Parameter Identification Method for Driving Behavior Model Considering Longitudinal Car-Following Behavior

Abstract

The present invention relates to a method for identifying parameters of a driving behavior model considering longitudinal car-following behavior. The driving behavior model takes the relative distance and relative speed between the host vehicle and the leading vehicle as inputs, the driver's pedal operation behavior as an intermediate variable, and the pedal angle as an output, and considers the longitudinal manipulation effect of human drivers during the driving of semi-automatic / automatic vehicles. The longitudinal manipulation behavior is characterized by the brain decision-making behavior, the neuromuscular signal conduction process, and the foot-pedal coupling execution process. The identification method identifies the state parameters of the driving behavior model based on an identification model using the recursive least squares method. The present invention can accurately describe the behavioral characteristics of the driver in the longitudinal car-following state and efficiently solve the time-varying parameters in the model, so as to accurately obtain the dynamic characteristic changes of the driver during the vehicle operation process. It can be widely applied to the research and application of personalized assistance control systems considering the longitudinal behavior of drivers.

Description

Technical Field

[0001] The present invention relates to the technical field of assisted driving, and in particular to a method for identifying parameters of a driving behavior model considering longitudinal car-following behavior. Background Art

[0002] In traffic accidents, vehicle rear-end accidents gradually account for a large proportion due to reasons such as inaccurate grasping of the relative speed and relative distance between the own vehicle and the vehicle in front by the driver and fatigue. Although the current adaptive cruise technology has developed a very mature advanced driving assistance system, its price is relatively high, and the interaction between the system and the driver is insufficient. The system control output is directly triggered, hardly considering the behavior and personality of the driver, which often leads to discomfort and distrust between the driver and the automatic controller. Therefore, researchers consider the behavioral characteristics of the driver and characterize the driver's behavior through mathematical and physical methods.

[0003] During the process of driving a vehicle, the driver will adjust his posture and force according to the target task to achieve corresponding action behaviors to control the movement of the vehicle. For example, in the task of human-machine interaction when the driver operates the vehicle in a car-following condition, the driver adjusts the dynamic characteristics of the limbs according to the external and internal information obtained from his own senses, thereby adjusting the control of the accelerator and brake pedals to achieve a car-following movement that conforms to his own driving style.

[0004] Therefore, the applicant believes that if a driver longitudinal behavior model that comprehensively considers physiological and manipulation behavior characteristics can be established to accurately and quantitatively describe the dynamic characteristic changes of the driver during the process of operating the vehicle, it will be helpful to design and develop a new type of personalized longitudinal human-machine system that considers the characteristics and styles of the driver, and then apply it to the design and development of personalized auxiliary controllers. Summary of the Invention

[0005] Aiming at the deficiencies of the prior art, the present invention provides a method for identifying parameters of a driving behavior model considering longitudinal car-following behavior, aiming to accurately and quantitatively describe the dynamic characteristic changes of the driver during the process of operating the vehicle.

[0006] The technical solution adopted by the present invention is as follows:

[0007] A method for identifying parameters of a driving behavior model considering longitudinal car-following behavior includes:

[0008] Establish a driver longitudinal behavior model characterized by a fourth-order system, which takes the relative distance d rel between the own vehicle and the vehicle in front and the relative speed v relTaking the input information as , with the depression force F of the driver on the accelerator or brake pedal as the intermediate variable and the angle α of the accelerator or brake pedal as the output information, the fourth-order system integrates the driver's physiological behavior link and the foot-pedal coupling execution link. The driver's physiological behavior link integrates the pure delay link of the driver's eye recognition of the input information and the brain response, as well as the first-order inertia link of the brain decision-making through muscle nerve conduction and response. The foot-pedal coupling execution link is characterized by a spring-damper-mass rotary system. The frequency-domain expression of the fourth-order system is:

[0009]

[0010] where K p , K c are the characteristic parameters representing the pre-operation behaviors of the driver with respect to the relative speed v rel and the relative distance d rel respectively. τ d1 is the pure delay time of the pure delay link of the driver's eye recognition of the input information and the brain response, and τ d2 is the time constant of the first-order inertia link of the brain decision-making through muscle nerve conduction and response. The moment of inertia J i , the damping coefficient b i , and the spring stiffness K i are the characteristic parameters of the spring-damper-mass rotary system. Throttle and brake represent the accelerator and the brake respectively, and s represents the complex frequency domain. Among them, the driver's physiological behavior link is a double-input single-output system with the relative distance d rel and the relative speed v rel between the host vehicle and the leading vehicle as the inputs and the depression force F of the driver on the accelerator and brake pedals as the output. The foot-pedal coupling execution link is a single-input single-output system with the output depression force F of the driver's physiological behavior link as the input and the angles α of the accelerator and brake pedals as the output.

[0011] Perform the first step of identification on the driver's longitudinal behavior model: For the frequency-domain transfer function of the driver's physiological behavior link, use the least squares identification method to identify the characteristic parameters K p , K c , τ d1 , τ d2 to obtain the time-varying state parameter values.

[0012] Perform the second step of identification on the driver's longitudinal behavior model: For the frequency-domain transfer function of the foot-pedal coupling execution link, use the least squares identification method to identify the characteristic parameters J i , b i , K i to obtain the time-varying state parameter values.

[0013] The further technical solution is as follows:

[0014] Perform the first-step identification on the longitudinal driver behavior model, including:

[0015] Establish the discrete difference equation of the frequency-domain transfer function of the driver's physiological behavior link:

[0016]

[0017]

[0018]

[0019]

[0020] where k represents the current sampling moment, and T s is the sampling time;

[0021] For the discrete difference equation, construct the first identification model based on the recursive least squares method:

[0022] F(k) = Ψ T Θ

[0023] Ψ = [F(k - 1) F(k - 2) v rel (k) + 2v rel (k - 1) + v rel (k - 2) d rel (k) + 2d rel (k - 1) + d rel (k - 2)] T

[0024]

[0025] Set the auxiliary variables G and H, and establish the first recurrence relation of the recursive least squares identification algorithm with a forgetting factor r for the first identification model:

[0026]

[0027] Solve the parameter set at each sampling moment according to the first recurrence relation:

[0028]

[0029] According to the functional mapping relationship between each element in the parameter set Θ(k) and the characteristic parameters K p , K c , τ d1 , τ d2 , the characteristic parameters at each sampling moment can be obtained.

[0030] Conduct the second identification of the longitudinal driver behavior model, including:

[0031] Establish the discrete difference equation of the frequency-domain transfer function of the foot-pedal coupling execution link:

[0032] d i α i (k)+e i α i (k - 1)+f i α i (k - 2)=M i (k)+2M i (k - 1)+M i (k - 2)

[0033]

[0034]

[0035]

[0036] i = throttle, brake

[0037] where k represents the current discrete time, T s is the sampling time, M i =F i l, where l is the distance from the acting point of the downward force F to the rotation axis of the throttle or brake pedal;

[0038] Construct a second identification model based on the recursive least squares method for the discrete difference equation:

[0039] α i (k)=Φ i T Ω i

[0040] Φ i =[α i (k - 1) α i (k - 2) M i (k)+2M i (k - 1)+M i (k - 2)] T

[0041]

[0042] i = throttle, brake

[0043] Set auxiliary variables Q and R, and establish a second recurrence relation of the recursive least squares identification algorithm with forgetting factor r for the second identification model:

[0044]

[0045] Solve the parameter set at each sampling moment according to the second recurrence relation:

[0046]

[0047] According to each element in the parameter set Ω i (k) and the functional mapping relationship with the characteristic parameters J i , b i , K i , the characteristic parameters at each sampling moment can be obtained.

[0048] The beneficial effects of the present invention are as follows:

[0049] The longitudinal driver behavior model proposed by the present invention takes into account the longitudinal manipulation of the driver during the driving of semi-automatic / automatic vehicles - the physiological behavior link of the driver (a pure delay link that combines the input information recognized by the driver's eyes and the brain's reaction, as well as a first-order inertia link of the brain's decision-making through muscle nerve conduction and response), and the foot-pedal coupling execution link. Therefore, it synthesizes the physiological behavior characteristics and manipulation behavior characteristics of the driver, and can accurately characterize the time-varying behavior characteristics of the driver under the following condition.

[0050] The present invention uses a least squares two-step identification method with a forgetting factor for the longitudinal driver behavior model, which can identify the state parameters representing the driver's behavior online and obtain the time-varying range of the state parameters. Therefore, based on this time-varying range, a robust shared controller design considering the uncertainty of the driver behavior state parameters can be realized. It can be widely applied to the research and application of personalized auxiliary control systems considering the longitudinal behavior of the driver, and has strong practicability.

[0051] Other features and advantages of the present invention will be described in the following specification, and part of them will be obvious from the specification or understood by implementing the present invention. Brief Description of the Drawings

[0052] Figure 1 is a schematic structural diagram of the longitudinal driver behavior model of the present invention.

[0053] Figure 2 is a flowchart of the identification method of the longitudinal driver behavior model of the present invention.

[0054] Figure 3 is the leading vehicle speed spectrum obtained in the embodiment of the present invention.

[0055] Figure 4 is a graph of the relative distance between the host vehicle and the leading vehicle under the driver's control in the embodiment of the present invention.

[0056] Figure 5 This is the relative speed result graph of the host vehicle and the leading vehicle under the control of the driver in the embodiment of the present invention.

[0057] Figure 6 This is the downward force result graph under the control of the driver in the embodiment of the present invention.

[0058] Figure 7 This is the pedal rotation angle result graph under the control of the driver in the embodiment of the present invention.

[0059] Figure 8 This is the identification result graph of the driver's state parameter K p in the embodiment of the present invention.

[0060] Figure 9 This is the identification result graph of the driver's state parameter K c in the embodiment of the present invention.

[0061] Figure 10 This is the identification result graph of the driver's state parameter τ d1 in the embodiment of the present invention.

[0062] Figure 11 This is the identification result graph of the driver's state parameter τ d2 in the embodiment of the present invention.

[0063] Figure 12 This is the identification result graph of the driver's state parameter J throttle in the embodiment of the present invention.

[0064] Figure 13 This is the identification result graph of the driver's state parameter b throttle in the embodiment of the present invention.

[0065] Figure 14 This is the identification result graph of the driver's state parameter K throttle in the embodiment of the present invention.

[0066] Figure 15 This is the identification result graph of the driver's state parameter J brake in the embodiment of the present invention.

[0067] Figure 16 This is the identification result graph of the driver's state parameter b brake in the embodiment of the present invention.

[0068] Figure 17 This is the identification result graph of the driver's state parameter K brake in the embodiment of the present invention. Detailed implementation manners

[0069] The specific embodiments of the present invention will be described below in conjunction with the accompanying drawings.

[0070] A method for parameter identification of a driving behavior model considering longitudinal following behavior in this application includes:

[0071] Establish a driver longitudinal behavior model characterized by a fourth-order system, which takes the relative distance d rel between the host vehicle and the preceding vehicle and the relative speed v rel as input information, the downward force F on the accelerator or brake pedal by the driver as an intermediate variable, and the angle α of the accelerator or brake pedal as output information. The fourth-order system integrates the driver's physiological behavior link and the foot-pedal coupling execution link. The driver's physiological behavior link integrates the pure delay link of the driver's eye recognition of input information and brain response, and the first-order inertia link of the brain's decision-making through muscle nerve conduction and response. The foot-pedal coupling execution link is characterized by a spring-damper-mass rotary system. The frequency-domain expression of the fourth-order system is:

[0072]

[0073] Among them, K p , K c are respectively the characteristic parameters representing the pre-operation behaviors of the driver with respect to the relative speed v rel and the relative distance d rel . τ d1 is the pure delay time of the pure delay link of the driver's eye recognition of input information and brain response, τ d2 is the time constant of the first-order inertia link of the brain's decision-making through muscle nerve conduction and response. The moment of inertia J i , the damping coefficient b i , and the spring stiffness K i are the characteristic parameters of the spring-damper-mass rotary system. Throttle and brake respectively represent the accelerator and the brake, and s represents the complex frequency domain. Among them, the driver's physiological behavior link is a double-input single-output system with the relative distance d rel between the host vehicle and the preceding vehicle and the relative speed v rel as inputs and the downward force F on the accelerator and brake pedals by the driver as output. The foot-pedal coupling execution link is a single-input single-output system with the output downward force F of the driver's physiological behavior link as input and the angle α of the accelerator and brake pedals as output;

[0074] Perform the first step of identification on the driver longitudinal behavior model: For the frequency-domain transfer function of the driver's physiological behavior link, use the least squares identification method for the characteristic parameters K p , K c , τ d1 , τ d2Identify to obtain time-varying state parameter values;

[0075] Perform the second identification on the driver longitudinal behavior model: For the frequency-domain transfer function of the foot-pedal coupling execution link, use the least squares identification method to identify the characteristic parameters J i , b i , K i and obtain time-varying state parameter values.

[0076] The present application innovatively proposes a driver longitudinal behavior model to describe the driving characteristics of a driver under longitudinal car-following conditions, comprehensively considering the physiological behavior characteristics of the driver's brain, muscles, and nerves and the driving behavior characteristics of the foot pedal, and accurately identifying the state parameters of the driver longitudinal behavior model based on the recursive least squares method to obtain time-varying state parameter values.

[0077] According to the range of state parameters obtained in the present application, a robust shared controller considering driver parameter uncertainty can be designed to realize the development and application of a high-precision personalized assistance control system.

[0078] The following further illustrates the technical solution of the present application with specific embodiments.

[0079] 1. Establish a driver longitudinal behavior model as shown in Figure 1 and include:

[0080] Consider the driver physiological behavior link: including considering the driver's brain decision-making behavior, using gains K p , K c to represent the pre-operation behavior of the driver with respect to relative speed and relative distance; consider the pure delay link of the driver's eye recognition input information and brain response whose pure delay time is represented by τ d1 ; consider the process of the driver's neuromuscular signal transmission, and use a first-order inertia link with a time constant of τ d2 to represent the conduction and response process of the brain decision-making information through the neuromuscular system, and establish the frequency-domain transfer function of the driver physiological behavior link:

[0081]

[0082] In the formula, s represents the complex frequency domain;

[0083] Through the first-order Taylor formula, approximate the pure delay link of the driver's brain according to the following formula:

[0084]

[0085] Considering the consistent rotational motion of the driver's foot and the pedal after the foot loads the pedal, the driver's foot and the accelerator and brake pedals are coupled into a spring-damper-mass rotational system with the center of rotation of the pedal as the fulcrum to describe the dynamic characteristics of the driver's manipulation behavior. The system characteristics of the spring-damper-mass rotational system are characterized by the moment of inertia J, the damping coefficient b, and the spring stiffness K, thereby establishing the frequency-domain transfer function of the foot-pedal coupling execution link as follows:

[0086]

[0087] M i =F i l, where l is the distance from the point of application of the downward force to the rotation axis of the brake / accelerator pedal. In this embodiment, the distance from the center point of the brake / accelerator pedal to the rotation axis is taken;

[0088] Among them, the acquisition of the input information, output information, and intermediate variables of the driver's longitudinal behavior model includes: installing a lidar on the front of the host vehicle to collect the relative speed v rel and the relative distance d rel ; installing inertial sensors on the back of the accelerator pedal and the brake pedal to collect the angle α throttle , α brake ; installing force sensors on the front of the accelerator pedal and the brake pedal to collect the downward force F exerted by the driver on the accelerator / brake pedal.

[0089] So far, a driver's longitudinal behavior model that combines the driver's physiological behavior link (a pure delay link that combines the driver's eye recognition input information and the brain's reaction, and a first-order inertial link that passes through muscle nerve conduction and response in the brain's decision-making) and the foot-pedal coupling execution link, which is expressed as a fourth-order system with two inputs and one output, is obtained. The frequency-domain expression is shown in Equation (1);

[0090] II. Refer to Figure 2 , and perform parameter identification on the constructed driver's longitudinal behavior model. Taking the downward force F as the intermediate variable, in the first step, identify the characteristic parameters in the driver's physiological behavior link, and in the second step, identify the characteristic parameters in the foot-pedal coupling execution link. And the driver's physiological behavior link is a two-input and one-output system with the relative distance d rel and the relative speed v rel as the inputs and the downward force F exerted by the driver on the accelerator and brake pedals as the output. The foot-pedal coupling execution link is a single-input and one-output system with the output downward force F of the driver's physiological behavior link as the input and the angles α of the accelerator and brake pedals as the output. Specifically, it includes:

[0091] The frequency-domain transfer function of the driver's physiological behavior link shown in Equation (2) is mapped to the z-plane through the bilinear transformation rule, that is, a variable substitution for the s complex frequency domain to the polar coordinate domain z-domain transformation:

[0092]

[0093] In Equation (5), T s is the sampling time, and the expression in the z-plane is:

[0094]

[0095] Arrange Equation (6) to transform the expression in the z-plane into the discrete time domain, and the discrete difference equation obtained is:

[0096]

[0097] In Equation (7), k represents the current sampling moment, and T s is the sampling time;

[0098] For the discrete difference equation of Equation (7), construct a first identification model based on the recursive least squares method:

[0099]

[0100] Set auxiliary variables G and H, and establish a first recurrence relationship of the recursive least squares identification algorithm with a forgetting factor r for the first identification model of Equation (8):

[0101]

[0102] According to the first recurrence relationship of Equation (9), solve the parameter set at each sampling moment:

[0103]

[0104] According to the functional mapping relationship between each element in the parameter set Θ(k) and the characteristic parameters K p , K c , τ d1 , τ d2 the characteristic parameters at each sampling moment can be obtained.

[0105] The frequency-domain transfer function of the foot-pedal coupling execution link shown in Equation (4) is mapped to the z-plane through the bilinear transformation rule, that is, a variable substitution for the s complex frequency domain to the polar coordinate domain z-domain transformation. Substitute Equation (5) into Equation (4), and the expression in the z-plane is:

[0106]

[0107] Arrange Equation (11), transform it into the discrete time domain, and obtain the discrete difference equation of the frequency domain transfer function of the foot and pedal coupling execution link:

[0108]

[0109] where k represents the current discrete time, and T s is the sampling time, M i = F i l, where l is the distance from the acting point of the depressing force F to the rotation axis of the accelerator or brake pedal;

[0110] For the discrete difference equation shown in Equation (12), construct a second identification model based on the recursive least squares method:

[0111]

[0112] Set auxiliary variables Q and R, and establish a second recurrence relationship of the recursive least squares identification algorithm with a forgetting factor r for the second identification model shown in Equation (13):

[0113]

[0114] According to the second recurrence relationship shown in Equation (14), solve the parameter set at each sampling time:

[0115]

[0116] According to the functional mapping relationship between each element in the parameter set Ω i (k) and the characteristic parameters J i , b i , K i , the characteristic parameters at each sampling time can be obtained.

[0117] In this way, all the parameters of the fourth-order system of the driver's longitudinal behavior model considering longitudinal car-following behavior can be obtained by the two-step identification method.

[0118] To verify the effectiveness of the method in this embodiment, the following is an experiment where the driver conducts tests on the semi-physical simulation experimental platform of the driving simulator and conducts online identification of the driver's longitudinal behavior characteristic parameters in the Matlab / Simulink-Prescan co-simulation experimental software environment.

[0119] Set the speed of the leading vehicle according to the speed spectrum of the NEDC driving cycle, and set the speed of the leading vehicle according to the suburban driving cycle in the NEDC driving cycle. The set speed of the leading vehicle is as Figure 3 shown. The collected system input information, intermediate variables, and output information are respectively as Figures 4 to 7 shown.

[0120] The speed of the host vehicle is controlled by the driver operating the accelerator and brake pedals of the driving simulator. The steering controls of both the host vehicle and the leading vehicle are cut off, and lateral movement is not considered.

[0121] Select a driver to conduct the experiment under the set experimental scenario. During the experiment, the driver operates the accelerator or brake pedal with the right foot, and the driver is not allowed to step on the accelerator and brake pedals simultaneously.

[0122] The experiment records the angles, depression forces of the driver's operation of the accelerator and brake pedals, the relative speed and relative distance from the leading vehicle, and the driver characteristic parameters solved by the identification algorithm. All experimental results are shown in Figures 8 to 17 .

[0123] The method of this embodiment can accurately describe the behavioral characteristics of the driver in the longitudinal car-following state, efficiently solve the time-varying ranges of the seven characteristic parameters as shown in Figure 2 , so as to accurately obtain the dynamic characteristic changes of the driver during the vehicle operation process. Based on the obtained time-varying range values of the characteristic parameters, a robust shared controller considering the uncertainty of driver parameters can be designed in the subsequent development process to achieve the development and application of a high-precision personalized auxiliary control system.

[0124] The above is only an example for the conception of the present invention. The present invention can also fine-tune and improve the driver longitudinal model and identification algorithm according to the specific traffic environment scenario and specific driver characteristics. Any non-substantive changes made to the present invention shall fall within the scope of infringement of the protection of the present invention.

Claims

1. A parameter identification method for a driving behavior model considering longitudinal car-following behavior, characterized in that, Including: Establish a driver longitudinal behavior model characterized by a fourth-order system, which takes the relative distance d between the host vehicle and the vehicle ahead rel and the relative speed v rel as input information, takes the depression force F of the driver on the accelerator or brake pedal as an intermediate variable, and takes the angle α of the accelerator or brake pedal as output information. The fourth-order system integrates the driver's physiological behavior link and the coupling execution link between the foot and the pedal. The driver's physiological behavior link integrates the pure delay link of the driver's eye recognition of the input information and the brain response, and the first-order inertia link of the brain decision-making through muscle nerve conduction and response. The coupling execution link between the foot and the pedal is characterized by a spring-damper-mass rotational system. The frequency-domain expression of the fourth-order system is as follows: i = throttle, brake Among them, K p , K c are respectively characteristic parameters representing the pre-operation behaviors of the driver with respect to the relative speed v rel and the relative distance d rel . τ d1 is the pure delay time of the pure delay link of the driver's eye recognition input information and brain response. τ d2 is the time constant of the first-order inertia link of the brain's decision-making through muscle nerve conduction and response. The moment of inertia J i , damping coefficient b i , and spring stiffness K i are characteristic parameters of the spring-damper-mass rotational system. Throttle and brake respectively represent the throttle and the brake, and s represents the complex frequency domain. Among them, the driver's physiological behavior link is a double-input single-output system with the relative distance d rel between the host vehicle and the leading vehicle and the relative speed v rel as inputs and the depression force F of the driver on the throttle and brake pedals as the output. The foot-pedal coupling execution link is a single-input single-output system with the output depression force F of the driver's physiological behavior link as the input and the angles α of the throttle and brake pedals as the output; Perform the first step of identification on the longitudinal driver behavior model: For the frequency-domain transfer function of the driver's physiological behavior link, use the least squares identification method to identify the characteristic parameters K p , K c , τ d1 , τ d2 to obtain the time-varying state parameter values; Perform the second identification on the longitudinal driver behavior model: For the frequency domain transfer function of the foot-pedal coupling execution link, use the least squares identification method to identify the characteristic parameters J i , b i , K i to obtain time-varying state parameter values.

2. The parameter identification method of the driving behavior model considering longitudinal car-following behavior according to claim 1, characterized in that Performing the first-step identification on the longitudinal driver behavior model, including: Establishing a discrete difference equation of the frequency-domain transfer function of the physiological behavior link of the driver: aF(k)+bF(k - 1)+cF(k - 2)=K p [v rel (k)+2v rel (k - 1)+v rel (k - 2)]+K c [d rel (k)+2d rel (k - 1)+d rel (k - 2)] where k represents the current sampling instant, and T s is the sampling time; Constructing a first identification model based on the recursive least squares method for the discrete difference equation: F(k) = Ψ T Θ Ψ = [F(k - 1) F(k - 2) v rel (k) + 2v rel (k - 1) + v rel (k - 2) d rel (k) + 2d rel (k - 1) + d rel (k - 2)] T Setting auxiliary variables G and H, and establishing a first recurrence relation of the recursive least squares identification algorithm with a forgetting factor r for the first identification model: Solving the parameter set at each sampling moment according to the first recurrence relation: According to the functional mapping relationship between each element in the parameter set Θ(k) and the characteristic parameter K p , K c , τ d1 , τ d2 , the characteristic parameter at each sampling moment can be obtained.

3. The parameter identification method of the driving behavior model considering longitudinal car-following behavior according to claim 1, characterized in that, Performing the second-step identification on the longitudinal driver behavior model, including: Establishing a discrete difference equation of the frequency-domain transfer function of the coupling execution link between the foot and the pedal: d i α i (k)+e i α i (k - 1)+f i α i (k - 2)=M i (k)+2M i (k - 1)+M i (k - 2) i = throttle,brake where k represents the current discrete time, T s is the sampling time, M i = F i l, where l is the distance from the acting point of the downward force F to the rotation axis of the accelerator or brake pedal; Constructing a second identification model based on the recursive least squares method for the discrete difference equation: α i (k) = Φ i T Ω i Φ i = [α i (k - 1)α i (k - 2)M i (k) + 2M i (k - 1) + M i (k - 2)] T i = throttle,brake Setting auxiliary variables Q and R, and establishing a second recurrence relation of the recursive least squares identification algorithm with a forgetting factor r for the second identification model: i = throttle, brake Solving the parameter set at each sampling moment according to the second recurrence relation: i = throttle, brake According to the parameter set Ω i Each element in (k) and the characteristic parameter J i , b i , K i Through the functional mapping relationship, the characteristic parameter at each sampling moment can be obtained.

Images