CN102009653A - Wheel barycenter distortion angle observation method integrated with Kalman filtering and acceleration integral - Google Patents

Abstract

The invention relates to a wheel barycenter distortion angle observation method integrated with Kalman filtering and acceleration integral, comprising the following steps: 1) setting a barycenter distortion angle observation system comprising a vehicle speed sensor, a longitudinal acceleration sensor, a transverse acceleration sensor, a yaw velocity sensor and a controller, and respectively obtaining the primary signals of longitudinal acceleration, transverse acceleration and yaw velocity; 2) carrying out Kalman filtering processing on the longitudinal acceleration, transverse acceleration and yaw velocity respectively, so as to obtain the processed estimated values of the longitudinal acceleration, the transverse acceleration and the yaw velocity; 3) carrying out barycenter distortion angle observation respectively by adopting the mode based on Kalman filtering and signal integral; and4) carrying out weighted process on the results of the two methods in the step 3), thus obtaining the barycenter distortion angle observation value. The weighted process is carried out based on the Kalman filtering and acceleration integral. Not only has the method wide application range, but also accurate barycenter distortion angle observation result can be obtained under the condition of low cost.

Description

The wheel side slip angle observation procedure of fusion card Kalman Filtering and integrated acceleration

Technical field

The present invention relates to a kind of vehicle-state In-Situ Observation Technique, particularly about a kind of in kinetic control system the wheel side slip angle observation procedure as the fusion card Kalman Filtering and the integrated acceleration technology of control variable.

Background technology

When automobile kinetic control system is in limiting condition at vehicle, vehicle-state (as side slip angle, yaw velocity, wheel slip etc.) by reality compares with the inner expectation value of formulating of controller, regulate the driving power of each wheel of vehicle, thereby improve the stability of vehicle under limiting condition.Wherein, control has great influence to the observation technology of vehicle-state for automobile dynamic quality.And side slip angle is extremely important and relatively be difficult to observe in the vehicle-state observation.Existing side slip angle observation procedure mainly contains three kinds: 1, according to preset parameter such as car gage, wheelbase, radius of wheel and respectively take turns wheel speed signal, utilization vehicle kinematical equation carries out side slip angle observation; 2, according to lateral acceleration sensor and yaw-rate sensor signal, utilization vehicle kinematical equation, integration obtains the horizontal speed of a motor vehicle, and then obtains side slip angle; 3, utilize GPS (global positioning system) sensor signal to carry out the observation of side slip angle.

But, there is following shortcoming in above-mentioned three kinds of barycenter sideslip angle observation procedures: 1, according to the preset parameters such as car gage, wheelbase, radius of wheel and the method for respectively taking turns wheel speed signal, will be no longer suitable when wheel big slippage takes place or trackslips, and a lot of limiting conditions often are accompanied by the slippage of wheel and trackslip, and this method field of application is narrow; 2, according to the method for lateral acceleration sensor and yaw-rate sensor,, bigger through cumulative errors behind the integration of long period because all there are noise in lateral acceleration sensor and yaw-rate sensor signal; 3, utilize the method for GPS (global positioning system) sensor signal, sensor device expense costliness is considered to be not suitable for applying on a large scale from the cost angle.

Summary of the invention

At the problems referred to above, the purpose of this invention is to provide the wheel side slip angle observation procedure of a kind of fusion card Kalman Filtering and integrated acceleration, can under lower cost, obtain side slip angle observed result more accurately.

For achieving the above object, the present invention takes following technical scheme: side slip angle observation system of the present invention comprises car speed sensor, longitudinal acceleration sensor, lateral acceleration sensor, yaw-rate sensor and controller.Controller is accepted the signal of car speed sensor, longitudinal acceleration sensor, lateral acceleration sensor and yaw-rate sensor, carries out signal conditioning, and side slip angle is observed.

Side slip angle observation procedure of the present invention may further comprise the steps:

1, by longitudinal acceleration sensor, lateral acceleration sensor, yaw-rate sensor, obtains original signal respectively: longitudinal acceleration

Transverse acceleration

Yaw velocity

2, to longitudinal acceleration

Transverse acceleration

Yaw velocity

Signal carries out Kalman filtering respectively, and signal is carried out preliminary signal conditioning, the estimated valve after obtaining handling: longitudinal acceleration

Transverse acceleration

Yaw velocity

Concrete operation method is as follows:

Suppose that the original signal that need do Filtering Processing is Actual signal is x (disturbing or error because have, so the value that sensor records not is its actual value), and the estimated valve after the processing is

X (k) expression k is the instantaneous value of x constantly, and Δ T is sampling time (time gap of adjacent moment), this signal k on time domain is carried out Taylor expansion constantly obtain:

$x(k+1)=x\left(k\right)+x^{\′}\left(k\right)\mathrm{\ΔT}+\frac{x^{\′\′}\left(k\right)}{2}{\mathrm{\ΔT}}^2+o\left({\mathrm{\ΔT}}^2\right)---\left(1\right)$

Ignore the above higher order term of second order, choosing x (k) and first derivative x ' thereof is state variable [x (k) x ' (k)] (k) ^T, then formula (1) can be write as equation of state as follows:

$\left[\begin{array}{c}x\left(k\right)\\ x^{\′}\left(k\right)\end{array}\right]=\left[\begin{array}{cc}1& \mathrm{\ΔT}\\ 0& 1\end{array}\right]\left[\begin{array}{c}x(k-1)\\ x^{\′}(k-1)\end{array}\right]+\left[\begin{array}{c}\frac{\mathrm{\Δ}{T}^2}{2}w\\ \mathrm{\ΔT}\·w\end{array}\right]---\left(2\right)$

Wherein, w=x " (k), can be considered as the random white noise error.

Suppose that sensor measurement signal is N wherein _SmBe actual signal institute noise superimposed, can be considered as the random white noise error, then have:

$\tilde{x}\left(k\right)=\left[\begin{array}{cc}1& 0\end{array}\right]\left[\begin{array}{c}x\left(k\right)\\ x^{\′}\left(k\right)\end{array}\right]+n_{\mathrm{sm}}---\left(3\right)$

Formula (2), (3) have constituted the space equation structure of complete Kalman filter:

X(k)＝A·X(k-1)+W(k) (4)

$\tilde{X}\left(k\right)=H\·X\left(k\right)+N\left(k\right)$

Wherein

H=[1 0], N (k)=n _Sm

If hypothesis Q, R are respectively the covariance matrix of W (k), N (k), next the Kalman filter of Gou Jianing is:

$\hat{X}\left(k\right)=A\·\hat{X}(k-1)+\mathrm{Kg}\left(k\right)\·(\tilde{X}\left(k\right)-H\·A\·\hat{X}(k-1))$

$\mathrm{Kg}\left(k\right)=\frac{(A\·P(k-1)\·A^T+Q)\·H^T}{H\·(A\·P(k-1)\·A^T+Q)\·H^T+R}---\left(5\right)$

P(k)＝(1-Kg(k)·H)·(A·P(k-1)·A ^T+Q)

Through type (5), the estimated valve after can obtaining handling: longitudinal acceleration

Transverse acceleration

Yaw velocity

3, adopt respectively based on Kalman filtering with based on the mode of signal integration and carry out side slip angle observation.

1) observes based on the side slip angle of Kalman filtering

The definition of side slip angle β is as the formula (6):

$\mathrm{\β}=\frac{v_y}{v_x}---\left(6\right)$

Wherein, v _x, v _yBe respectively the vertical speed of a motor vehicle and the horizontal speed of a motor vehicle.Formula (6) differential is obtained:

${\mathrm{\β}}^{\′}=-\frac{a_x}{v_x}\mathrm{\β}-\mathrm{\γ}{\mathrm{\β}}^2+(\frac{a_y}{v_x}-\mathrm{\γ})---\left(7\right)$

Simultaneously, learn, have following relation between side slip angle and the yaw velocity according to vehicle movement:

$\frac{{v^{\′}}_x-a_x}{v_x\mathrm{\γ}}=\mathrm{\β}---\left(8\right)$

As follows to obtaining side slip angle extended Kalman filter space equation structure after formula (7), (8) discretization:

$\mathrm{\β}\left(k\right)=(1-\frac{{\hat{a}}_x(k-1)\·\mathrm{\ΔT}}{{\hat{v}}_x(k-1)})\·\mathrm{\β}(k-1)-\widehat{\mathrm{\γ}}(k-1)\·\mathrm{\ΔT}\·{\mathrm{\β}}^2(k-1)+(\frac{{\hat{a}}_y(k-1)}{{\hat{v}}_x(k-1)}-\widehat{\mathrm{\γ}}(k-1))\·\mathrm{\ΔT}---\left(9\right)$

$\frac{{{\hat{v}}^{\′}}_x\left(k\right)-{\hat{a}}_x\left(k\right)}{{\hat{v}}_x\left(k\right)\·\widehat{\mathrm{\γ}}\left(k\right)}=\mathrm{\β}\left(k\right)+N_{\mathrm{\β}}\left(k\right)$

Wherein, vertical speed of a motor vehicle

Obtain by car speed sensor;

Be respectively processing obtains in the step 2 longitudinal acceleration, transverse acceleration, yaw velocity estimated valve; N _β(k) be actual signal β (k) institute noise superimposed, can be considered as the random white noise error.The standard form that (9) formula is changed into extended Kalman filter space equation structure is as follows:

X _β(k)＝A _β·X _β(k-1)+W _β(k) (10)

${\tilde{X}}_{\mathrm{\β}}\left(k\right)=H_{\mathrm{\β}}\·X_{\mathrm{\β}}\left(k\right)+N_{\mathrm{\β}}\left(k\right)$

Wherein, X _β(k)=β (k),

H _β=1, $W_{\mathrm{\β}}\left(k\right)=-\widehat{\mathrm{\γ}}(k-1)\·\mathrm{\ΔT}\·{\mathrm{\β}}^2(k-1)+(\frac{{\hat{a}}_y(k-1)}{{\hat{v}}_x(k-1)}-\widehat{\mathrm{\γ}}(k-1))\·\mathrm{\ΔT}.$

Herein, W _β(k) be treated to the random white noise error.If hypothesis Q _β, R _βBe respectively W _β(k), N _β(k) covariance matrix, next the Kalman filter of Gou Jianing is:

$\widehat{\mathrm{\β}}\left(k\right)=A_{\mathrm{\β}}\·\widehat{\mathrm{\β}}(k-1)+\mathrm{Kg}\left(k\right)\·({\tilde{X}}_{\mathrm{\β}}\left(k\right)-H_{\mathrm{\β}}\·A\·\widehat{\mathrm{\β}}(k-1))$

${\mathrm{Kg}}_{\mathrm{\β}}\left(k\right)=\frac{(A_{\mathrm{\β}}\·P_{\mathrm{\β}}(k-1)\·{A_{\mathrm{\β}}}^T+Q_{\mathrm{\β}})\·{H_{\mathrm{\β}}}^T}{H_{\mathrm{\β}}\·(A_{\mathrm{\β}}\·P_{\mathrm{\β}}(k-1)\·{A_{\mathrm{\β}}}^T+Q_{\mathrm{\β}})\·{H_{\mathrm{\β}}}^T+R_{\mathrm{\β}}}---\left(11\right)$

P _β(k)＝(1-Kg _β(k)·H _β)·(A _β·P _β(k-1)·A _β ^T+Q _β)

In the ordinary course of things, can make observation preferably to side slip angle according to the designed extended Kalman filter of formula (11).

2) observe based on the side slip angle of signal integration

V appears in the observational equation of formula (9) _x(k) during the situation of γ (k)=0, Kalman filter will be no longer suitable.General, do not consider v _xThe situation of=0 (being that vertical speed of a motor vehicle is 0), satisfy γ=0 this moment, and cooresponding operating mode is that pure lateral deviation appears in vehicle, as when being subjected to the influencing of side direction wind.At this moment, formula (7) is changed to following form:

$\stackrel{\·}{\mathrm{\β}}=-\frac{a_x}{v_x}\mathrm{\β}+\frac{a_y}{v_x}---\left(12\right)$

What formula (10) provided is the expression formula of side slip angle derivative, and this moment, employing obtained side slip angle to the mode that the side slip angle derivative carries out integration, and formula (10) is carried out discretization, obtained based on the observed result of signal integration as follows:

$\widehat{\mathrm{\β}}\left(k\right)=(1-\frac{{\hat{a}}_x(k-1)\·\mathrm{\ΔT}}{{\hat{v}}_x(k-1)})\·\widehat{\mathrm{\β}}(k-1)+\frac{{\hat{a}}_y(k-1)}{{\hat{v}}_x(k-1)}\·\mathrm{\ΔT}---\left(13\right)$

The physical meaning of formula (13) promptly is that transverse acceleration signal is carried out integration, and rejects therefrom that influence that longitudinal acceleration produces obtains.

4, set up algorithm and switch method of discrimination, the result who adopts above-mentioned two kinds of barycenter sideslip angles observation is weighted.Yaw velocity and weight coefficient K relation curve are seen Fig. 2.

If the observed result that utilizes the Kalman filtering mode of expansion to obtain is

The observed result that utilizes the signal integration mode to obtain is

The final observed result of side slip angle observer is

Following relational expression is then arranged:

$\widehat{\mathrm{\β}}=(1-k){\widehat{\mathrm{\β}}}_{\mathrm{kal}}+k{\widehat{\mathrm{\β}}}_{\mathrm{int}}---\left(14\right)$

When

The time, think tangible yaw not occur that this moment, k=1 taked the observed pattern of signal integration, promptly fully

When

The time, think tangible yaw to occur this moment, this moment k=0, will be by the Kalman filtering observed pattern of expansion, promptly

When

The time, two kinds of barycenter sideslip angle observed results are weighted fusion, obtain the final observed result of side slip angle observer

The two kinds of methods of Kalman filtering and integrated acceleration that the present invention is based on are calculated, and the result of two kinds of methods is weighted processing, thereby side slip angle is observed.The inventive method not only has wider Applicable scope, and can obtain side slip angle observed result more accurately under lower cost.

Description of drawings

Fig. 1 is side slip angle observation algorithm structure figure of the present invention;

Fig. 2 is that algorithm of the present invention switches the weight coefficient curve.

The specific embodiment

Below in conjunction with drawings and Examples the present invention is described in detail.

Side slip angle observation system of the present invention is based on conventional car speed sensor, longitudinal acceleration sensor, lateral acceleration sensor, yaw-rate sensor and controller and sets up.Controller is accepted the signal of car speed sensor, longitudinal acceleration sensor, lateral acceleration sensor and yaw-rate sensor, carries out signal conditioning, and side slip angle is observed.，

Side slip angle observation procedure of the present invention is introduced as shown in Figure 1 below step by step:

1, by longitudinal acceleration sensor, lateral acceleration sensor, yaw-rate sensor, obtains original signal respectively: longitudinal acceleration

Transverse acceleration

Yaw velocity

2, to longitudinal acceleration Transverse acceleration

Yaw velocity

Signal carries out Kalman filtering respectively, and signal is carried out preliminary signal conditioning, the estimated valve after obtaining handling: longitudinal acceleration Transverse acceleration Yaw velocity

Concrete operation method is as follows:

Suppose that the original signal that need do Filtering Processing is

Actual signal is x (disturbing or error because have, so the value that sensor records not is its actual value), and the estimated valve after the processing is

X (k) expression k is the instantaneous value of x constantly, and Δ T is sampling time (time gap of adjacent moment), this signal k on time domain is carried out Taylor expansion constantly obtain:

$x(k+1)=x\left(k\right)+x^{\′}\left(k\right)\mathrm{\ΔT}+\frac{x^{\′\′}\left(k\right)}{2}{\mathrm{\ΔT}}^2+o\left({\mathrm{\ΔT}}^2\right)---\left(1\right)$

Ignore the above higher order term of second order, choosing x (k) and first derivative x ' thereof is state variable [x (k) x ' (k)] (k) ^T, then formula (1) can be write as equation of state as follows:

$\left[\begin{array}{c}x\left(k\right)\\ x^{\′}\left(k\right)\end{array}\right]=\left[\begin{array}{cc}1& \mathrm{\ΔT}\\ 0& 1\end{array}\right]\left[\begin{array}{c}x(k-1)\\ x^{\′}(k-1)\end{array}\right]+\left[\begin{array}{c}\frac{\mathrm{\Δ}{T}^2}{2}w\\ \mathrm{\ΔT}\·w\end{array}\right]---\left(2\right)$

Wherein, w=x " (k), can be considered as the random white noise error.

Suppose that sensor measurement signal is

N wherein _SmBe actual signal institute noise superimposed, can be considered as the random white noise error, then have:

$\tilde{x}\left(k\right)=\left[\begin{array}{cc}1& 0\end{array}\right]\left[\begin{array}{c}x\left(k\right)\\ x^{\′}\left(k\right)\end{array}\right]+n_{\mathrm{sm}}---\left(3\right)$

Formula (2), (3) have constituted the space equation structure of complete Kalman filter:

X(k)＝A·X(k-1)+W(k) (4)

$\tilde{X}\left(k\right)=H\·X\left(k\right)+N\left(k\right)$

Wherein

H=[1 0], N (k)=n _Sm

If hypothesis Q, R are respectively the covariance matrix of W (k), N (k), next the Kalman filter of Gou Jianing is:

$\hat{X}\left(k\right)=A\·\hat{X}(k-1)+\mathrm{Kg}\left(k\right)\·(\tilde{X}\left(k\right)-H\·A\·\hat{X}(k-1))$

$\mathrm{Kg}\left(k\right)=\frac{(A\·P(k-1)\·A^T+Q)\·H^T}{H\·(A\·P(k-1)\·A^T+Q)\·H^T+R}---\left(5\right)$

P(k)＝(1-Kg(k)·H)·(A·P(k-1)·A ^T+Q)

Through type (5), the estimated valve after can obtaining handling: longitudinal acceleration Transverse acceleration Yaw velocity

3, adopt respectively based on Kalman filtering with based on the mode of signal integration and carry out side slip angle observation.

1) observes based on the side slip angle of Kalman filtering

The definition of side slip angle β is as the formula (6):

$\mathrm{\β}=\frac{v_y}{v_x}---\left(6\right)$

Wherein, v _x, v _yBe respectively the vertical speed of a motor vehicle and the horizontal speed of a motor vehicle.Formula (6) differential is obtained:

${\mathrm{\β}}^{\′}=-\frac{a_x}{v_x}\mathrm{\β}-\mathrm{\γ}{\mathrm{\β}}^2+(\frac{a_y}{v_x}-\mathrm{\γ})---\left(7\right)$

Simultaneously, learn, have following relation between side slip angle and the yaw velocity according to vehicle movement:

$\frac{{v^{\′}}_x-a_x}{v_x\mathrm{\γ}}=\mathrm{\β}---\left(8\right)$

As follows to obtaining side slip angle extended Kalman filter space equation structure after formula (7), (8) discretization:

$\mathrm{\β}\left(k\right)=(1-\frac{{\hat{a}}_x(k-1)\·\mathrm{\ΔT}}{{\hat{v}}_x(k-1)})\·\mathrm{\β}(k-1)-\widehat{\mathrm{\γ}}(k-1)\·\mathrm{\ΔT}\·{\mathrm{\β}}^2(k-1)+(\frac{{\hat{a}}_y(k-1)}{{\hat{v}}_x(k-1)}-\widehat{\mathrm{\γ}}(k-1))\·\mathrm{\ΔT}$ (9)

$\frac{{{\hat{v}}^{\′}}_x\left(k\right)-{\hat{a}}_x\left(k\right)}{{\hat{v}}_x\left(k\right)\·\widehat{\mathrm{\γ}}\left(k\right)}=\mathrm{\β}\left(k\right)+N_{\mathrm{\β}}\left(k\right)$

Wherein, vertical speed of a motor vehicle

Obtain by car speed sensor;

Be respectively processing obtains in the step 2 longitudinal acceleration, transverse acceleration, yaw velocity estimated valve; N _β(k) be actual signal β (k) institute noise superimposed, can be considered as the random white noise error.The standard form that (9) formula is changed into extended Kalman filter space equation structure is as follows:

X _β(k)＝A _β·X _β(k-1)+W _β(k)(10)

${\tilde{X}}_{\mathrm{\β}}\left(k\right)=H_{\mathrm{\β}}\·X_{\mathrm{\β}}\left(k\right)+N_{\mathrm{\β}}\left(k\right)$

Wherein, X _β(k)=β (k),

H _β=1, $W_{\mathrm{\β}}\left(k\right)=-\widehat{\mathrm{\γ}}(k-1)\·\mathrm{\ΔT}\·{\mathrm{\β}}^2(k-1)+(\frac{{\hat{a}}_y(k-1)}{{\hat{v}}_x(k-1)}-\widehat{\mathrm{\γ}}(k-1))\·\mathrm{\ΔT}.$

Herein, W _β(k) be treated to the random white noise error.If hypothesis Q _β, R _βBe respectively W _β(k), N _β(k) covariance matrix, next the Kalman filter of Gou Jianing is:

$\widehat{\mathrm{\β}}\left(k\right)=A_{\mathrm{\β}}\·\widehat{\mathrm{\β}}(k-1)+\mathrm{Kg}\left(k\right)\·({\tilde{X}}_{\mathrm{\β}}\left(k\right)-H_{\mathrm{\β}}\·A\·\widehat{\mathrm{\β}}(k-1))$

${\mathrm{Kg}}_{\mathrm{\β}}\left(k\right)=\frac{(A_{\mathrm{\β}}\·P_{\mathrm{\β}}(k-1)\·{A_{\mathrm{\β}}}^T+Q_{\mathrm{\β}})\·{H_{\mathrm{\β}}}^T}{H_{\mathrm{\β}}\·(A_{\mathrm{\β}}\·P_{\mathrm{\β}}(k-1)\·{A_{\mathrm{\β}}}^T+Q_{\mathrm{\β}})\·{H_{\mathrm{\β}}}^T+R_{\mathrm{\β}}}---\left(11\right)$

P _β(k)＝(1-Kg _β(k)·H _β)·(A _β·P _β(k-1)·A _β ^T+Q _β)

In the ordinary course of things, can make observation preferably to side slip angle according to the designed extended Kalman filter of formula (11).

2) observe based on the side slip angle of signal integration

V appears in the observational equation of formula (9) _x(k) during the situation of γ (k)=0, Kalman filter will be no longer suitable.General, do not consider v _xThe situation of=0 (being that vertical speed of a motor vehicle is 0), satisfy γ=0 this moment, and cooresponding operating mode is that pure lateral deviation appears in vehicle, as when being subjected to the influencing of side direction wind.At this moment, formula (7) is changed to following form:

$\stackrel{\·}{\mathrm{\β}}=-\frac{a_x}{v_x}\mathrm{\β}+\frac{a_y}{v_x}---\left(12\right)$

What formula (12) provided is the expression formula of side slip angle derivative, and this moment, employing obtained side slip angle to the mode that the side slip angle derivative carries out integration, and formula (12) is carried out discretization, obtained based on the observed result of signal integration as follows:

$\widehat{\mathrm{\β}}\left(k\right)=(1-\frac{{\hat{a}}_x(k-1)\·\mathrm{\ΔT}}{{\hat{v}}_x(k-1)})\·\widehat{\mathrm{\β}}(k-1)+\frac{{\hat{a}}_y(k-1)}{{\hat{v}}_x(k-1)}\·\mathrm{\ΔT}---\left(13\right)$

The physical meaning of formula (13) promptly is that transverse acceleration signal is carried out integration, and rejects therefrom that influence that longitudinal acceleration produces obtains.

4, set up algorithm and switch method of discrimination, the result who adopts above-mentioned two kinds of barycenter sideslip angles observation is weighted.Yaw velocity and weight coefficient k relation curve are seen Fig. 2.

If the observed result that utilizes the Kalman filtering mode of expansion to obtain is

The observed result that utilizes the signal integration mode to obtain is

The final observed result of side slip angle observer is

Following relational expression is then arranged:

$\widehat{\mathrm{\β}}=(1-k){\widehat{\mathrm{\β}}}_{\mathrm{kal}}+k{\widehat{\mathrm{\β}}}_{\mathrm{int}}---\left(14\right)$

When

The time, think tangible yaw not occur that this moment, k=1 taked the observed pattern of signal integration, promptly fully

When The time, think tangible yaw to occur this moment, this moment k=0, will be by the Kalman filtering observed pattern of expansion, promptly

When

The time, two kinds of barycenter sideslip angle observed results are weighted fusion, obtain the final observed result of side slip angle observer

Claims (5)

1. the wheel side slip angle observation procedure of fusion card Kalman Filtering and integrated acceleration is characterized in that may further comprise the steps:

1) a side slip angle observation system is set, comprises car speed sensor, longitudinal acceleration sensor, lateral acceleration sensor, yaw-rate sensor and controller, obtain original signal respectively: longitudinal acceleration Transverse acceleration

Yaw velocity

2) to longitudinal acceleration Transverse acceleration Yaw velocity

Signal carries out Kalman filtering respectively and handles the estimated valve after obtaining handling: longitudinal acceleration

Transverse acceleration

Yaw velocity

3) adopt respectively based on Kalman filtering with based on the mode of signal integration and carry out side slip angle observation:

4) result to two kinds of methods of step 3) is weighted processing, obtains the side slip angle observed value.

2. the wheel side slip angle observation procedure of fusion card Kalman Filtering as claimed in claim 1 and integrated acceleration, it is characterized in that: in the time of execution in step 2), concrete grammar is as follows:

Suppose that the original signal that need do Filtering Processing is

Actual signal is x, and the estimated valve after the processing is

X (k) expression k is the instantaneous value of x constantly, and Δ T is a sampling time interval, this signal k on time domain is carried out Taylor expansion constantly obtain:

$x(k+1)=x\left(k\right)+x^{\′}\left(k\right)\mathrm{\ΔT}+\frac{x^{\′\′}\left(k\right)}{2}{\mathrm{\ΔT}}^2+o\left({\mathrm{\ΔT}}^2\right)---\left(1\right)$

Ignore the above higher order term of second order, choosing x (k) and first derivative x ' thereof is state variable [x (k) x ' (k)] (k) ^T, then formula (1) can be write as equation of state as follows:

$\left[\begin{array}{c}x\left(k\right)\\ x^{\′}\left(k\right)\end{array}\right]=\left[\begin{array}{cc}1& \mathrm{\ΔT}\\ 0& 1\end{array}\right]\left[\begin{array}{c}x(k-1)\\ x^{\′}(k-1)\end{array}\right]+\left[\begin{array}{c}\frac{\mathrm{\Δ}{T}^2}{2}w\\ \mathrm{\ΔT}\·w\end{array}\right]---\left(2\right)$

Wherein, w=x " (k), can be considered as the random white noise error,

Suppose that sensor measurement signal is

N wherein _SmBe actual signal institute noise superimposed, can be considered as the random white noise error, then have:

$\tilde{x}\left(k\right)=\left[\begin{array}{cc}1& 0\end{array}\right]\left[\begin{array}{c}x\left(k\right)\\ x^{\′}\left(k\right)\end{array}\right]+n_{\mathrm{sm}}---\left(3\right)$

Formula (2), (3) have constituted the space equation structure of complete Kalman filter:

X(k)＝A·X(k-1)+W(k)(4)

$\tilde{X}\left(k\right)=H\·X\left(k\right)+N\left(k\right)$

Wherein

H=[1 0], N (k)=n _Sm

If hypothesis Q, R are respectively the covariance matrix of W (k), N (k), the Kalman filter of structure is:

$\hat{X}\left(k\right)=A\·\hat{X}(k-1)+\mathrm{Kg}\left(k\right)\·(\tilde{X}\left(k\right)-H\·A\·\hat{X}(k-1))$

$\mathrm{Kg}\left(k\right)=\frac{(A\·P(k-1)\·A^T+Q)\·H^T}{H\·(A\·P(k-1)\·A^T+Q)\·H^T+R}---\left(5\right)$

P(k)＝(1-Kg(k)·H)·(A·P(k-1)·A ^T+Q)

Through type (5), the estimated valve after can obtaining handling: longitudinal acceleration

Transverse acceleration

Yaw velocity

3. the wheel side slip angle observation procedure of fusion card Kalman Filtering as claimed in claim 1 or 2 and integrated acceleration, it is characterized in that: in the time of execution in step 3), concrete grammar is as follows:

1. observe based on the side slip angle of Kalman filtering

The definition of side slip angle β is:

$\mathrm{\β}=\frac{v_y}{v_x}---\left(6\right)$

Wherein, v _x, v _yBe respectively the vertical speed of a motor vehicle and the horizontal speed of a motor vehicle, formula (6) differential obtained:

${\mathrm{\β}}^{\′}=-\frac{a_x}{v_x}\mathrm{\β}-\mathrm{\γ}{\mathrm{\β}}^2+(\frac{a_y}{v_x}-\mathrm{\γ})---\left(7\right)$

Simultaneously, learn, have following relation between side slip angle and the yaw velocity according to vehicle movement:

$\frac{{v^{\′}}_x-a_x}{v_x\mathrm{\γ}}=\mathrm{\β}---\left(8\right)$

As follows to obtaining side slip angle extended Kalman filter space equation structure after formula (7), (8) discretization:

$\mathrm{\β}\left(k\right)=(1-\frac{{\hat{a}}_x(k-1)\·\mathrm{\ΔT}}{{\hat{v}}_x(k-1)})\·\mathrm{\β}(k-1)-\widehat{\mathrm{\γ}}(k-1)\·\mathrm{\ΔT}\·{\mathrm{\β}}^2(k-1)+(\frac{{\hat{a}}_y(k-1)}{{\hat{v}}_x(k-1)}-\widehat{\mathrm{\γ}}(k-1))\·\mathrm{\ΔT}---\left(9\right)$

$\frac{{{\hat{v}}^{\′}}_x\left(k\right)-{\hat{a}}_x\left(k\right)}{{\hat{v}}_x\left(k\right)\·\widehat{\mathrm{\γ}}\left(k\right)}=\mathrm{\β}\left(k\right)+N_{\mathrm{\β}}\left(k\right)$

Wherein, N _β(k) be actual signal β (k) institute noise superimposed, the standard form that then (9) formula is changed into extended Kalman filter space equation structure is as follows:

X _β(k)＝A _β·X _β(k-1)+W _β(k)(10)

${\tilde{X}}_{\mathrm{\β}}\left(k\right)=H_{\mathrm{\β}}\·X_{\mathrm{\β}}\left(k\right)+N_{\mathrm{\β}}\left(k\right)$

Wherein, X _β(k)=β (k),

H _β=1, $W_{\mathrm{\β}}\left(k\right)=-\widehat{\mathrm{\γ}}(k-1)\·\mathrm{\ΔT}\·{\mathrm{\β}}^2(k-1)+(\frac{{\hat{a}}_y(k-1)}{{\hat{v}}_x(k-1)}-\widehat{\mathrm{\γ}}(k-1))\·\mathrm{\ΔT};$

Herein, W _β(k) be the random white noise error, if hypothesis Q _β, R _βBe respectively W _β(k), N _β(k) covariance matrix, the Kalman filter of structure is:

$\widehat{\mathrm{\β}}\left(k\right)=A_{\mathrm{\β}}\·\widehat{\mathrm{\β}}(k-1)+\mathrm{Kg}\left(k\right)\·({\tilde{X}}_{\mathrm{\β}}\left(k\right)-H_{\mathrm{\β}}\·A\·\widehat{\mathrm{\β}}(k-1))$

${\mathrm{Kg}}_{\mathrm{\β}}\left(k\right)=\frac{(A_{\mathrm{\β}}\·P_{\mathrm{\β}}(k-1)\·{A_{\mathrm{\β}}}^T+Q_{\mathrm{\β}})\·{H_{\mathrm{\β}}}^T}{H_{\mathrm{\β}}\·(A_{\mathrm{\β}}\·P_{\mathrm{\β}}(k-1)\·{A_{\mathrm{\β}}}^T+Q_{\mathrm{\β}})\·{H_{\mathrm{\β}}}^T+R_{\mathrm{\β}}}---\left(11\right)$

P _β(k)＝(1-Kg _β(k)·H _β)·(A _β·P _β(k-1)·A _β ^T+Q _β)

Draw the observed value of side slip angle according to formula (11);

2. observe based on the side slip angle of signal integration

V appears in the observational equation of formula (9) _x(k) during the situation of γ (k)=0, Kalman filter will be no longer suitable, and cooresponding operating mode is the pure lateral deviation of vehicle, and at this moment, formula (7) is changed to following form:

$\stackrel{\·}{\mathrm{\β}}=-\frac{a_x}{v_x}\mathrm{\β}+\frac{a_y}{v_x}---\left(12\right)$

Formula (12) is carried out discretization, obtains based on the observed result of signal integration as follows:

$\widehat{\mathrm{\β}}\left(k\right)=(1-\frac{{\hat{a}}_x(k-1)\·\mathrm{\ΔT}}{{\hat{v}}_x(k-1)})\·\widehat{\mathrm{\β}}(k-1)+\frac{{\hat{a}}_y(k-1)}{{\hat{v}}_x(k-1)}\·\mathrm{\ΔT}---\left(13\right).$

4. the wheel side slip angle observation procedure of fusion card Kalman Filtering as claimed in claim 1 or 2 and integrated acceleration, it is characterized in that: in the time of execution in step 4), concrete grammar is as follows:

If the observed result that utilizes the Kalman filtering mode of expansion to obtain is

The observed result that utilizes the signal integration mode to obtain is

The final observed result of side slip angle observer is

Following relational expression is then arranged:

$\widehat{\mathrm{\β}}=(1-k){\widehat{\mathrm{\β}}}_{\mathrm{kal}}+k{\widehat{\mathrm{\β}}}_{\mathrm{int}}---\left(14\right)$

When The time, think tangible yaw not occur that this moment, k=1 taked the observed pattern of signal integration, promptly fully

When

The time, think tangible yaw to occur this moment, this moment k=0, will be by the Kalman filtering observed pattern of expansion, promptly

When

The time, two kinds of barycenter sideslip angle observed results are weighted fusion, obtain the final observed result of side slip angle observer

5. the wheel side slip angle observation procedure of fusion card Kalman Filtering as claimed in claim 3 and integrated acceleration, it is characterized in that: in the time of execution in step 4), concrete grammar is as follows:

If the observed result that utilizes the Kalman filtering mode of expansion to obtain is

The observed result that utilizes the signal integration mode to obtain is

The final observed result of side slip angle observer is

Following relational expression is then arranged:

$\widehat{\mathrm{\β}}=(1-k){\widehat{\mathrm{\β}}}_{\mathrm{kal}}+k{\widehat{\mathrm{\β}}}_{\mathrm{int}}---\left(14\right)$

When

The time, think tangible yaw not occur that this moment, k=1 taked the observed pattern of signal integration, promptly fully

When

The time, think tangible yaw to occur this moment, this moment k=0, will be by the Kalman filtering observed pattern of expansion, promptly When

The time, two kinds of barycenter sideslip angle observed results are weighted fusion, obtain the final observed result of side slip angle observer

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