JP4086759B2 - Road model estimation apparatus and method - Google Patents

Description

  The present invention relates to a road model estimation apparatus and a method for estimating a road model during traveling.

  Conventionally, an image obtained by imaging the front of a vehicle with a camera mounted on a traveling vehicle is processed, and a predetermined road parameter such as a road curvature indicating a straight road or a curved road of the traveling road is derived to obtain the road. A model is being estimated.

In this case, the Kalman filter is used to derive the lateral displacement of the vehicle lane marker as the state estimator of the state equation, the road curvature of the curve drawn by the lane marker, the vehicle yaw angle, and the vehicle pitch angle road parameters. A road model is estimated using the parameters and the ground height of the mounting position of the imaging unit (see, for example, Patent Document 1).
JP 2002-109695A (pages 3-6)

  However, in the conventional method, a Kalman filter is used, and this Kalman filter is vulnerable to disturbance and has a disadvantage that a modeling error becomes large. When this result is used for control such as follow-up running, there is a problem that stable control cannot be performed.

  In view of the above, the present invention has an object to make it possible to estimate a road model with higher reliability, and to further simplify and speed up the calculation of the estimation process.

In order to achieve the above-described object, a road model estimation apparatus according to a first aspect of the present invention includes an imaging unit that is mounted on a vehicle and images the front of the vehicle, and density values of all pixels of an image captured by the imaging unit. A forming unit that forms an edge image including a lane marker formed on a running road by differentiating, and obtains coordinates of a plurality of lane marker candidate points from the edge image formed by the forming unit, and for these A derivation unit that derives a road parameter that determines a road model that is running by applying an H∞ filter, and the derivation unit includes a diagonal determinant of Formula 3 that does not include an inverse matrix: It is characterized by performing calculations.

A road model estimation apparatus according to a second aspect of the present invention is a road model estimation apparatus for estimating a running road model, the imaging section being mounted on a vehicle and imaging the front of the vehicle, and the imaging section A forming unit for differentiating density values of all pixels of the captured image by the image forming unit to form an edge image including a lane marker formed on a running road, and a plurality of lane marker candidates from the edge image formed by the forming unit A derivation unit that obtains the coordinates of the points and derives road parameters that apply a H∞ filter to determine the road model during traveling, and the derivation unit includes the following equation 6 that does not include an inverse matrix: The H∞ filter is calculated according to an angle determinant.

Next, a road model estimation method according to a third aspect of the present invention is a road model estimation method for estimating a running road model, and an imaging step of imaging the front of the vehicle by an imaging unit mounted on the vehicle. And forming an edge image including a lane marker formed on a running road by differentiating density values of all pixels of the image captured in the imaging process, and the edge image formed in the formation process And a derivation step of deriving road parameters for determining a road model that is running by applying the H∞ filter to the coordinates of a plurality of candidate lane marker points from the lane marker, and the derivation step does not include an inverse matrix The calculation of the H∞ filter is performed according to the diagonal determinant of the following equation (9).

A road model estimation method according to a fourth aspect of the present invention is a road model estimation method for estimating a running road model, the imaging step of imaging the front of the vehicle with an imaging unit mounted on the vehicle, and A forming step of differentiating density values of all pixels of the picked-up image in the image pickup step to form an edge image including a lane marker formed on a running road, and the edge image formed in the forming step A derivation step of obtaining coordinates of a plurality of candidate lane marker points and deriving road parameters for determining a road model by applying an H∞ filter to the lane marker candidate points, wherein the derivation step does not include an inverse matrix The H∞ filter is calculated according to the diagonal determinant of Formula 12.

First, according to the first and third aspects of the present invention, road parameters for determining a road model during traveling are derived by applying an H∞ filter. At that time, the calculation of the H∞ filter that does not include the inverse matrix is performed according to the specific diagonal determinants of Equations 3 and 9 in which the observation matrix is the time-invariant matrix H.

In this case, since the H∞ filter has a characteristic that is strong against disturbance and can suppress a modeling error as compared with the case where the conventional Kalman filter is used, it is possible to estimate a road model with higher reliability than the conventional method. When the result is used for follow-up running, stable follow-up running can be performed. Moreover, since the calculation of the H∞ filter does not include an inverse matrix, the calculation burden is reduced as compared with the case of performing an operation including an inverse matrix, the calculation time is significantly reduced, the calculation of the estimation process is simplified, and the operation speed is high. Can be achieved.

Further, according to the inventions of claims 2 and 4, the diagonal determinants of the above-mentioned formulas 6 and 12 are used for the calculation of the H∞ filter that does not include the inverse matrix and the observation matrix is the time-varying matrix H _k. The effects of the inventions of claims 1 and 3 can be obtained.

  Next, in order to describe the present invention in more detail, an embodiment thereof will be described in detail with reference to FIGS.

  FIG. 1 is a block diagram, FIGS. 2 to 11 are operation explanatory diagrams, and FIG. 12 is a flowchart for explaining operations.

<< Overall explanation >>
First, an apparatus configuration and a series of processes from photographing based on this configuration to estimating a road model will be described.

  As shown in FIG. 1, a CCD camera 1 as an imaging unit is mounted on the own vehicle, the front of the own vehicle is imaged by the CCD camera 1, and the obtained captured image is transmitted from a microcomputer via a video capture board 2. It is taken in by the ECU 3 and processed.

  The imaging process by the CCD camera 1 corresponds to the imaging process in the present invention. The ECU 3 operates as, for example, an image processing / estimation processing ECU, an actuator ECU that performs traveling control of the vehicle 1 and processing of an alarm based on the processing result, and an alarm ECU.

  Further, when the ECU 3 captures a captured image of each frame by the CCD camera 1, the ECU 3 performs differential binarization processing on the density values of all pixels of the captured image by the image processing / estimation processing ECU operation, thereby performing edge image processing. Are extracted, a plurality of lane marker candidate points corresponding to the lane marker (white line) formed on the road are extracted from the formed edge image, the coordinates of the extracted plurality of lane marker candidate points are obtained, and H∞ filter is obtained for these , That is, H∞ filtering is performed to derive road parameters that define a road model.

  At this time, the ECU 3 uses the pitch angle of the vehicle and the ground height of the CCD camera 1 to estimate the lateral displacement of the vehicle with respect to the lane marker, the road curvature of the curve drawn by the lane marker, and the yaw angle of the vehicle. Calculate.

  The edge image forming process by the ECU 3 corresponds to the forming part process and forming process, and the road parameter deriving process by the ECU 3 corresponds to the deriving part process and deriving process.

  Next, the derivation of the road parameters will be specifically described.

  First, the relationship between the image coordinate system xy on the imaging surface of the CCD camera 1 and the road coordinate system XYZ corresponding to the actual road surface is as shown in FIG. The x-axis and y-axis are parallel to the X-axis and Y-axis of the road coordinate system, and the center of the road coordinate system coincides with the center of the lens of the CCD camera 1 and the center of the imaging surface.

  In FIG. 2, f is the focal length of the lens of the CCD camera 1, and h0 is the height above the CCD camera 1 mounting position.

  In such an arrangement, the following relationship is established between the road coordinate system and the image coordinate system.

  Further, when the road coordinate system is set in this way, it is well known that the road model indicating the road structure can be approximated by independent polynomials with respect to X and Y as shown in the following two equations X and Y. It has been.

  However, Equation (2) assumes that the curvature is small and smoothly changes as in an expressway, the longitudinal gradient of the road is constant, and there is no crossing gradient.

  Then, rearranging the formulas (13) and (14) gives the following formula (15), which is the road model parameter that is also the coordinate value (x, y) of the lane marker candidate point on the imaging surface and the vehicle behavior. The relationship with (ρ, ψ, yc) is shown.

  As shown in FIG. 3, ρ is the road curvature, ψ is the vehicle yaw angle, and yc is the lateral displacement of the vehicle with respect to the lane marker.

  As shown in FIG. 4, f in the equation 15 is the focal length, WL is the road width, h0 is the ground height of the CCD camera 1, and β is the depression angle of the CCD camera 1, that is, the pitch angle of the vehicle. Yes, these are known.

  Then, based on the image coordinate values (x, y) of the lane marker candidate points obtained by the image processing, the road model and the vehicle behavior, that is, the road parameters (ρ, ψ, yc) are calculated by the estimation calculation (filtering) of the H∞ filter. The estimation is as follows.

Assume that the coordinates of the i-th (i = 0, 1,..., I) lane marker candidate point detected in the image frame at time k are expressed as (posx (i), posy (i)). When the power state variable is x _k = (ρ _k , ψ _k , ^y c _k ) ^t and the H∞ filter is driven by white Gaussian noise, the state equation is expressed by the following equation (16). .

Further, when the equation of the equation 16 is converted into a discrete equation and the equation of the equation 15 is used as an output equation of the H∞ filter, the state space model of the H∞ filter can be expressed by the following state variable (state vector) x _{k + 1} and observation value (observation vector) y _k are represented by two expressions (state equation, output equation), and F, G, and H in the expression are a state transition matrix, a drive matrix, and an observation matrix of the state space model, v _k is observation noise (unknown noise), and w _k is system noise (known noise).

  Since the y coordinate (see FIG. 2) of the lane marker candidate point can be a fixed value, it is assumed here that the observation matrix H is time-invariant.

Then, the filtering algorithm of the H∞ filter for the state variable x _{k + 1} and the observed value y _k of Equation 17 described above is based on the control parameter γ _f > 0 that sets the filter characteristic (level) of the H∞ filter. A filter that minimizes the norm is constructed and is given by the following equations (18) to (20).

At this time, the error covariance matrix P _{k | k−1} with ^ indicating the estimated value needs to satisfy the inequality (existence condition) shown in Equation 21, that is, the filter existence condition expression.

Then, when the estimation of the state variables x _k = (ρ _k, ψ _k, ^y c _k ) ^t was simulated by the H∞ filter that performs the filtering operation according to the equations (18) to (20), the following results were obtained. .

  In this simulation, the vehicle speed is constant at 40 km / h, the road width WL is 3.15 m, the ground height h0 of the CCD camera 1 is 1.25 m, and the pitch angle of the CCD camera 1 is 9.5 °. As shown in FIG. 5, the lane marker candidate points when the vehicle travels straight in the center of the straight course, laterally displaces 1.3 m from the front of time 2s to the left (+ side), then returns to the center and travels straight again. Are input to the H∞ filter of the ECU 3 and calculated for each frame, and the performance is evaluated.

  FIG. 5 shows simulation data of road curvature ρ, yaw angle ψ, and lateral displacement yc of the vehicle in order from the top.

FIG. 6 shows the result when noise (error) does not exist when variance of estimation error σv ² = 0, FIG. 7 shows the result when noise of σv ² = 4, and the camera pitch angle is 9.5 °. FIG. 8 shows the results when there is noise of σv ² = 4 by changing the angle from 7.5 ° to 7.5 °.

  For comparison, the estimation results when the Kalman filter is used are also shown in each figure. The dashed line in FIGS. 6 to 8 is the true value shown in FIG. 5, the solid line is the estimation result of the H∞ filter, and the broken line is It shows the estimation result of the Kalman filter.

  From the results of FIG. 6, both the H∞ filter and the Kalman filter are almost true values in the estimation of the yaw angle ψ and the vehicle lateral displacement yc, whereas in the estimation of the curvature ρ, the error due to the Kalman filter is particularly significant. You can see that it is getting bigger. This is considered to be due to a model error caused by applying a road model in consideration of curvature to a straight road. On the other hand, the H∞ filter has a characteristic robust to the modeling error, and thus it can be seen that a value almost equal to the true value is estimated.

  Further, from the result of FIG. 7, it can be seen that the variation of the estimation result increases according to the noise level, but the H∞ filter shows an estimation result closer to the true value. In particular, there is a delay in the estimation of the lateral displacement yc by the Kalman filter, but there is no delay in the estimation of the lateral displacement yc by the H∞ filter, and it can be seen that the H∞ filter is excellent in followability to the input.

  Further, FIG. 8 shows the deterioration due to the pitching motion that occurs during the traveling of the vehicle. From the result, even if there is a modeling error, the H∞ filter is better than the Kalman filter. It can be seen that

  Next, a case where a lane marker candidate point is detected from the captured image shown in FIG. 9 of the CCD camera 1 actually mounted on the vehicle will be described.

  First, lane marker candidate points are detected by binarizing the input image (see FIG. 9) by the ECU 3 to obtain a binarized binarized image (edge image) as shown in FIG. The image was scanned in the horizontal direction, and if there were continuous white spots corresponding to the number of pixels corresponding to the width of the lane marker, this was performed as a lane marker candidate point.

  A sorbet filter was used for the differentiation process. Further, during the test run, the run was performed about 1.3 m to the left between the frames 20 to 60 and the frames 70 to 120. At this time, the road width WL is 3.15 m, the ground height h0 of the CCD camera 1 is 1.25 m, and the pitch angle β of the CCD camera 1 is 9.5 °.

  FIG. 11 shows the estimation results. The solid line represents the H∞ filter and the one-dot chain line represents the Kalman filter for comparison. The estimation error at the yaw angle ψ is larger than this, but the vehicle lateral displacement yc is estimated well. You can see that

  In addition, in the detection of lane marker candidate points by image processing, the input value deteriorates due to the influence of shadows and noise, but there is a concern about the influence. However, as shown in FIG. It can be seen that the estimation error of the Kalman filter is very large, whereas the H∞ filter performs the estimation relatively stably even when such a disturbance exists.

  That is, in the case of this embodiment, in order to derive the road parameters that determine the road model that is running by applying the H∞ filter, compared to the case of using the conventional Kalman filter, based on the robust characteristics of the H∞ filter, Since the modeling error can be suppressed strongly against disturbance, a more reliable road model can be estimated.

  For this reason, the ECU 3 operates as the actuator ECU and the alarm ECU based on the road parameter estimation result by the H∞ filter, so that, for example, the follow-up running control and the alarm can be performed accurately, giving a sense of security. Realizes stable follow-up driving.

<< Determination of control parameter γ _f >>
Next, the determination of the control parameter γ _f of the filter existence conditional expression of Equation 21 will be described.

When the filtering operation is performed by the H∞ filter, the estimation accuracy is improved as the control parameter γ _f of the filter existence conditional expression (21 ₎ is decreased. However, it is difficult to satisfy the filter existence conditional expression. How to determine and set the parameter γ _f is extremely important for filter design.

Then, in the field of H∞ filter theory, after initializing the control parameter γ _f to an appropriate value by a technique called “γ-iteration”, while confirming that the filter existence formula of the formula 21 is satisfied. It is known to repeatedly reduce the control parameter γ _f little by little and determine and set the control parameter γ _f to an optimum value.

However, when applying the H∞ filter for estimation of the road model, to define the appropriate initial value of the control parameter gamma _f is difficult, when repeating the operation to reduce the control parameter gamma _f slightly, computational burden ECU3 Becomes extremely large, takes time for calculation, and cannot be estimated quickly, which is not practical.

Therefore, the control parameter γ _f is quickly determined and set to the optimum value without repeating the calculation as described below.

First, the filter presence condition of the number 21, by using the observation noise v _k, deformed equation of the number of the next 22.

The observation noise v _{k in} the equation (22) is such that the error covariance matrix P _{k | k−1} with ^ is a real symmetric matrix, and the observation noise v _k is also a real symmetric matrix. Diagonalization is possible, as shown in the diagonalization equation of Equation 23.

In Equation 23, when U = (v ₁ , v ₂ ,..., V _N ) and the eigenvalue of the observation noise v _k is λ _i , (i = 1, 2,..., N), v _i is an eigenvector for the eigenvalue λ _i . However, the norm ‖v _i ‖ = 1.

  Then, from the two expressions of Expressions 22 and 23, the filter existence conditional expression of Expression 21 can be transformed into the following inequality of Expression 24.

Further, similarly to the observation matrix of various estimation problems, the observation matrix H can be the unit matrix I, and U ^t U = I. This is equivalent to the inequality of number 25.

  In order to hold the inequality of Equation 25, the left side must be a positive definite matrix, and the necessary and sufficient condition for this positive definite matrix is that all of its eigenvalues are positive.

The control parameter γ _f is determined based on the necessary and sufficient condition of the positive definite matrix and the formula (25). The control formula (2) (the formula 5), that is, the control consisting of the following inequality λ _i inequality A determinant of the parameter γ _f can be derived, and this determinant becomes an inequality with a constant ε.

Then, ECU 3, the control parameter when setting determines the gamma _f, wherein the "γ- iteration" and repeated without performing the computation by a method called, from the calculation of the number 26 determination formulas immediately control parameter gamma _f Determine and set. Therefore, in the case of this embodiment, the calculation amount burden of the ECU 3 is small, and the control parameter γ _f can be determined quickly and the road model can be estimated quickly.

<< Filtering operation >>
Next, the filtering operation of the H∞ filter will be described.

First, the filtering algorithm of the H∞ filter is to construct a filter that minimizes the H∞ norm based on the control parameter γ _f as described above. The ECU 3 performs the calculation given by the following equation.

Equation (19) is a filter equation, and Equations (a) and (b) are so-called Riccati equations. In particular, in the operation of this Riccati equation, a matrix R _{e, It} is necessary to obtain _{k and} to obtain the inverse matrix R ⁻¹ _{e, k} using equation (a).

In this case, for example, if the order of the observation vector y _k is 10 and the order of the state variable x _k is 3, that is, if the unknown is 3 and the observation data is 10 _, the order of the matrix _{Re, k} is 3 The amount of data to be calculated becomes x13 and the amount of data to be calculated becomes extremely large.

In general, the amount of computation of the inverse matrix is proportional to the cube of its size. For example, the ratio of the amount of computation O (N ³ ) between the inverse operation of the 3 × 3 matrix and the inverse operation of the 13 × 13 matrix is O (3 ³ ): O (13 ³ ) = O (27): O (2197), and the latter calculation amount is about 80 times the former calculation amount.

  Then, in order to reduce the calculation amount and reduce the calculation time by not performing the inverse matrix calculation, this embodiment will be described next.

  That is, since the matrix H is time-invariant, when the Riccati equations of the equations (a) and (b) of the equation (20) are arranged using the matrix D of the following equation (27), the equation of the equation (28) is obtained. be able to.

  When the inverse matrix lemma (inverse matrix lemma) is applied to the part of “{}” in Equation 28, the following Equation 29 is obtained.

Further, the matrix of the observation noise v _k can be expressed by the equation (22). At this time, the observation noise v _k is a real symmetric matrix and can be diagonalized as shown in the equation (23). Therefore, the formula 29 can be expressed by the formula 30.

  Then, by multiplying the two matrices A and B of the following equation 31 by both sides of the equation 30 to obtain the equation 32, the equation 32 can be obtained by rearranging the equation 32. .

  Therefore, it has been found that the Ricacci equation of the number 20 including the inverse matrix can be formulated by the diagonal determinant of the number 33 not including the inverse matrix.

Therefore, instead of calculating the Riccati equation of Formula 20, the ECU 3 performs the filtering by performing the formula calculation of the diagonal determinant of Formula 34, and the state variables x _k = (ρ _k, ψ _k, ^y c _k ) ^t Is estimated.

In this case, the calculation burden on the ECU 3 is reduced as compared with the case of calculating the number 20 Riccati equation including the calculation of the inverse matrix, and the calculation time is greatly reduced (about 1/2) and quickly. State variables x _k = (ρ _k, ψ _k, ^y c _k ) ^t can be estimated.

  The operation of the ECU 3 as the image processing / estimation processing ECU is, for example, as shown in the flowchart of steps S1 to S3 in FIG.

<< When the observation matrix is time-varying >>
In the above-described embodiment, the observation matrix H is time-invariant and the matrices F, G, H, etc. are time-invariant matrices (constant matrix). In such a case, a time-varying system in which the observation matrix H is time-varying and the matrices F, G, H, etc. are time-varying (time-varying) is required as an H∞ filter. Even in this case, the present invention can be similarly applied.

<Determination of control parameter γ _f >
In the case of a time-varying system, by using the time k, the state equation and the output equation are expressed by the following two equations 34 instead of equation 17.

Further, the filtering algorithm of the H∞ filter represented by the two expressions of Expression 34 is expressed by Expression 35 of the linear combination z _{k | k} with a sign ˜ including the observation error of the state variable x _k and Expression 18 ## EQU20 ## Expressions 36, 37, and 38 are substituted for the expression (20).

  In addition, the filter existence formula of the equation (21) can be replaced with the following filter existence condition equation of the equation (39).

Further, the observation noise v _{k in} the formula 22 is expressed by the following formula 40 in the case of time variation.

  Then, based on the diagonalization expression of Expression 23 and the expression of Expression 40, an inequality as a filter existence condition expression of Expression 41 corresponding to Expression 24 is obtained.

Also, with respect to the filter existence formula of Formula 41, the determination formula of the control parameter γ _f is expressed by the inequality of the eigenvalue of Formula 26.

Accordingly, even in the case of a time-varying system, the ECU 3 can immediately determine and set the control parameter γ _f from the calculation of the inequality of Equation 26 without repeating the calculation.

<Filtering operation of H∞ filter>
Next, in the case of this time-varying system, the Riccati equation becomes an equation (a *) and an equation (b *) in the equation 38 instead of the equations (a) and (b) in the equation 20.

In the case of Equations (a *) and (b *) in Expression 38, the matrix R _{e, k} is included in the (b *) equation, and the inverse matrix R ⁻¹ _{e, k} is included in the (a *) equation. but are number 38 (a *) equation using the matrix D _k number 42 following an alternative to expression of matrix D having 27, and rearranging the Riccati equation of (b *) type, number 28 the formula Equation 43 in place of is obtained.

  Then, when the inverse matrix lemma (inverse matrix lemma) is applied to the part of “{}” in Expression 43, the following Expression 44 is obtained.

Further, in the case of a time-varying system, the observation noise v _{k in} the equation (40) is also a real symmetric matrix, and the equation (23) can be diagonalized, and the observation noise v _k in the equation (40) is used. Thus, the formula 44 can be expressed by the following formula 45.

Then, the two formulas A _k and B _k of the following formula 46 corresponding to the formula 2 are multiplied by both sides of the formula 45 to obtain the formula 47, and the formula 47 is rearranged. , 48 can be obtained.

Therefore, even in the case of a time-varying system, the Riccati equation of the number 38 including the inverse matrix can be formulated by the diagonal determinant of the number 48 not including the inverse matrix, and the ECU 3 can formulate the diagonal determinant of the number 48. Formula operations are performed to estimate the state variables x _k = (ρ _k, ψ _k, ^y c _k ) ^t .

Since the inverse matrix is not calculated, the calculation burden on the ECU 3 is reduced as compared with the case of calculating the Riccati equation of Equation 38, the calculation time is greatly reduced, and the calculation time is greatly reduced. The state variable x _k = (ρ _k, ψ _k, ^y c _k ) ^t can be estimated quickly.

  The present invention is not limited to the above-described embodiment, and various modifications other than those described above can be made without departing from the spirit of the present invention.

  By the way, the application range of the estimation result by the H∞ filter is not limited to the control such as the follow-up traveling described above, and it is needless to say that it can be applied to various travel assist controls during other vehicle travels.

It is a block diagram of one embodiment of this invention. It is operation | movement explanatory drawing of one Embodiment of this invention. It is operation | movement explanatory drawing of one Embodiment of this invention. It is operation | movement explanatory drawing of one Embodiment of this invention. It is operation | movement explanatory drawing of one Embodiment of this invention. It is operation | movement explanatory drawing of one Embodiment of this invention. It is operation | movement explanatory drawing of one Embodiment of this invention. It is operation | movement explanatory drawing of one Embodiment of this invention. It is operation | movement explanatory drawing of one Embodiment of this invention. It is operation | movement explanatory drawing of one Embodiment of this invention. It is operation | movement explanatory drawing of one Embodiment of this invention. It is a flowchart for operation | movement description of one Embodiment of this invention.

Explanation of symbols

1 CCD camera (imaging part)
3 ECU (Forming part, Deriving part)

Claims (4)

A road model estimation device for estimating a road model during traveling,
An imaging unit mounted on the vehicle for imaging the front of the vehicle;
A forming unit that forms an edge image including a lane marker formed on a running road by differentiating density values of all pixels of the image captured by the imaging unit;
A derivation unit for obtaining coordinates of a plurality of lane marker candidate points from the edge image formed by the forming unit, and deriving road parameters for determining a road model that is running by applying an H∞ filter to the coordinates;
The derivation unit performs the calculation of the H∞ filter according to a diagonal determinant of the following formula 3 that does not include an inverse matrix:

A road model estimation device for estimating a road model during traveling,
An imaging unit mounted on the vehicle for imaging the front of the vehicle;
A forming unit that forms an edge image including a lane marker formed on a running road by differentiating density values of all pixels of the image captured by the imaging unit;
A derivation unit for obtaining coordinates of a plurality of lane marker candidate points from the edge image formed by the forming unit, and deriving road parameters for determining a road model that is running by applying an H∞ filter to the coordinates;
The road derivation apparatus is characterized in that the derivation unit performs the calculation of the H∞ filter according to a diagonal determinant of the following formula 6 that does not include an inverse matrix.

A road model estimation method for estimating a road model during traveling,
An imaging step of imaging the front of the vehicle with an imaging unit mounted on the vehicle;
A forming step of forming an edge image including a lane marker formed on a running road by differentiating density values of all pixels of the captured image in the imaging step;
Obtaining the coordinates of a plurality of lane marker candidate points from the edge image formed in the forming step, and deriving a road parameter for determining a road model that is running by applying an H∞ filter thereto,
The derivation step performs the calculation of the H∞ filter according to a diagonal determinant of the following formula 9 that does not include an inverse matrix:

A road model estimation method for estimating a road model during traveling,
An imaging step of imaging the front of the vehicle with an imaging unit mounted on the vehicle;
A forming step of forming an edge image including a lane marker formed on a running road by differentiating density values of all pixels of the captured image in the imaging step;
Obtaining the coordinates of a plurality of lane marker candidate points from the edge image formed in the forming step, and deriving a road parameter for determining a road model that is running by applying an H∞ filter thereto,
The road model estimation method, wherein the derivation step performs the calculation of the H∞ filter according to a diagonal determinant of the following formula 12 that does not include an inverse matrix.

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