CN111942399A - Vehicle speed estimation method and system based on unscented Kalman filtering - Google Patents
Vehicle speed estimation method and system based on unscented Kalman filtering Download PDFInfo
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- B60W2510/00—Input parameters relating to a particular sub-units
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Abstract
本申请公开了一种基于无迹卡尔曼滤波的车速估算方法及系统,涉及车速估算技术领域,该车速估算方法包括步骤:建立高精度车辆模型,获取整车参数;建立多自由度车辆动力学模型,根据所述整车参数,确定无迹卡尔曼滤波器的状态方程和观测方程,并确定所述无迹卡尔曼滤波器的输入量、状态量以及观测量,所述状态量至少包括纵向速度和侧向速度;利用车速估算器,结合当前时刻的状态量,以及所述状态方程和观测方程,估算下一时刻的纵向速度和侧向速度。本申请的基于无迹卡尔曼滤波的车速估算方法及系统,通过车速估算器结合无迹卡尔曼滤波算法,可在车辆运行过程中准确地估算出车辆的实时纵向速度和侧向速度,以提高车辆动力学控制的精度。
The present application discloses a vehicle speed estimation method and system based on unscented Kalman filtering, and relates to the technical field of vehicle speed estimation. The vehicle speed estimation method includes the steps of: establishing a high-precision vehicle model, obtaining vehicle parameters; establishing multi-degree-of-freedom vehicle dynamics model, according to the vehicle parameters, determine the state equation and observation equation of the unscented Kalman filter, and determine the input quantity, state quantity and observation quantity of the unscented Kalman filter, the state quantity at least includes longitudinal Speed and lateral speed: Using the vehicle speed estimator, combined with the state quantity at the current moment, and the state equation and observation equation, estimate the longitudinal speed and lateral speed at the next moment. The vehicle speed estimation method and system based on the unscented Kalman filter of the present application can accurately estimate the real-time longitudinal speed and lateral speed of the vehicle during the running process of the vehicle by combining the vehicle speed estimator and the unscented Kalman filter algorithm, so as to improve the Accuracy of vehicle dynamics control.
Description
技术领域technical field
本申请涉及车速估算技术领域,具体涉及一种基于无迹卡尔曼滤波的车速估算方法及系统。The present application relates to the technical field of vehicle speed estimation, and in particular to a vehicle speed estimation method and system based on unscented Kalman filtering.
背景技术Background technique
目前,在车辆动力学控制中,车速是一个至关重要的状态量,它是计算车轮滑移率的基础,而滑移率是车辆动力学控制中的主要控制量。由于在车上安装直接测量车速的传感器成本太高,因此,在实际研究和开发中,车速一般都是作为一个不可直接获取的状态量,采用各种估算算法对车速进行估算。At present, in vehicle dynamics control, vehicle speed is a crucial state quantity, it is the basis for calculating wheel slip rate, and slip rate is the main control quantity in vehicle dynamics control. Due to the high cost of installing a sensor that directly measures the speed of the vehicle, in practical research and development, the vehicle speed is generally regarded as a state quantity that cannot be directly obtained, and various estimation algorithms are used to estimate the vehicle speed.
相关技术中,现有的估算算法有最大轮速法、斜率法和综合法,上述算法过程简单,实现方便,且成本低廉,但是估算精度不高,只适用于对控制精度要求不高的传统车辆。随着汽车智能化、网联化的发展,现代汽车对车辆动力学的集成控制精度要求进一步提高,因此亟需重新设计车速估算的数学模型和相应估算算法。In the related art, the existing estimation algorithms include the maximum wheel speed method, the slope method and the comprehensive method. The above algorithms are simple in process, convenient in implementation, and low in cost, but their estimation accuracy is not high, and they are only suitable for traditional methods that do not require high control accuracy. vehicle. With the development of automobile intelligence and networking, modern automobiles require further improvement in the integrated control accuracy of vehicle dynamics. Therefore, it is urgent to redesign the mathematical model of vehicle speed estimation and the corresponding estimation algorithm.
在车速估算过程中存在不可避免的过程误差和观测误差,由于卡尔曼滤波KF(Kalman Filter)是一种线性估算算法,只能在线性高斯模型下解决线性系统的状态估算问题,而实际工程应用中的系统总是存在不同程度的非线性,例如车辆系统中的轮胎就是一个典型的高度非线性系统,因此,基本的卡尔曼滤波算法并不适合引入到车辆状态估算领域,估算误差较大。There are inevitable process errors and observation errors in the process of vehicle speed estimation. Since KF (Kalman Filter) is a linear estimation algorithm, it can only solve the state estimation problem of linear systems under the linear Gaussian model, while practical engineering applications There are always different degrees of nonlinearity in the system in the vehicle system. For example, the tire in the vehicle system is a typical highly nonlinear system. Therefore, the basic Kalman filter algorithm is not suitable to be introduced into the field of vehicle state estimation, and the estimation error is large.
发明内容SUMMARY OF THE INVENTION
针对现有技术中存在的缺陷之一,本申请的目的在于提供一种基于无迹卡尔曼滤波的车速估算方法及系统以解决相关技术中车速估算精度不高的问题。In view of one of the defects in the prior art, the purpose of the present application is to provide a vehicle speed estimation method and system based on unscented Kalman filtering to solve the problem of low vehicle speed estimation accuracy in the related art.
本申请第一方面提供一种基于无迹卡尔曼滤波的车速估算方法,其包括步骤:A first aspect of the present application provides a vehicle speed estimation method based on unscented Kalman filtering, comprising the steps of:
建立高精度车辆模型,获取整车参数;Build high-precision vehicle models and obtain vehicle parameters;
建立多自由度车辆动力学模型,根据上述整车参数,确定无迹卡尔曼滤波器的状态方程和观测方程,并确定上述无迹卡尔曼滤波器的输入量、状态量以及观测量,上述状态量至少包括纵向速度和侧向速度;Establish a multi-degree-of-freedom vehicle dynamics model, determine the state equation and observation equation of the unscented Kalman filter according to the above vehicle parameters, and determine the input quantity, state quantity and observation quantity of the above unscented Kalman filter, the above state The quantities include at least longitudinal and lateral velocities;
利用车速估算器,结合当前时刻的状态量,以及上述状态方程和观测方程,估算下一时刻的纵向速度和侧向速度。Using the vehicle speed estimator, combined with the state quantity at the current moment, as well as the above state equation and observation equation, estimate the longitudinal speed and lateral speed at the next moment.
一些实施例中,上述获取整车参数之前,还包括:In some embodiments, before obtaining the vehicle parameters, the method further includes:
整车控制器输出各车轮的制动压力至上述高精度车辆模型;The vehicle controller outputs the braking pressure of each wheel to the above-mentioned high-precision vehicle model;
上述高精度车辆模型根据上述各车轮的制动压力,对车辆进行实时模拟,得到上述整车参数;The above-mentioned high-precision vehicle model performs real-time simulation on the vehicle according to the braking pressure of the above-mentioned wheels, and obtains the above-mentioned parameters of the whole vehicle;
上述整车参数包括纵向加速度、侧向加速度、横摆角速度、四个车轮的轮速以及四个车轮处的路面附着系数。The above vehicle parameters include longitudinal acceleration, lateral acceleration, yaw rate, wheel speeds of the four wheels, and road adhesion coefficients at the four wheels.
一些实施例中,上述获取整车参数之后,还包括:In some embodiments, after obtaining the vehicle parameters, the method further includes:
上述高精度车辆模型输出四个车轮的轮速至上述整车控制器。The above-mentioned high-precision vehicle model outputs the wheel speeds of the four wheels to the above-mentioned vehicle controller.
一些实施例中,上述输入量包括四个车轮的轮速,上述状态量还包括纵向加速度、侧向加速度、横摆角速度、以及四个车轮处的路面附着系数,上述观测量包括纵向加速度、侧向加速度、以及横摆角速度。In some embodiments, the above-mentioned input quantities include the wheel speeds of the four wheels, the above-mentioned state quantities also include longitudinal acceleration, lateral acceleration, yaw rate, and road adhesion coefficients at the four wheels, and the above-mentioned observation quantities include longitudinal acceleration, lateral acceleration, and yaw rate.
一些实施例中,上述利用车速估算器,结合当前时刻的状态量,以及无迹卡尔曼滤波器的状态方程和观测方程,估算下一时刻的纵向速度和侧向速度,具体包括:In some embodiments, the above-mentioned vehicle speed estimator is used, combined with the state quantity at the current moment, and the state equation and observation equation of the unscented Kalman filter to estimate the longitudinal speed and lateral speed at the next moment, specifically including:
对当前时刻的状态量进行无迹变换,得到多个sigma点,并计算每个sigma点的权值;Perform unscented transformation on the state quantity at the current moment to obtain multiple sigma points, and calculate the weight of each sigma point;
根据上述状态方程和观测方程,计算先验状态估计值、先验误差协方差和先验观测估计值;According to the above state equation and observation equation, calculate the prior state estimate, prior error covariance and prior observation estimate;
根据上述先验状态估计值、先验误差协方差和先验观测估计值,更新下一步观测值和误差协方差。According to the prior state estimate, prior error covariance, and prior observation estimate, the next observation and error covariance are updated.
一些实施例中,上述无迹卡尔曼滤波器的状态方程和观测方程为:In some embodiments, the state equation and observation equation of the above-mentioned unscented Kalman filter are:
其中,xk+1为k+1时刻的状态向量,xk为k时刻的状态向量,zk为k时刻的观测向量,uk为k时刻的输入向量,wk为k时刻的过程噪声,vk为k时刻的观测噪声。where x k+1 is the state vector at time k+1, x k is the state vector at time k, z k is the observation vector at time k, uk is the input vector at time k, and w k is the process noise at time k , v k is the observation noise at time k.
一些实施例中,上述状态方程进一步为:In some embodiments, the above state equation is further:
其中,u(k)为k时刻的纵向速度,为k时刻的纵向速度的导数,v(k)为k时刻的侧向速度,ax(k)为k时刻的纵向加速度,ay(k)为k时刻的侧向加速度,ωr(k)为k时刻的横摆角速度,为k时刻的横摆角速度的导数,μfl(k)为k时刻的左前轮路面附着系数,μfr(k)为k时刻的右前轮路面附着系数,μrl(k)为k时刻的左后轮路面附着系数,μrr(k)为k时刻的右后轮路面附着系数,Ts为k到k+1时刻之间的时间步长。where u(k) is the longitudinal velocity at time k, is the derivative of the longitudinal velocity at time k, v(k) is the lateral velocity at time k, a x (k) is the longitudinal acceleration at time k, a y (k) is the lateral acceleration at time k, ω r (k ) is the yaw rate at time k, is the derivative of the yaw rate at time k, μ fl (k) is the road adhesion coefficient of the left front wheel at time k, μ fr (k) is the road adhesion coefficient of the right front wheel at time k, μ rl (k) is the time k The left rear wheel road adhesion coefficient of , μ rr (k) is the right rear wheel road adhesion coefficient at time k, and T s is the time step between time k and time k+1.
一些实施例中,多自由度车辆动力学模型为与车速相关的七自由度动力学模型。In some embodiments, the multi-degree-of-freedom vehicle dynamics model is a vehicle-speed dependent seven-degree-of-freedom dynamic model.
本申请第二方面提供一种基于无迹卡尔曼滤波的车速估算系统,其包括:A second aspect of the present application provides a vehicle speed estimation system based on unscented Kalman filtering, which includes:
第一建模模块,其用于建立高精度车辆模型,并通过上述高精度车辆模型获取整车参数;a first modeling module, which is used to establish a high-precision vehicle model, and obtain vehicle parameters through the above-mentioned high-precision vehicle model;
第二建模模块,其用于建立多自由度车辆动力学模型,并根据上述整车参数,确定无迹卡尔曼滤波器的状态方程和观测方程,并确定上述无迹卡尔曼滤波器的输入量、状态量以及观测量,上述状态量至少包括纵向速度和侧向速度;The second modeling module is used to establish a multi-degree-of-freedom vehicle dynamics model, and according to the above vehicle parameters, determine the state equation and observation equation of the unscented Kalman filter, and determine the input of the unscented Kalman filter Quantities, state quantities and observation quantities, the above state quantities at least include longitudinal velocity and lateral velocity;
车速估算器,其用于结合当前时刻的状态量,以及无迹卡尔曼滤波器的状态方程和观测方程,估算下一时刻的纵向速度和侧向速度。The vehicle speed estimator is used to estimate the longitudinal speed and lateral speed at the next moment by combining the state quantity at the current moment, and the state equation and observation equation of the unscented Kalman filter.
一些实施例中,还包括:In some embodiments, it also includes:
整车控制器,其用于输出各车轮的制动压力至上述第一建模模块;a vehicle controller, which is used for outputting the braking pressure of each wheel to the above-mentioned first modeling module;
上述高精度车辆模型根据上述各车轮的制动压力,对车辆进行实时模拟,得到上述整车参数;The above-mentioned high-precision vehicle model performs real-time simulation on the vehicle according to the braking pressure of the above-mentioned wheels, and obtains the above-mentioned parameters of the whole vehicle;
上述整车参数包括纵向加速度、侧向加速度、横摆角速度、四个车轮的轮速以及四个车轮处的路面附着系数。The above vehicle parameters include longitudinal acceleration, lateral acceleration, yaw rate, wheel speeds of the four wheels, and road adhesion coefficients at the four wheels.
本申请提供的技术方案带来的有益效果包括:The beneficial effects brought by the technical solution provided by this application include:
本申请的基于无迹卡尔曼滤波的车速估算方法及系统,通过高精度车辆模型对车辆进行实时模拟,以获取整车参数,然后通过多自由度车辆动力学模型,根据该整车参数,确定无迹卡尔曼滤波器的状态方程和观测方程,并确定无迹卡尔曼滤波器的输入量、状态量以及观测量,进而利用车速估算器,结合当前时刻的状态量,以及状态方程和观测方程,实现对下一时刻的纵向速度和侧向速度的估算,因此,通过车速估算器结合无迹卡尔曼滤波算法,可在车辆运行过程中准确地估算出车辆的实时纵向速度和侧向速度,以提高车辆动力学控制的精度。The vehicle speed estimation method and system based on the unscented Kalman filter of the present application performs real-time simulation of the vehicle through a high-precision vehicle model to obtain vehicle parameters, and then uses the multi-degree-of-freedom vehicle dynamics model to determine the vehicle parameters according to the vehicle parameters. The state equation and observation equation of the unscented Kalman filter, and determine the input quantity, state quantity and observation quantity of the unscented Kalman filter, and then use the vehicle speed estimator to combine the state quantity at the current moment, as well as the state equation and observation equation , to realize the estimation of the longitudinal speed and lateral speed at the next moment. Therefore, through the vehicle speed estimator combined with the unscented Kalman filter algorithm, the real-time longitudinal speed and lateral speed of the vehicle can be accurately estimated during the running process of the vehicle, To improve the precision of vehicle dynamics control.
附图说明Description of drawings
图1为本申请实施例提供的基于无迹卡尔曼滤波的车速估算方法的流程图;1 is a flowchart of a method for estimating vehicle speed based on unscented Kalman filtering provided by an embodiment of the present application;
图2为本申请实施例中的基于无迹卡尔曼滤波的车速估算的原理图;2 is a schematic diagram of vehicle speed estimation based on unscented Kalman filtering in an embodiment of the application;
图3为本申请实施例中的步骤S3的流程图;3 is a flowchart of step S3 in the embodiment of the application;
图4为本申请实施例的车速估算结果图;FIG. 4 is a diagram of a vehicle speed estimation result according to an embodiment of the application;
图5为本申请实施例的车速估算误差图。FIG. 5 is a diagram of a vehicle speed estimation error according to an embodiment of the present application.
具体实施方式Detailed ways
以下结合附图及实施例对本申请作进一步详细说明。The present application will be further described in detail below with reference to the accompanying drawings and embodiments.
参见图1所示,本申请实施例提供一种基于无迹卡尔曼滤波的车速估算方法,其包括步骤:Referring to FIG. 1 , an embodiment of the present application provides a vehicle speed estimation method based on unscented Kalman filtering, which includes the steps:
S1.建立高精度车辆模型,获取整车参数。其中,高精度车辆模型是基于仿真软件CarSim的高精度车辆模型,用于对真实车辆进行实时模拟。高精度车辆模型自由度高,仿真结果精确。S1. Establish a high-precision vehicle model and obtain vehicle parameters. Among them, the high-precision vehicle model is a high-precision vehicle model based on the simulation software CarSim, which is used for real-time simulation of real vehicles. The high-precision vehicle model has high degrees of freedom and accurate simulation results.
S2.建立多自由度车辆动力学模型,根据上述整车参数,确定无迹卡尔曼滤波器UKF(Unscented Kalman Filter)的状态方程和观测方程,并确定上述无迹卡尔曼滤波器的输入量、状态量以及观测量,上述状态量至少包括纵向速度和侧向速度。S2. Establish a multi-degree-of-freedom vehicle dynamics model, determine the state equation and observation equation of the unscented Kalman filter UKF (Unscented Kalman Filter) according to the above vehicle parameters, and determine the input of the above unscented Kalman filter, State quantity and observation quantity, the above state quantity includes at least longitudinal velocity and lateral velocity.
S3.利用车速估算器,结合当前时刻的状态量,以及上述状态方程和观测方程,估算下一时刻的纵向速度和侧向速度。S3. Using the vehicle speed estimator, combined with the state quantity at the current moment, and the above-mentioned state equation and observation equation, estimate the longitudinal speed and lateral speed at the next moment.
本申请的基于无迹卡尔曼滤波的车速估算方法及系统,通过高精度车辆模型对车辆进行实时模拟,以获取整车参数,然后通过多自由度车辆动力学模型,根据该整车参数,确定无迹卡尔曼滤波器的状态方程和观测方程,并确定无迹卡尔曼滤波器的输入量、状态量以及观测量,进而利用车速估算器,结合当前时刻的状态量,以及状态方程和观测方程,实现对下一时刻的纵向速度和侧向速度的估算,因此,通过车速估算器结合无迹卡尔曼滤波算法,可在车辆运行过程中准确地估算出车辆的实时纵向速度和侧向速度,以提高车辆动力学控制的精度。The vehicle speed estimation method and system based on the unscented Kalman filter of the present application performs real-time simulation of the vehicle through a high-precision vehicle model to obtain vehicle parameters, and then uses the multi-degree-of-freedom vehicle dynamics model to determine the vehicle parameters according to the vehicle parameters. The state equation and observation equation of the unscented Kalman filter, and determine the input quantity, state quantity and observation quantity of the unscented Kalman filter, and then use the vehicle speed estimator to combine the state quantity at the current moment, as well as the state equation and observation equation , to realize the estimation of the longitudinal speed and lateral speed at the next moment. Therefore, through the vehicle speed estimator combined with the unscented Kalman filter algorithm, the real-time longitudinal speed and lateral speed of the vehicle can be accurately estimated during the running process of the vehicle, To improve the precision of vehicle dynamics control.
本实施例中,多自由度车辆动力学模型是基于MATLAB/simulink的中等精度车辆模型,运行于车速估算器中,用于车速估算器对状态的一步预测。In this embodiment, the multi-degree-of-freedom vehicle dynamics model is a medium-precision vehicle model based on MATLAB/simulink, which runs in the vehicle speed estimator and is used for one-step prediction of the state by the vehicle speed estimator.
优选地,上述多自由度车辆动力学模型为与车速相关的七自由度动力学模型。其中,七自由度动力学模型主要考虑车身的纵向运动、横向运动、横摆运动以及四个车轮的旋转运动,忽略了车辆的俯仰运动、侧倾运动以及垂向运动。Preferably, the above-mentioned multi-degree-of-freedom vehicle dynamics model is a seven-degree-of-freedom dynamic model related to vehicle speed. Among them, the seven-degree-of-freedom dynamic model mainly considers the longitudinal motion, lateral motion, yaw motion of the body and the rotational motion of the four wheels, ignoring the pitch motion, roll motion and vertical motion of the vehicle.
进一步地,上述步骤S1中获取整车参数之前,还包括:Further, before acquiring the vehicle parameters in the above step S1, it also includes:
首先,整车控制器输出各车轮的制动压力至上述高精度车辆模型。First, the vehicle controller outputs the braking pressure of each wheel to the above-mentioned high-precision vehicle model.
然后,上述高精度车辆模型根据各车轮的制动压力,对车辆进行实时模拟,得到上述整车参数。Then, the above-mentioned high-precision vehicle model simulates the vehicle in real time according to the braking pressure of each wheel to obtain the above-mentioned parameters of the entire vehicle.
上述整车参数包括车辆行驶过程中的纵向加速度、侧向加速度、横摆角速度、四个车轮的轮速以及四个车轮处的路面附着系数。The above vehicle parameters include longitudinal acceleration, lateral acceleration, yaw angular velocity, wheel speeds of the four wheels, and road adhesion coefficients at the four wheels during the running of the vehicle.
本实施例中,上述步骤S1中的获取整车参数之后,还包括:In this embodiment, after obtaining the vehicle parameters in the above step S1, the method further includes:
上述高精度车辆模型输出四个车轮的轮速至上述整车控制器。The above-mentioned high-precision vehicle model outputs the wheel speeds of the four wheels to the above-mentioned vehicle controller.
进一步地,上述输入量包括四个车轮的轮速,上述状态量还包括纵向加速度、侧向加速度、横摆角速度、以及四个车轮处的路面附着系数,上述观测量包括纵向加速度、侧向加速度、以及横摆角速度。Further, the above-mentioned input quantities include the wheel speeds of the four wheels, the above-mentioned state quantities also include longitudinal acceleration, lateral acceleration, yaw rate, and the road adhesion coefficient at the four wheels, and the above-mentioned observations include longitudinal acceleration, lateral acceleration. , and the yaw rate.
参见图2所示,高精度车辆模型输出整车纵向加速度、侧向加速度、横摆角速度、四个车轮的轮速以及四个车轮处的路面附着系数作为观测值,输入到车速估算器中,以多自由度车辆动力学模型为基础,车速估算器估算出下一时刻的纵向速度和侧向速度后,输出给整车控制器,整车控制器输出各个车轮的制动压力给高精度车辆模型,以此形成一个闭环控制,完成车辆动力学控制。可选地,高精度车辆模型还输出方向盘转角δ到车速估算器中。本实施例中,方向盘转角δ为默认值。Referring to Figure 2, the high-precision vehicle model outputs the vehicle's longitudinal acceleration, lateral acceleration, yaw rate, the wheel speed of the four wheels, and the road adhesion coefficient at the four wheels as the observed values, which are input into the vehicle speed estimator, Based on the multi-degree-of-freedom vehicle dynamics model, the vehicle speed estimator estimates the longitudinal speed and lateral speed at the next moment, and outputs it to the vehicle controller. The vehicle controller outputs the braking pressure of each wheel to the high-precision vehicle. The model forms a closed-loop control to complete the vehicle dynamics control. Optionally, the high precision vehicle model also outputs the steering wheel angle δ into the vehicle speed estimator. In this embodiment, the steering wheel angle δ is a default value.
本实施例中,上述无迹卡尔曼滤波器的非线性状态方程和观测方程分别为:In this embodiment, the nonlinear state equation and observation equation of the above-mentioned unscented Kalman filter are respectively:
其中,xk+1为k+1时刻的状态向量,xk为k时刻的状态向量,zk为k时刻的观测向量,uk为k时刻的输入向量,wk为k时刻的过程噪声,vk为k时刻的观测噪声。where x k+1 is the state vector at
参见图3所示,上述步骤S3中,利用车速估算器,结合当前时刻的状态量,以及无迹卡尔曼滤波器的状态方程和观测方程,估算下一时刻的纵向速度和侧向速度,具体包括:Referring to Fig. 3, in the above step S3, the vehicle speed estimator is used, combined with the state quantity at the current moment, and the state equation and observation equation of the unscented Kalman filter, to estimate the longitudinal speed and lateral speed at the next moment, specifically include:
A1.初始化,获取初始状态估计值和初始误差协方差矩阵。A1. Initialize, obtain the initial state estimate and the initial error covariance matrix.
由于过程噪声来源于多自由度车辆动力学模型的不准确,观测噪声来源于观测的不准确,在卡尔曼滤波中假设过程噪声w和观测噪声v都是均值为0的高斯白噪声,二者的协方差阵分别为Q和R,即E[wwT]=Q,E[vvT]=R,E[wvT]=0。Since the process noise comes from the inaccuracy of the multi-degree-of-freedom vehicle dynamics model and the observation noise comes from the inaccuracy of the observation, it is assumed in the Kalman filter that the process noise w and the observation noise v are both Gaussian white noises with a mean value of 0. The covariance matrices of are Q and R respectively, that is, E[ww T ]=Q, E[vv T ]=R, and E[wv T ]=0.
A2.对当前时刻的状态量进行无迹变换,得到多个sigma点,并计算每个sigma点的权值。A2. Perform unscented transformation on the state quantity at the current moment to obtain multiple sigma points, and calculate the weight of each sigma point.
本实施例中,无迹卡尔曼滤波是基于:对非线性函数概率密度分布的近似比对非线性函数本身的近似更容易这一思想。利用无迹变换UT(Unscented Transformation)对概率密度的传递进行近似,需先选取(2n+1)个采样点,即Sigma点,其中Sigma点选取的要求是其均值和协方差与原系统状态分布的均值和协方差相等。然后将Sigma点带入状态方程中得到传播后的样本点,最后用传播后样本点的统计特性代替非线性系统传播后的统计特性。In this embodiment, the unscented Kalman filter is based on the idea that it is easier to approximate the probability density distribution of the nonlinear function than to approximate the nonlinear function itself. Using unscented transformation UT (Unscented Transformation) to approximate the transfer of probability density, it is necessary to select (2n+1) sampling points, namely Sigma points. The requirements for Sigma point selection are its mean and covariance and the state distribution of the original system. The mean and covariance are equal. Then the Sigma point is brought into the state equation to obtain the sample points after propagation, and finally the statistical properties of the sample points after propagation are used to replace the statistical properties of the nonlinear system after propagation.
首先,获取2n+1个Sigma点,如下所示:First, get 2n+1 Sigma points as follows:
其中,Pk-1|k-1为系统即状态方程表示的状态空间在k-1时刻的误差协方差,为k-1时刻的状态预测值,和分别为k-1时刻第i个和第i+n个Sigma点(对称),λ为缩放系数,且λ=α2(n+κ)-n,α,β,κ均根据状态空间的实际状态确定。上述选取方法保证了第1和n+1,2和n+2…n和2n个点都在第0个点(即均值点)的周围,从而满足样本点均值和协方差与原系统状态分布的均值和协方差相等的要求。Among them, P k-1|k-1 is the error covariance of the system, that is, the state space represented by the state equation at time k-1, is the state prediction value at time k-1, and are the i-th and i+n-th Sigma point (symmetric) at the time k-1, respectively, λ is the scaling factor, and λ=α 2 (n+κ)-n, α, β, κ are all based on the actual state space Status OK. The above selection method ensures that the 1st and n+1, 2 and n+2...n and 2n points are all around the 0th point (ie the mean point), so as to satisfy the mean and covariance of the sample points and the state distribution of the original system The mean and covariance are equal.
然后,计算(2n+1)个Sigma点的权值,如下所示:Then, calculate the weights of (2n+1) Sigma points as follows:
其中,为第0个Sigma点的均值权值,为第0个Sigma点的方差权值,Wi m为第i个Sigma点的均值权值,Wi c为第i个Sigma点的方差权值。in, is the mean weight of the 0th Sigma point, is the variance weight of the 0th Sigma point, W i m is the mean weight of the i th Sigma point, and W i c is the variance weight of the i th Sigma point.
A3.时间更新,根据上述状态方程和观测方程,计算先验状态估计值、先验误差协方差和先验观测估计值。A3. Time update, according to the above state equation and observation equation, calculate the prior state estimate, prior error covariance and prior observation estimate.
首先,对Sigma点进行预测计算,得到先验状态估计值并对Sigma点的先验状态估计值进行加权求和,得到先验状态估计值均值:First, perform the prediction calculation on the Sigma point to obtain the prior state estimate and estimate the prior state of the Sigma point Do a weighted summation to get the mean of the prior state estimates:
其中,为k-1时刻对状态量在k时刻的先验估计值均值。in, is the mean value of a priori estimates of the state quantity at time k at time k-1.
然后,根据先验状态估计值和先验状态估计值均值,计算先验误差协方差:Then, the prior error covariance is calculated from the prior state estimate and the mean prior state estimate:
其中,Pk|k-1为k-1时刻对状态量在k时刻的先验误差协方差。Among them, P k|k-1 is the prior error covariance of the state quantity at time k-1 at time k.
最后,计算先验观测估计值:Finally, compute the prior observation estimate:
其中,为k-1时刻对k时刻Sigma点的先验观测值,为k-1时刻对k时刻的先验观测值均值。in, is the prior observation of the Sigma point at time k at time k-1, is the mean of the prior observations at time k-1 to time k.
A4.根据上述先验状态估计值、先验误差协方差和先验观测估计值,更新下一步观测值和误差协方差。A4. Update the next observation value and the error covariance according to the above prior state estimate value, prior error covariance and prior observation estimate value.
首先,计算修正矩阵:First, calculate the correction matrix:
其中,为观测协方差,为预测观测互方差,Kk为卡尔曼增益。in, is the observation covariance, To predict the observed cross-variance, K k is the Kalman gain.
然后,更新观测值:Then, update the observations:
其中,为对状态量在k时刻的观测值,即后验估计值。in, is the observed value of the state quantity at time k, that is, the posterior estimate.
最后,更新误差协方差:Finally, update the error covariance:
其中,Pk|k为对状态量在k时刻的观测值的误差协方差,即后验误差协方差。Among them, P k|k is the error covariance of the observation value of the state quantity at time k, that is, the posterior error covariance.
此时,得到的对状态量在k时刻的观测值中包括估算得到的k时刻的纵向速度和侧向速度。当在k时刻估算k+1时刻的状态量时,令k=k+1,返回步骤A2,进行下一轮计算,即可估算得到k+1时刻的纵向速度和侧向速度,以此类推循环计算,即可得到每一时刻的纵向速度和侧向速度。At this time, the obtained observation value of the state quantity at time k includes the estimated longitudinal and lateral velocities at time k. When estimating the state quantity at time k+1 at time k, let k=k+1, return to step A2, and perform the next round of calculation, the longitudinal speed and lateral speed at time k+1 can be estimated, and so on By cyclic calculation, the longitudinal speed and lateral speed at each moment can be obtained.
状态量即状态向量x=[u v ax ay ωr μfl μfr μrl μrr]T,上述观测量即观测向量z=[ax ay ωr]T,上述输入量即输入向量u=[ωfl ωfr ωrl ωrr]T。The state quantity is the state vector x=[uva x a y ω r μ fl μ fr μ rl μ rr ] T , the above observation quantity is the observation vector z=[a x a y ω r ] T , and the above input quantity is the input vector u =[ω fl ω fr ω rl ω rr ] T .
其中,u为纵向速度,v为侧向速度,ax为纵向加速度,ay为侧向加速度,ωr为横摆角速度,ωfl、ωfr、ωrl、ωrr分别为左前轮轮速、右前轮轮速、左后轮轮速、右后轮轮速,μfl、μfr、μrl、μrr分别为左前轮路面附着系数、右前轮路面附着系数、左后轮路面附着系数、右后轮路面附着系数。where u is the longitudinal velocity, v is the lateral velocity, a x is the longitudinal acceleration, a y is the lateral acceleration, ω r is the yaw rate, ω fl , ω fr , ω rl , and ω rr are the left front wheel, respectively speed, right front wheel speed, left rear wheel speed, right rear wheel speed, μ fl , μ fr , μ rl , μ rr are the left front wheel road adhesion coefficient, right front wheel road adhesion coefficient, left rear wheel Road adhesion coefficient, right rear wheel road adhesion coefficient.
本实施例中,需作出一些合理的假设,第一假设加速度不会发生突变,第二假设路面附着系数不会发生突变,则上述状态方程进一步为:In this embodiment, some reasonable assumptions need to be made. The first assumption is that the acceleration will not change abruptly, and the second assumption that the road adhesion coefficient will not change abruptly. The above state equation is further:
其中,u(k)为k时刻的纵向速度,为k时刻的纵向速度的导数,v(k)为k时刻的侧向速度,为k时刻的侧向速度的导数,ax(k)为k时刻的纵向加速度,ay(k)为k时刻的侧向加速度,ωr(k)为k时刻的横摆角速度,为k时刻的横摆角速度的导数,μfl(k)为k时刻的左前轮路面附着系数,μfr(k)为k时刻的右前轮路面附着系数,μrl(k)为k时刻的左后轮路面附着系数,μrr(k)为k时刻的右后轮路面附着系数,Ts为k到k+1之间的时间步长。where u(k) is the longitudinal velocity at time k, is the derivative of the longitudinal velocity at time k, v(k) is the lateral velocity at time k, is the derivative of the lateral velocity at time k, a x (k) is the longitudinal acceleration at time k, a y (k) is the lateral acceleration at time k, ω r (k) is the yaw rate at time k, is the derivative of the yaw rate at time k, μ fl (k) is the road adhesion coefficient of the left front wheel at time k, μ fr (k) is the road adhesion coefficient of the right front wheel at time k, μ rl (k) is the time k The left rear wheel road adhesion coefficient of , μ rr (k) is the right rear wheel road adhesion coefficient at time k, and T s is the time step between k and k+1.
本实施例中,在MATLAB/simulink中搭建UKF车速估算器模型以及用于状态估算的多自由度车辆动力学模型,由于该多自由度车辆动力学模型仅用于验证估算算法而不涉及底层执行机构的控制,因此,可采用一个一阶惯性系统代替整个制动系统,在CarSim中设置高精度车辆模型的车辆模型参数,同时采用CarSim自带的ABS(Anti-lock BrakingSystem,防抱死制动系统)算法进行ABS控制,在路面设置窗口中选择中等附着系数的平直干路面,路面附着系数设置为0.5,制动控制设置为突加制动,即在0.25s时突然施加1.5Mpa的制动压力;制动初速度设置为70km/h。In this embodiment, the UKF vehicle speed estimator model and the multi-degree-of-freedom vehicle dynamics model for state estimation are built in MATLAB/simulink, because the multi-degree-of-freedom vehicle dynamics model is only used to verify the estimation algorithm and does not involve the underlying execution Therefore, a first-order inertial system can be used to replace the entire braking system, the vehicle model parameters of the high-precision vehicle model are set in CarSim, and the ABS (Anti-lock Braking System, Anti-lock Braking System, Anti-lock Braking System) that comes with CarSim is used at the same time. System) algorithm for ABS control, select a straight and dry road with a medium adhesion coefficient in the road setting window, set the road adhesion coefficient to 0.5, and set the brake control to sudden braking, that is, suddenly apply a brake of 1.5Mpa at 0.25s. Dynamic pressure; initial braking speed is set to 70km/h.
参见图4所示,以纵向车速为例进行验证,Carsim的高精度车辆模型输出车辆的实时车速,仿真过程中估算车速和实际车速基本重合。参见图5所示,从估算误差曲线中可以看出,减速过程中的估算误差最大值为1.2km/h(车速减到0后的误差不做考虑),说明本实施例的车速估算方法能较好的估算车辆实时车速,保证ABS控制过程的稳定性。Referring to Figure 4, taking the longitudinal vehicle speed as an example to verify, the high-precision vehicle model of Carsim outputs the real-time vehicle speed, and the estimated vehicle speed and the actual vehicle speed basically coincide during the simulation process. Referring to Fig. 5, it can be seen from the estimation error curve that the maximum estimation error during the deceleration process is 1.2km/h (the error after the vehicle speed is reduced to 0 is not considered), indicating that the vehicle speed estimation method of this embodiment can It can better estimate the real-time speed of the vehicle and ensure the stability of the ABS control process.
本申请实施例还提供一种基于无迹卡尔曼滤波的车速估算系统,其包括第一建模模块、第二建模模块和车速估算器。An embodiment of the present application further provides a vehicle speed estimation system based on unscented Kalman filtering, which includes a first modeling module, a second modeling module and a vehicle speed estimator.
第一建模模块用于建立高精度车辆模型,并通过上述高精度车辆模型获取整车参数。The first modeling module is used to establish a high-precision vehicle model, and obtain vehicle parameters through the above-mentioned high-precision vehicle model.
第二建模模块用于建立多自由度车辆动力学模型,第二建模模块还用于根据上述整车参数和多自由度车辆动力学模型,确定无迹卡尔曼滤波器的状态方程和观测方程,并确定上述无迹卡尔曼滤波器的输入量、状态量以及观测量,上述状态量至少包括纵向速度和侧向速度。The second modeling module is used to establish a multi-degree-of-freedom vehicle dynamics model, and the second modeling module is also used to determine the state equation and observation of the unscented Kalman filter according to the above vehicle parameters and the multi-degree-of-freedom vehicle dynamics model equation, and determine the input quantity, state quantity and observation quantity of the above-mentioned unscented Kalman filter, and the above-mentioned state quantity at least includes longitudinal velocity and lateral velocity.
车速估算器用于结合当前时刻的状态量,以及无迹卡尔曼滤波器的状态方程和观测方程,估算下一时刻的纵向速度和侧向速度。The vehicle speed estimator is used to estimate the longitudinal speed and lateral speed at the next moment by combining the state quantity at the current moment, and the state equation and observation equation of the unscented Kalman filter.
进一步地,上述车速估算系统还包括整车控制器。Further, the above-mentioned vehicle speed estimation system further includes a vehicle controller.
整车控制器用于输出各车轮的制动压力至上述第一建模模块。然后,高精度车辆模型根据上述各车轮的制动压力,可对车辆进行实时模拟,得到上述整车参数。The vehicle controller is used to output the braking pressure of each wheel to the above-mentioned first modeling module. Then, the high-precision vehicle model can simulate the vehicle in real time according to the braking pressures of the above-mentioned wheels, and obtain the above-mentioned parameters of the whole vehicle.
上述整车参数包括纵向加速度、侧向加速度、横摆角速度、四个车轮的轮速以及四个车轮处的路面附着系数。对应的,上述输入量包括四个车轮的轮速,上述状态量还包括纵向加速度、侧向加速度、横摆角速度、以及四个车轮处的路面附着系数,上述观测量包括纵向加速度、侧向加速度、以及横摆角速度。The above vehicle parameters include longitudinal acceleration, lateral acceleration, yaw rate, wheel speeds of the four wheels, and road adhesion coefficients at the four wheels. Correspondingly, the above-mentioned input quantities include the wheel speeds of the four wheels, the above-mentioned state quantities also include longitudinal acceleration, lateral acceleration, yaw angular velocity, and the road adhesion coefficient at the four wheels, and the above-mentioned observations include longitudinal acceleration, lateral acceleration. , and the yaw rate.
本实施例的车速估算系统,适用于上述各车速估算方法,在整个估算过程中只需存储前一时刻的估计值和当前时刻的观测值,即可循环计算,得到每一时刻的纵向速度和侧向速度,最大限度的降低对车载控制器的性能要求。The vehicle speed estimation system of this embodiment is applicable to the above-mentioned vehicle speed estimation methods. In the whole estimation process, only the estimated value at the previous moment and the observed value at the current moment can be stored, and then the calculation can be performed cyclically to obtain the longitudinal speed and Lateral speed, to minimize the performance requirements of the on-board controller.
本申请不局限于上述实施方式,对于本技术领域的普通技术人员来说,在不脱离本申请原理的前提下,还可以做出若干改进和润饰,这些改进和润饰也视为本申请的保护范围之内。The present application is not limited to the above-mentioned embodiments. For those skilled in the art, without departing from the principles of the present application, several improvements and modifications can be made, and these improvements and modifications are also regarded as the protection of the present application. within the range.
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