
x t ＝g(u t ,x t-1 )+ε t
z t ＝h(x t )+δ t
wherein x is t For the state vector at time t, g (·) is the motion model, x t-1 Is the state vector at time t-1, u t Epsilon is the control input of the system from t-1 to t t Is the noise of the motion model, obeys Gaussian distribution (0, Q t )，z t An observation vector of a road mark point at the moment t, h (·) is an observation model, delta t For observing the modelIs subjected to Gaussian distribution (0, R t )。
In the step 3, the process of pose estimation based on the iterative kalman filtering algorithm of the materialized model comprises the following steps:
step 31: EKF prediction;
step 32: updating EKF;
step 33: status augmentation.
In the step 31, the EKF prediction process specifically includes:
predicting the system pose at the time t according to the state estimation value at the time t-1 and the control input at the time t to obtain a priori state estimation valueAnd the corresponding covariance matrix->
The prior state estimation valueThe expression of (2) is:
wherein,for the prior state estimation value at the time t, g (·) is a motion model, u t Mu, for the control input of the system from time t-1 to time t t-1 The state estimate at time t-1.
The covariance matrixThe expression of (2) is:
wherein,a priori state estimate for time t +.>Corresponding covariance matrix, G t The Jacobian matrix which is the motion model g (·) represents the motion model g (·) versus the state estimate μ t Deviation-finding, sigma t-1 State estimation value mu for time t-1 t-1 Corresponding covariance matrix, R t Is the covariance matrix of the noise of the observation model.
In the step 32, the EKF updating process specifically includes:
acquiring covariance corresponding to the prior state estimation value at the moment t, jacobian matrix of the observation model and covariance matrix corresponding to noise of the motion model through a sensor, and further calculating Kalman gain K t And performing optimal estimation of the pose:
wherein K is t Kalman gain at time t, H t For the jacobian matrix of the observation model h (),a priori state estimate for time t +.>Corresponding coordinationVariance matrix, Q t Covariance matrix, μ, of noise for motion model t For the state estimate at time t +.>For the a priori state estimate at time t, z t For the observation at time t, h (·) is the observation model, representing the nonlinear mapping of the state space to the measurement space,/->For observing the estimated value, +.>Is the residual r (t), is->And the covariance matrix corresponding to the state estimation value at the time t.
In the step 33, the state augmentation process specifically includes:
and (3) carrying out state augmentation when the observation model is reversible, namely initializing newly discovered road marking points when the robot discovers the road marking points which are not observed, adding the state of the newly discovered road marking points into a map through an observation equation, and further increasing the size of the total state vector, namely dynamically changing a filter in the EKF-SLAM.
Compared with the prior art, the invention has the following advantages:
firstly, the invention improves the EKF algorithm, proposes an iterative Kalman filtering (RIEKF) algorithm based on a concrete model to estimate the pose, can effectively reduce the accumulated error of a motion model, improves the precision of pose estimation, and has the characteristic of good robustness;
secondly, the invention adopts a concrete model, and carries out algorithm experiments on a simplified model of a real trolley, so that the pose estimation and the real track have high fitting degree, and the high accuracy, the high availability in a real environment and the high robustness of the invention are verified.
Drawings
FIG. 1 is a schematic flow chart of the present invention.
Fig. 2 is a graph of simulation results of the present invention on a MATLAB platform.
Fig. 3 is a graph of error comparisons in the X and Y directions using the EKF algorithm and using the present invention, respectively.
Fig. 4 is a graph of two-norm error comparisons using the EKF algorithm and using the present invention, respectively.
Detailed Description
The invention will now be described in detail with reference to the drawings and specific examples.
Examples
The invention provides an iterative Kalman filtering positioning method based on a concrete model, which comprises the following steps:
step 1: initializing a map, wherein no information of any road mark point exists before the robot starts to move, only state information of the robot is in the map, the initial pose of the robot is taken as an origin of the map, and the initial covariance of the initial pose is set according to actual conditions;
step 2: initializing a motion model, solving SLAM real-time mapping and positioning problems based on an iterative Kalman filtering algorithm of a concrete model, wherein a system state equation of the robot is as follows:
x t ＝g(u t ,x t-1 )+e t
z t ＝h(x t )+δ t
wherein x is t For the state vector at time t, g (·) is the motion model, x t-1 Is the state vector at time t-1, u t Epsilon is the control input of the system from t-1 to t t Is the noise of the motion model, obeys Gaussian distribution (0, Q t )，z t An observation vector of a road mark point at the moment t, h (·) is an observation model, delta t To observe the noise of the model, the Gaussian distribution (0, R t )；
Step 3: EKF prediction, in the prediction stage, predicting a system pose estimated value at the time t according to a state estimated value at the time t-1 and a control input at the time tAnd the corresponding covariance matrix->
Wherein,for the prior state estimation value at the time t, g (·) is a motion model, u t Mu, for the control input of the system from time t-1 to time t t-1 For the state estimate at time t-1, < >>A priori state estimate for time t +.>Corresponding covariance matrix, G t The Jacobian matrix which is the motion model g (·) represents the motion model g (·) versus the state estimate μ t Deviation-finding, sigma t-1 State estimation value mu for time t-1 t-1 Corresponding covariance matrix, R t Covariance matrix of noise of observation model;
step 4: EKF updating, in the updating stage, calculating Kalman gain K according to the value obtained by the sensor t And performing optimal estimation of the pose:
wherein K is t Kalman gain at time t, H t For the jacobian matrix of the observation model h (),a priori state estimate for time t +.>Corresponding covariance matrix, Q t Covariance matrix, μ, of noise for motion model t For the state estimate at time t +.>For the a priori state estimate at time t, z t For the observation at time t, h (·) is the observation model, representing the nonlinear mapping of the state space to the measurement space,/->For observing the estimated value, +.>Is the residual r (t), is->The covariance matrix corresponding to the state estimation value at the time t;
step 5: the observation equation is reversible, state augmentation is performed, the state augmentation refers to the initialization of newly discovered road marking points, when a robot discovers a road marking point which is not observed at all, the new road marking state is added into a map by utilizing the observation equation, and the size of the total state vector is increased by one step of operation, so that the size of a filter in the EKF-SLAM is dynamically changed, namely, a motion model is dynamically changed.
In step 1, there is no information of any road mark point before the robot starts to move, so only the state information of the robot is set in the map, n=0, x=r, and the initial pose of the robot is often used as the origin of the map in SLAM, and the initial covariance can be set according to practical situations, for example:
wherein,the initial pose of the robot is shown, and P is the initial covariance.
In order to verify the performance of the invention, experiments are carried out on a real trolley, a model used in the research experiment is an intelligent trolley, a radium LS01G laser radar is equipped, the trolley model is provided with an outdoor cross-country chassis, a differential mechanism is arranged on the front wheel and the rear wheel, the laser radar measuring range is 8 meters, the measuring frequency is 3600-4000 HZ, the scanning frequency is 3-11 HZ, the precision is within 1 meter, and the precision of the pose estimation by adopting an EKF algorithm and an IEKF algorithm is respectively analyzed and compared on the experimental trolley, as can be seen from the table 1, the error of the pose estimation by adopting the IEKF (iterative Kalman filter) algorithm after the materialization model is much smaller than that of the EKF (extended Kalman filter) algorithm after the materialization model is adopted in the X direction and the two norms, and the precision of the iterative Kalman filter pose estimation by adopting the materialization model can be obviously superior to the original EKF algorithm:
table 1 method comparative experiment data table
Mean value of X-direction errors Mean value of Y-direction errors Mean value of two-norm error
Materialized EKF 1.1072 0.5047 1.3247
Materialized IEKF 0.4341 0.5275 0.7430
While the invention has been described with reference to certain preferred embodiments, it will be understood by those skilled in the art that various changes and substitutions may be made without departing from the spirit and scope of the invention as defined by the appended claims. Therefore, the protection scope of the invention is subject to the protection scope of the claims.

Claims (1)

1. An iterative Kalman filtering positioning method based on a materialized model is characterized by comprising the following steps:
step 1: initializing a map, namely setting an initial value for a variable of the map;
step 2: establishing a system state equation of the robot, and initializing a motion model;
step 3: performing pose estimation based on an iterative Kalman filtering algorithm of the materialized model so as to improve the precision of the pose estimation;
in the step 1, the variables of the map comprise the state of the road mark point and the origin of the map, the initial value of the state of the road mark point is set to be 0, and the initial pose of the robot is set to be the origin of the map;
in the step 2, the motion model is initialized specifically as follows:
setting an initial value of the state of the robot at the initial moment and an initial value of the corresponding covariance;
the system state equation of the robot is:
x t ＝g(u t ,x t-1 )+ε t
z t ＝h(x t )+δ t
wherein x is t For the state vector at time t, g (·) is the motion model, x t-1 Is the state vector at time t-1, u t Epsilon is the control input of the system from t-1 to t t Is the noise of the motion model, obeys Gaussian distribution (0, Q t )，z t An observation vector of a road mark point at the moment t, h (·) is an observation model, delta t To observe the noise of the model, the Gaussian distribution (0, R t )；
In the step 3, the process of pose estimation based on the iterative kalman filtering algorithm of the materialized model comprises the following steps:
step 31: EKF prediction;
step 32: updating EKF;
step 33: status augmentation;
in the step 31, the EKF prediction process specifically includes:
predicting the system pose at the time t according to the state estimation value at the time t-1 and the control input at the time t to obtain a priori state estimation valueAnd the corresponding covariance matrix->
The prior state estimation valueThe expression of (2) is:
wherein,for the prior state estimation value at the time t, g (·) is a motion model, u t Mu, for the control input of the system from time t-1 to time t t-1 The state estimation value at the time t-1;
the covariance matrixThe expression of (2) is:
wherein,a priori state estimate for time t +.>Corresponding covariance matrix, G t The Jacobian matrix which is the motion model g (·) represents the motion model g (·) versus the state estimate μ t Deviation-finding, sigma t-1 State estimation value mu for time t-1 t-1 Corresponding covariance matrix, R t Covariance matrix of noise of observation model;
in the step 32, the EKF updating process specifically includes:
acquiring covariance corresponding to the prior state estimation value at the moment t, jacobian matrix of the observation model and covariance matrix corresponding to noise of the motion model through a sensorAnd calculate Kalman gain K t And performing optimal estimation of the pose:
wherein K is t Kalman gain at time t, H t For the jacobian matrix of the observation model h (),a priori state estimate for time t +.>Corresponding covariance matrix, Q t Covariance matrix, μ, of noise for motion model t For the state estimate at time t +.>For the a priori state estimate at time t, z t For the observation at time t, h (·) is the observation model, representing the nonlinear mapping of the state space to the measurement space,/->For observing the estimated value, +.>Is the residual r (t), is->The covariance matrix corresponding to the state estimation value at the time t;
in the step 33, the state augmentation process specifically includes:
and (3) carrying out state augmentation when the observation model is reversible, namely initializing newly discovered road marking points when the robot discovers the road marking points which are not observed, adding the state of the newly discovered road marking points into a map through an observation equation, and further increasing the size of the total state vector, namely dynamically changing a filter in the EKF-SLAM.
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