Misfire detection device and misfire detection method for internal combustion engine

Abstract

To provide a misfire detection device and a misfire detection method for an internal combustion engine capable of inexpensively and highly accurately detecting misfire by reducing effects of disturbance in misfire detection to the extent possible.SOLUTION: A misfire detection device detects presence / absence of misfire in an internal combustion engine (1) in which each of an intake stroke, a compression stroke, a combustion stroke and an exhaust stroke is performed in a cylinder (3) through rotation of a crank shaft (6), and includes: a crank position sensor (32) for detecting a crank angle signal (Sn) synchronized with a rotating angle of the crank shaft (6); and a control unit (31) that calculates a plurality of inter-signal times (Xn) that are reception intervals of respective crank angle signals (Sn) on the basis of the plurality of crank angle signals (Sn) detected by the crank position sensor (32). The control unit (31) detects presence / absence of misfire on the basis of each inter-signal time (Xn) in the combustion stroke.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present invention relates to a misfire detection device and a misfire detection method for an internal combustion engine. [Background technology]

[0002] In an internal combustion engine in which the rotation of the crankshaft causes intake, compression, combustion, and exhaust strokes within a cylinder, misfires can occur due to ignition errors within the cylinder. Patent Document 1 discloses a misfire detection method that detects the difference in rotational speed of the crankshaft between after the expansion stroke or the latter part of the expansion stroke and before the expansion stroke or the early part of the expansion stroke, and detects a misfire when this rotational speed difference is equal to or less than a set value.

[0003] A crank position sensor is also known that outputs a crank angle signal synchronized with the rotational angle of the crankshaft. A vehicle control unit receives multiple crank angle signals output by the crank position sensor and is configured to detect multiple inter-signal times, which are the intervals between the received crank angle signals. Conventionally, the vehicle control unit detects the inter-signal times for each of the intake, compression, combustion, and exhaust strokes, and detects a misfire when the inter-signal times for each stroke are outside a predetermined range. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Unexamined Patent Publication No. 58-19532 Summary of the Invention [Problem to be solved by the invention]

[0005] In the above-described conventional technology, it is necessary to monitor the crankshaft rotational speed difference and the time interval between signals detected by the crank position sensor throughout the intake, compression, combustion, and exhaust strokes. Furthermore, when disturbances such as vehicle acceleration, deceleration, clutch operation, shifting, or changes in road surface due to bumps occur, the parameters used for misfire detection, i.e., the crankshaft rotational speed difference and the time interval between signals detected by the crank position sensor, fluctuate. Therefore, when such disturbances occur, a control to inhibit misfire detection is typically performed to prevent erroneous misfire detection. However, it is extremely difficult to anticipate all disturbances that could lead to erroneous misfire detection and then inhibit misfire detection when all disturbances occur. Therefore, there is a need for a low-cost, highly accurate misfire detection system that minimizes the influence of disturbances on misfire detection.

[0006] The present invention has been made in consideration of these problems, and aims to provide a misfire detection device and a misfire detection method for an internal combustion engine that can detect misfires at low cost and with high accuracy by minimizing the influence of external disturbances on misfire detection. [Means for solving the problem]

[0007] In order to achieve the above-mentioned object, the misfire detection device for an internal combustion engine of the present invention is a misfire detection device that detects the presence or absence of misfire in an internal combustion engine in which the intake, compression, combustion, and exhaust strokes occur within a cylinder as the crankshaft rotates, and is equipped with a crank position sensor that detects a crank angle signal synchronized with the rotation angle of the crankshaft, and a control unit that calculates multiple inter-signal times, which are the reception intervals between each of the crank angle signals, based on the multiple crank angle signals detected by the crank position sensor, and the control unit detects the presence or absence of misfire based on each inter-signal time during the combustion stroke.

[0008] In addition, the misfire detection method for an internal combustion engine of the present invention is a misfire detection method for detecting the presence or absence of misfire in an internal combustion engine in which intake, compression, combustion, and exhaust strokes occur within a cylinder as a result of the rotation of a crankshaft, and includes a crank angle signal detection step for detecting a crank angle signal synchronized with the rotation angle of the crankshaft, a signal interval calculation step for calculating multiple signal intervals, which are the reception intervals between each crank angle signal, based on the multiple crank angle signals detected in the crank angle signal detection step, and a determination step for determining the presence or absence of misfire based on each signal interval of the combustion stroke calculated in the signal interval calculation step. [Effects of the Invention]

[0009] According to the misfire detection device and misfire detection method for an internal combustion engine of the present invention, the influence of disturbances on misfire detection can be reduced as much as possible, thereby enabling misfire detection to be performed at low cost and with high accuracy. [Brief explanation of the drawings]

[0010] [Figure 1] 1 is a diagram illustrating a system configuration including a misfire detection device according to an embodiment of the present invention. [Figure 2] 1 is a graph showing time-series changes in inter-signal times during intake, compression, combustion, and exhaust strokes of an engine. [Figure 3] 1 is a table showing the change in the inter-signal time of the combustion stroke with respect to the crank number both in normal and misfire states. [Figure 4] 4 is a graph based on the table of FIG. 3. [Figure 5] 3 is a flowchart illustrating a misfire detection method according to an embodiment of the present invention. [Figure 6] 10 is a table showing the change in the signal intervals during the combustion stroke of the second cylinder in both normal and misfire states when the engine has two cylinders. [Figure 7] 7 is a graph based on the tables of FIGS. 3 and 6. DETAILED DESCRIPTION OF THE INVENTION

[0011] A misfire detection device and a misfire detection method for an internal combustion engine according to the present invention will be described below with reference to the drawings. FIG. 1 shows a system configuration diagram including a misfire detection device according to one embodiment of the present invention. The internal combustion engine 1 shown in FIG. 1 is configured as a 50cc four-stroke single-cylinder gasoline engine and is mounted on, for example, a motorcycle as a power source for driving. A piston 4 is slidably disposed within a cylinder 3 formed in a cylinder block 2 of the engine 1. The piston 4 is connected to a crankshaft 6 via a connecting rod 5, and the crankshaft 6 rotates in conjunction with the reciprocating motion of the piston 4. A flywheel 7 is attached to the rear end (on the transmission side, not shown) of the crankshaft 6, and a number of protruding reluctors 7a are formed at predetermined positions on the outer periphery of the flywheel 7 to detect the rotational angle of the crankshaft (crank angle).

[0012] A cylinder head 9 fixed to the cylinder block 2 is formed with an intake port 9a and an exhaust port 9b, and is provided with an ignition plug 10 with its tip facing into the cylinder 3. An air cleaner 12, a throttle valve 13, and an injector 16 are provided in an intake passage 11 connected to the intake port 9a, from upstream to downstream. The throttle valve 13 opens and closes in response to throttle operation by the driver. The injector 16 injects fuel toward the intake port 9a. An exhaust passage 17 connected to the exhaust port 9b is provided with a three-way catalyst 18 for purifying exhaust gases and a silencer (not shown).

[0013] An intake valve 20 is disposed in the intake port 9a, and an exhaust valve 21 is disposed in the exhaust port 9b. These intake and exhaust valves 20, 21 are biased toward the valve closing direction by a valve spring 22 and are opened by an intake camshaft 23 and an exhaust camshaft 24 that are rotated on the cylinder head 9 in synchronization with the crankshaft 6. As a result, the intake valve 20 and the exhaust valve 21 open and close at predetermined timing synchronized with the reciprocating motion of the piston 4, and the combustion cycle of the engine 1, consisting of four strokes: intake, compression, combustion (expansion), and exhaust, is repeated every 720° CA of crank angle. Fuel (gasoline) stored in a fuel tank (not shown) is supplied to the injector 16 by a fuel pump (not shown), and the fuel is injected toward the intake port 9a at a predetermined injection timing and injection amount in response to the opening of the injector 16.

[0014] During engine 1 operation, outside air is drawn into intake passage 11 through air cleaner 12 due to negative pressure generated by the downward movement of piston 4 during the intake stroke. The intake air has its flow rate adjusted according to the opening of throttle valve 13, and then flows into cylinder 3 of engine 1 while intake valve 20 is open, while being mixed with fuel injected from injector 16. After being compressed during the subsequent compression stroke, the mixture is ignited by spark plug 10 near top dead center of compression and burns during the combustion stroke, imparting rotational force to crankshaft 6 via piston 4. During the subsequent exhaust stroke, burned exhaust gas is discharged from cylinder 3 while exhaust valve 21 is open, flows through exhaust passage 17, passes through three-way catalyst 18 and a silencer, and is then discharged to the outside.

[0015] The combustion cycle of the engine 1 described above is executed under the control of an ECU 31 (control unit). Various sensors, such as a crank position sensor 32, a throttle sensor 33, an O2 sensor 34, and a water temperature sensor 35, are connected to the input side of the ECU 31. The crank position sensor 32 is disposed opposite the flywheel 7 and outputs a crank angle signal S (described later) synchronized with the reluctor 7a. nThe throttle sensor 33 detects the opening of the throttle valve 13. The O2 sensor 34 is disposed in the exhaust passage 17 and varies its output in a stepwise manner in response to fluctuations in the exhaust air-fuel ratio around the stoichiometric (theoretical air-fuel ratio). The water temperature sensor 35 detects the coolant temperature Tw of the engine 1. In addition, various devices such as the injector 16, the fuel pump, and an igniter 36 that drives the spark plug 10 are connected to the output side of the ECU 31.

[0016] Based on the information from these sensors, the ECU 31 executes various controls, such as fuel injection control for driving the injector 16, ignition timing control for driving the spark plug 10, and pump control for driving the fuel pump, to operate the engine 1. For example, as fuel injection control, the ECU 31 determines a target fuel injection amount based on the engine rotation speed Ne calculated from the signal of the crank position sensor 32 and the throttle opening θth detected by the throttle sensor 33, and so on, and drives the injector 16 at a predetermined timing synchronized with the combustion cycle of the engine 1 to perform fuel injection.

[0017] The ECU 31 controls the ignition timing by determining the target ignition timing based on the engine rotation speed Ne and the throttle opening θth, etc., and also by shaping the waveform of the signal from the crank position sensor 32 to generate a square-wave crank angle signal S synchronized with the reluctor 7a (in other words, the crank angle). n Then, the crank angle signal S n The ECU 31 determines the timing corresponding to the target ignition timing based on the crank angle signal S detected by the crank position sensor 32, and drives the igniter 36 to ignite the spark plug 10. n Based on this, each crank angle signal S n The signal interval time X is the reception interval of n Furthermore, the ECU 31 includes a gradient calculation unit 37 and a determination unit 38, which will be described in detail later.

[0018] Figure 2 shows the signal intervals X during the intake, compression, combustion, and exhaust strokes of engine 1. nThe graph shows the time series change of the signal time X during normal operation when no misfire occurs. n 2 in each stroke. In particular, in the combustion stroke, as a result of the combustion of fuel in the cylinder 3, the rotational speed of the crankshaft 6 increases, in other words, the engine speed increases, and the signal interval time X n On the other hand, when a misfire occurs, fuel does not burn in the cylinder 3, so the rotation speed of the crankshaft 6 decreases during the combustion stroke. In other words, the engine speed decreases, so the signal interval time X n The misfire detection device of this embodiment detects the time between signals X during a normal combustion stroke and the time between signals X during a misfire stroke, and the time between signals X during a normal combustion stroke and the time between signals X during a misfire stroke. n Focusing on the significant difference between the signals, X n Based on this, the presence or absence of misfire in cylinder 3 is detected.

[0019] Figure 3 shows the signal interval X of the combustion stroke in both normal and misfire conditions. n FIG. 4 shows a graph based on the table of FIG. 3. FIG. 4 shows in more detail the graph lines in the combustion stroke shown in FIG. 2 based on the data in the table of FIG. 3. Crank numbers N from 0 to 23 corresponding to the crank angles are defined, and the crank angle signals S corresponding to each crank number 0 to 23 are 0~23 For example, crank number 0 corresponds to a crank angle of 0 degrees, crank number 1 corresponds to a crank angle of 15 degrees, crank number 12 corresponds to a crank angle of 180 degrees, and crank number 23 corresponds to a crank angle of 345 degrees. The ECU 31 generates a crank angle signal S corresponding to each crank number N in each stroke. n is received from the crank position sensor 32.

[0020] In this embodiment, the crank angle signals S of the crank angles corresponding to the crank numbers 12, 17, 18, 19, and 20 in the combustion stroke are 12,17,18,19,20 is used to detect misfires. As shown in Figure 3, the crank angle signal S12,17,18,19,20 The normal signal interval X when receiving n are X 12,17,18,19,20 On the other hand, the crank angle signal S 12,17,18,19,20 Time between signals when misfire occurs when receiving X n are X' respectively. 12,17,18,19,20 Here, the gradient calculation unit 37 built in the ECU 31 calculates the time interval X n When the above equations are plotted, an approximate line L is created by the least squares method, and then the slope a of the approximate line L is calculated. The least squares method is a technique for finding the most likely relational equation of an approximate line by performing calculations so as to minimize the sum of the squares of the errors when processing measured values ​​that involve errors. This technique itself is well known, so a detailed explanation will be omitted.

[0021] The determination unit 38 built in the ECU 31 determines whether the slope a of the approximate line L calculated by the slope calculation unit 37 is equal to or greater than a predetermined threshold a s The number of times (number of times misfire is detected) n is equal to or exceeds a predetermined number n s When this is the case, it is determined that a misfire has occurred. Specifically, as shown by the dashed line in Figure 4, the approximate line L1 during normal operation is expressed by the formula y = a1·X + b1. On the other hand, the approximate line L2 during misfire is expressed by the formula y = a2·X + b2, as shown by the dashed line in Figure 4. The slope a1 is the time between signals X n The crank angle signal S used for misfire detection is calculated from an approximate straight line when the crank angle signal S is plotted on the vertical axis and the time when the crank number N changes over time is plotted on the horizontal axis. In this embodiment, the slope a1 is a negative value and the slope a2 is a positive value. However, the present invention is not limited to this. n Depending on the selection of the threshold a, the slopes a1 and a2 can be either positive or negative. s is set to an appropriate value that is at least between the slope a1 in normal operation and the slope a2 in misfire operation and that allows reliable detection of misfire.

[0022] FIG. 5 is a flowchart illustrating a misfire detection method according to one embodiment of the present invention. When misfire detection is initiated in the ECU 31, first in step S1 it is determined whether or not misfire detection is permitted. The misfire detection permission is output based on specific conditions under which misfire detection is permitted under regulations, such as the altitude at which the vehicle is located, atmospheric pressure, engine speed, and whether the crank position sensor 32 is malfunctioning. If the determination result is Yes, meaning that misfire detection is permitted, the process proceeds to step S2. On the other hand, if the determination result is No, meaning that misfire detection is not permitted, the misfire detection ends. Next, in step S2, the crank position sensor 32 outputs a crank angle signal S synchronized with the rotation angle of the crankshaft 6, i.e., the crank angle. n Next, in step S3, the ECU 31 detects the crank angle signals S detected in the crank angle signal detection step. n Based on this, each crank angle signal S n The signal interval time X is the reception interval of n (signal time calculation step).

[0023] Next, in step S4, the gradient calculation unit 37 calculates the time interval X between signals in the combustion stroke. n After creating an approximate line L by the least squares method when plotting, the gradient a of the approximate line L is calculated (gradient calculation step). Next, in step S5, the determination unit 38 determines whether the gradient a of the approximate line L calculated in the gradient calculation step is greater than or equal to a predetermined threshold a s It is determined whether or not the result is equal to or greater than a (determination step). If the determination result is Yes, and a≧a s If the result is No, and a≧a s If the above equation is not satisfied, it is determined that no misfire has occurred, and the misfire detection is terminated.

[0024] Next, in step S6, a ≧ a s is satisfied, that is, the number of times N of misfire detections is a predetermined number N s If the result of the determination is Yes, and N≧N, it is determined whether N is equal to or greater than N (step of determining the number of times of misfire detection). sIf the above is true, it is determined that a misfire has occurred, and the process proceeds to step S7, where a "misfire has occurred" message is output, and then misfire detection is terminated. If it is determined that a misfire has occurred, appropriate measures are taken, such as flashing the malfunction warning light or stopping the engine 1. On the other hand, if the determination result is No, and N≧N s If the condition is not satisfied, it is determined that a misfire has not actually occurred, although a temporary misfire is detected, and the misfire detection is terminated. n In other words, in this embodiment, the presence or absence of a misfire is determined based on the signal intervals X n is not used to determine misfire.

[0025] FIG. 6 shows the signal interval X of the combustion stroke in both the normal state and the misfire state of the second cylinder 3B when the engine 1 has two cylinders (hereinafter referred to as the first cylinder 3A and the second cylinder 3B). n The change in the signal interval X of the combustion stroke of the first cylinder 3A is shown in a table. Also, FIG. 7 shows a graph based on the tables of FIG. 3 and FIG. 6. n 3, and the graph line (dotted line) for "#1 misfire" and the graph line (solid line) for "#1 normal" are shown in FIG. 7. In the second cylinder 3B, as shown in FIG. 6, the crank angle signal S 22,23,0,1,2,3,4 is used for misfire detection.

[0026] As shown in FIG. 6, the crank angle signal S 22,23,0,1,2,3,4 The normal signal interval X when receiving n are X 22,23,0,1,2,3,4 On the other hand, the crank angle signal S 22,23,0,1,2,3,4 Time between signals when misfire occurs when receiving X n are X' respectively. 22,23,0,1,2,3,4 The signal interval X of the combustion stroke of the second cylinder 3B is n7 shows a graph line (two-dot chain line) for "#2 misfire" and a graph line (solid line) for "#2 normal." Also shown in FIG. 7 are the "#1 compression top dead center" of the first cylinder 3A and the "#2 compression top dead center" of the second cylinder 3B. Additionally, FIG. 7 shows the equations of the approximate straight line L1 (y=a1·X+b1) for "#1 normal" and the equations of the approximate straight line L2 (y=a2·X+b2) for "#1 misfire." Furthermore, FIG. 7 shows the equations of the approximate straight line L3 (y=a3·X+b3) for "#2 normal" and the equations of the approximate straight line L4 (y=a4·X+b4) for "#2 misfire."

[0027] In a gradient calculation step S4, the gradient calculation unit 37 creates an approximate straight line L in the combustion stroke of the first cylinder 3A and the second cylinder 3B by the least squares method, and then calculates the gradient a of each approximate straight line L. In a judgment step S5, the judgment unit 38 judges whether or not the gradient a of any of the approximate straight lines L is equal to or greater than a predetermined threshold a. s It is determined that the number of misfire detections n is equal to or greater than the predetermined number n in the determination step S6. s In other words, if the slope a of the approximate line L for either the first cylinder 3A or the second cylinder 3B deviates from a1 or a3 and becomes closer to a2 or a4, respectively, it is determined that either or both of the first cylinder 3A and the second cylinder 3B have misfired.

[0028] As described above, in the misfire detection device and the misfire detection method using the device of this embodiment, in the crank angle signal detection step S2, the crank position sensor 32 detects the crank angle signal S synchronized with the rotation angle of the crankshaft 6. n Next, in a signal interval calculation step S3, the ECU 31 calculates the interval between the detected crank angle signals S n Based on this, each crank angle signal S n The signal interval time X is the reception interval of n Then, in a determination step S5, the ECU 31 calculates a plurality of inter-signal times X n In this way, the parameter used for misfire detection is the signal interval X nBy limiting it to only the signal interval X n Furthermore, since it is sufficient to monitor only the combustion stroke, it is not necessary to anticipate all disturbances that could lead to erroneous misfire detection, and it is not necessary to perform control to inhibit misfire detection when all disturbances occur. Therefore, the influence of disturbances on misfire detection can be minimized, allowing for low-cost and highly accurate misfire detection.

[0029] More specifically, in the gradient calculation step S4, the gradient calculation unit 37 of the ECU 31 calculates the time interval X between signals in the combustion stroke. n After plotting the above, an approximate line L is created by the least squares method, and then the gradient a of the approximate line L is calculated. In addition, in the determination step S5, the determination unit 38 of the ECU 31 determines whether the gradient a of the approximate line L calculated by the gradient calculation unit 37 is equal to or greater than a predetermined threshold a s The number of times n s When the above signal intervals occur, it is determined that a misfire has occurred. n By creating an approximate straight line L based on the above equation and determining whether or not a misfire has occurred based on the slope a of the approximate straight line L, misfire detection can be performed easily and reliably.

[0030] 7, even if the engine 1 is a two-cylinder engine, the slope calculation unit 37 creates an approximate line L for each of the cylinders 3A and 3B by the least squares method in the slope calculation step S4, and then calculates the slope a of each approximate line L. Furthermore, the determination unit 38 determines in the determination step S5 whether the slope a of any of the approximate lines L is greater than or equal to the threshold value a s The number of times n s When any of the above occurs, it is determined that a misfire has occurred. This allows misfire detection in each of the cylinders 3A and 3B to be detected at low cost and with high accuracy, even in the case of a two-cylinder engine, by minimizing the influence of external disturbances on misfire detection.

[0031] Although the description of the embodiment of the present invention has been completed above, the present invention is not limited to the above embodiment, and various modifications can be made without departing from the spirit of the present invention. For example, the crank angle signal S used for misfire detection may be n The crank number N corresponding to the number N is not limited to that described in the above embodiment, but a crank number N that facilitates misfire detection during the combustion stroke can be appropriately selected depending on the processing load of the ECU 31. The present invention is also applicable to engine 1 having three or more cylinders. [Explanation of symbols]

[0032] 1. Engine (internal combustion engine) 3 cylinders 6 crankshaft 31 ECU (control unit) 32 Crank position sensor 37 Tilt calculation section 38 Judgment section S n Crank angle signal X n Inter-signal time L approximate straight line a Tilt a s Threshold n s Predetermined number of times S2 Crank angle signal detection step S3 Signal time calculation step S4 Slope calculation step S5 Judgment step

Claims

1. A misfire detection device for detecting the presence or absence of misfire in an internal combustion engine in which intake, compression, combustion, and exhaust strokes occur in a cylinder as a result of rotation of a crankshaft, a crank position sensor that detects a crank angle signal synchronized with the rotation angle of the crankshaft; a control unit that calculates a plurality of inter-signal times, which are reception intervals of the crank angle signals, based on the plurality of crank angle signals detected by the crank position sensor; Equipped with The control unit detects whether or not a misfire has occurred based on the time between each of the signals during the combustion stroke.

2. The control unit a gradient calculation unit that calculates a gradient of an approximate straight line when the time between the signals in the combustion stroke is plotted on the vertical axis and time is plotted on the horizontal axis; a determination unit that determines that the misfire has occurred when the gradient of the approximation line calculated by the gradient calculation unit is equal to or greater than a predetermined threshold value a predetermined number of times or more; 2. The misfire detection device for an internal combustion engine according to claim 1, further comprising:

3. the internal combustion engine has a plurality of the cylinders, the gradient calculation unit calculates the gradient of the approximate straight line for each of the cylinders; 3. The misfire detection device for an internal combustion engine according to claim 2, wherein the determination unit determines that the misfire has occurred when the slope of any of the approximate lines is equal to or greater than the threshold value a predetermined number of times or more.

4. 4. The misfire detection device for an internal combustion engine according to claim 2, wherein the gradient calculation section creates the approximation line by a least squares method.

5. A misfire detection method for detecting the presence or absence of a misfire in an internal combustion engine in which intake, compression, combustion, and exhaust strokes occur in a cylinder as a result of rotation of a crankshaft, comprising: a crank angle signal detecting step of detecting a crank angle signal synchronized with the rotation angle of the crankshaft; a signal interval calculation step of calculating a plurality of signal intervals, which are reception intervals of the crank angle signals, based on the plurality of crank angle signals detected in the crank angle signal detection step; a determination step of determining whether or not a misfire has occurred based on the signal intervals of the combustion stroke calculated in the signal interval calculation step; A method for detecting misfire in an internal combustion engine, comprising:

6. a gradient calculation step of calculating a gradient of an approximate straight line when the time between the signals in the combustion stroke is plotted on the vertical axis and time is plotted on the horizontal axis, 6. The misfire detection method for an internal combustion engine according to claim 5, wherein the determining step determines that the misfire has occurred when the slope of the approximate straight line calculated in the slope calculating step is equal to or greater than a predetermined threshold value a predetermined number of times or more.

7. the internal combustion engine has a plurality of the cylinders, the gradient calculation step calculates the gradient of the approximate straight line for each of the cylinders; 7. The misfire detection method for an internal combustion engine according to claim 6, wherein the determining step determines that the misfire has occurred when the gradient of any of the approximate straight lines is equal to or greater than the threshold value a predetermined number of times or more.

8. 8. The method for detecting a misfire in an internal combustion engine according to claim 6, wherein said gradient calculation step creates said approximation line by a least squares method.

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