Method and control unit for estimating fuel injection quantity

Abstract

A method performed by a processing circuit (e.g., a control unit of or coupled to a vehicle) for estimating an amount of fuel injected by a fuel injector of an internal combustion engine. A processing circuit is coupled to the one or more pressure sensors configured to output a rail pressure of a fuel common rail that supplies fuel to the fuel injector in use. The fuel injector is configured to inject fuel in response to receiving each of one or more drive pulses (e.g., from the processing circuitry), the drive pulses having a predetermined duration. The method includes receiving a plurality of pre-injection rail pressure values and a plurality of post-injection rail pressure values corresponding to rail pressure values before and after a drive pulse, respectively. An upper rail pressure value at the index value at a predetermined point in time within the drive pulse is then determined by extrapolating from the pre-injection rail pressure value. Similarly, a lower rail pressure value at the index value at the predetermined point in time is determined by extrapolating from the post-injection rail pressure value. The upper rail pressure value and the lower rail pressure value are preferably obtained by estimating a pre-injection regression line and a post-injection regression line through a least square method based on the rail pressure values; and the pressure drop is preferably obtained by determining the difference between the upper rail pressure value and the lower rail pressure value at the center of the drive pulse. An amount of fuel injected by the fuel injector is then derived from the determined pressure drop. The invention further discloses a control unit and a vehicle comprising the control unit.

Description

Technical Field

[0001] This invention generally relates to internal combustion engines and their fuel injectors. More specifically, it relates to an improved method and control unit for estimating the amount of fuel injected by a fuel injector. Background Technology

[0002] It is known to estimate the amount of fuel injected by a fuel injector using pressure drop analysis (PDA), in which one or more sensors measure the rail pressure drop of the fuel common rail supplying fuel to the injector—the pressure difference before and after injection—and then use this pressure drop to calculate the fuel quantity. GB 2533104 A discloses a common PDA strategy. This estimation is useful because the fuel quantity can be compared with a calculated / expected fuel quantity (e.g., based on the current torque demand of the engine using the injector) to record discrepancies or issue an alert when the discrepancy exceeds a threshold.

[0003] Typically, under the control of a control unit (such as the vehicle's electronic control unit (ECU)), drive pulses are provided to the injectors (e.g., via power electronics), and the timing and duration of these drive pulses, determined by the control unit, cause the fuel injectors to operate in order to inject fuel.

[0004] As discussed in more detail below, existing methods use averaging or other techniques to determine the rail pressure before and after injection.

[0005] Technical issues

[0006] One problem is that the estimation of low fuel injection quantities is not ideal for known technologies, particularly in high-pressure systems such as diesel and gasoline direct injection engines and hydrogen propulsion systems. Furthermore, these technologies cannot adequately handle variations in (fuel) temperature and injector seat wear, and are susceptible to static leakage.

[0007] The purpose of this invention is to avoid the aforementioned problems and to provide a method and control unit that takes into account the actual static leakage of the injector when calculating pressure drop (especially in PDA analysis). Summary of the Invention

[0008] To address the above problems, the present invention provides a method according to claim 1.

[0009] The method of the present invention is executed by a processing circuit (or a control unit) for estimating the amount of fuel injected by a fuel injector of an internal combustion engine. The processing circuit is coupled to one or more pressure sensors configured to output the rail pressure of the common rail supplying fuel to the fuel injector during use. The fuel injector is configured to inject fuel in response to receiving each of one or more drive pulses having a predetermined duration. The method includes: Receive multiple pre-injection rail pressure values ​​and multiple post-injection rail pressure values, which correspond to the rail pressure values ​​before and after the time window corresponding to the timing of the injection event, respectively; By extrapolating from the pre-jet rail pressure value, the upper rail pressure value at a predetermined time point within the time period corresponding to the jetting event is determined; The lower rail pressure value at the predetermined time point is determined by extrapolating from the jetting rear rail pressure value. The pressure drop is determined as the difference between the upper rail pressure value and the lower rail pressure value; and The amount of fuel injected by the fuel injector is derived from the determined pressure drop.

[0010] The method of this invention provides an improved PDA strategy that relies on the processing of rail pressure data before and after the corresponding injection event. Advantageously, the pressure data / values ​​before and after injection are fitted by regression analysis, and the upper and lower rail pressure values ​​are determined by extrapolation over a time period during the duration of the injection event. The method of this invention accounts for static leakage more reliably than prior art strategies.

[0011] The method of this invention was developed for use in diesel engines, where fuel injectors typically exhibit static leakage (leading to a drop in rail pressure) due to design flaws. However, the method of this invention can also be applied to other types of fuel systems, particularly fuel delivery systems for gaseous fuels (H2 or CNG), where there is continuous filling of the common rail (more likely to cause a rise in rail pressure). In other words, the method of this invention can be applied to fuel delivery systems where the fuel rail pressure exhibits a continuous trend of change (rising or falling) due to system design.

[0012] The method of the present invention can generally be implemented in methods for controlling internal combustion engines, wherein the obtained fuel quantity injected by the fuel injector is used for fuel injection control. In particular, the obtained fuel quantity can be used to develop injector-specific calibration parameters for constructing command signals applied to the respective injectors.

[0013] In this process, the pressure drop is determined based on extrapolated pre- and post-injection values ​​within a time period corresponding to the injection event. The start and end times of this time period can correspond to the start and end times of the drive (or command) pulse applied to the injector, or to the start and end times of the corresponding hydraulic pulse. The term hydraulic pulse here refers to the actual duration for which the injector is open.

[0014] In an implementation, a predetermined time point within a time window is (i) the center of the time window, or (ii) located within a predetermined time interval from the center of the time window. Preferably, the value of the predetermined time interval is in the range of 1% to 40% of the duration of the time window.

[0015] Preferably, (i) determining the upper rail pressure value includes deriving the injection front line from the injection front rail pressure value, and / or (ii) determining the lower rail pressure value includes deriving the injection rear line from the injection rear rail pressure value.

[0016] The received pressure values ​​can be "associated with the corresponding index value corresponding to the duration elapsed since the initial point," which essentially means that these values ​​can be associated with a corresponding point in time, which can be expressed in time (e.g., seconds or milliseconds) or crankshaft rotation angles.

[0017] In fact, deriving the injection front line from the rail pressure values ​​before / after injection may mean calculating the parameters of a line, namely the slope and the y-intercept.

[0018] Preferably, (i) the injection front line is derived by calculating a mathematical regression of the received injection front rail pressure values ​​so as to estimate the injection front regression line on the index value graph using the least squares method, and / or (ii) the injection back line is derived by calculating a mathematical regression of multiple received injection back rail pressure values ​​so as to estimate the injection back regression line on the graph using the least squares method.

[0019] Preferably, the plurality of received post-jet rail pressure values ​​include a set of rail pressure values ​​received after a time margin since the end of the drive pulse.

[0020] Preferably, (i) determining the upper rail pressure value includes extrapolating along the injection front line, wherein the upper rail pressure value is the pressure value at the intersection of the extrapolated injection front line and the straight line passing through the index value at the predetermined time point, and / or (ii) determining the lower rail pressure value includes extrapolating along the injection back line, wherein the lower rail pressure value is the pressure value at the intersection of the extrapolated injection back line and the straight line passing through the index value at the predetermined time point.

[0021] In one embodiment, extrapolation along the injection front line includes extrapolating from the last of the plurality of injection front rail pressure values ​​received.

[0022] In one embodiment, extrapolating along the post-injection line includes (i) extrapolating from the first one received from the plurality of post-injection rail pressure values, or (ii) extrapolating from the first rail pressure value in the set of rail pressure values ​​after a time margin has elapsed.

[0023] In one embodiment, pushing outward along the front spray line includes pushing outward from its lower end, and / or pushing outward along the rear spray line includes pushing outward from its top end.

[0024] Preferably, (i) the lower end of the injection front line or the last one received among the plurality of injection front rail pressure values ​​corresponds to the start of the drive pulse, and / or (ii) the top end of the injection rear line or the first one received among the plurality of injection rear rail pressure values ​​corresponds to the end of the drive pulse or the time point after the time margin has elapsed since the end of the drive pulse.

[0025] Preferably, deriving the injected fuel quantity involves using the relationship between rail pressure drop and the injected fuel quantity, which preferably depends on at least one of fuel type, temperature, injector type, and system pressure. For example, deriving the injected fuel quantity involves using the determined pressure drop to access a pre-stored lookup table to return the injected fuel quantity as an estimate, preferably based on one or more of these parameters.

[0026] Preferably, the initial point corresponds to the end of the previous pumping operation by the fuel injector, or to the start of receiving the plurality of injection front rail pressure values.

[0027] Preferably, the lower end of the injection rail corresponds to the start of the next pumping operation by the fuel injector, or to the end of receiving the plurality of injection rail pressure values.

[0028] Preferably, the index value corresponds to the engine angular position.

[0029] This method can typically be implemented by software (program code / instructions) implemented by a computer (such as an engine control unit or its modules).

[0030] According to another aspect of the invention, an engine control unit is provided for estimating the amount of fuel injected by the fuel injector of an internal combustion engine, the control unit including processing circuitry configured to perform the method of any one of the appended claims 1 to 13.

[0031] According to another aspect of the present invention, a vehicle comprising the engine control unit described in the foregoing paragraphs is provided.

[0032] According to another aspect of the present invention, a computer program product is provided, comprising instructions that, when executed by a processing circuit, cause the method of any one of claims 1 to 16 to be performed.

[0033] One advantage of this invention is that it can more accurately estimate fuel injection quantity in order to account for actual static leakage of the injector, especially in high-pressure systems. Attached Figure Description

[0034] Further details and advantages of the invention will become apparent from the detailed description of non-limiting embodiments with reference to the accompanying drawings, in which: Figure 1 (Prior art) is a known technique for estimating fuel quantity in gasoline systems, which is a graph of fuel rail pressure relative to engine angle. Figure 2 (Prior art) is a graph of fuel rail pressure relative to an index, used for, for example Figure 1 Known techniques for estimating fuel quantity in the gasoline system shown; Figure 3(a) (Prior Art) and Figure 3(b) (Prior Art) are curves of fuel rail pressure relative to the index under normal fuel quantity and low fuel quantity conditions in known techniques for fuel quantity estimation in diesel systems, respectively. Figure 4 It is a graph illustrating the fuel rail pressure relative to an index according to an embodiment of the fuel quantity estimation technique of the present invention; Figure 5 This is a flowchart of the fuel quantity estimation process according to an embodiment of the present invention; Figure 6 This is a graph of fuel rail pressure drop versus rail pressure, comparing known median-based techniques (upper graph) with a technique according to an embodiment of the present invention (lower graph); and Figure 7 This is a schematic diagram of a vehicle fuel system in which the technology according to embodiments of the present invention can be used. Detailed Implementation

[0035] In the following text, the same reference numerals denote the same parts, and unless otherwise stated herein, any element, design feature, or method step of any embodiment may be used in combination with elements, design features, or method steps of any other embodiment.

[0036] First, refer to Figure 7 This is a schematic diagram of a vehicle fuel system 10, in which the technology according to an embodiment of the present invention can be used. Such a fuel system is well known and will only be briefly described.

[0037] Fuel system 10 includes a common fuel rail 1 (or accumulator) that fluidly connects fuel therein to a series of injectors 2 (e.g., electromagnetically driven fuel injectors). This circuit typically includes an in-tank electric fuel pump 3, a fuel filter 4, and a high-pressure pump 5. A high-pressure sensor 6, as shown, is located on the common rail 1 to measure the fuel pressure within the common rail 1. A high-pressure valve 8 is provided on the common rail 1; it is a safety valve that opens (potentially passive or controllable) when the pressure exceeds a preset value. Reference numeral 7 indicates a return circuit that includes a return regulator and injector return lines, which is typically present in diesel fuel injection systems. This return circuit 7 is typically used for indirectly controlled fuel injectors (diesel injectors include electromagnetically controlled valves with hydraulically controlled needle valves), but is not required for injectors whose needles are directly controlled by electromagnets (typically via an armature connected to the needle, such as gasoline or gas fuel injectors). Fuel system 10 also includes an electronic controller 36, such as an engine control unit, which is connected to various operating components of the fuel delivery system, fuel pumps, sensors, and injectors. The controller 36 typically includes at least one processor and memory, and is configured to control functions such as fuel injection. The controller 36 is configured to operate the method of the present invention via hardware and / or software.

[0038] Now back Figure 1 (Prior art) It is a known technique for estimating fuel quantity in a gasoline system, which uses a graph of fuel rail pressure relative to engine angle. Fuel quantity estimation is performed by processing the rail pressure signal (e.g., from pressure sensor 6), cleaning it, and analyzing the pressure levels before and after injection. The injection (cycle) is specified as 100, and its duration substantially corresponds to the duration of the drive (or command) pulse (e.g., from controller 36), i.e. D P .

[0039] Used to calculate the rail pressure drop Δ of the fuel injected by the injector. P The assessment and handling are as follows: Calculate the average (or median) value of the pre-injection pressure level 102 (see... Figure 1 (the "maximum pressure") Calculate the average (or median) value of the pressure level 104 after injection (see... Figure 1 "Minimum pressure" in the text, and By using the determined pressure drop Δ P The amount of fuel injected is retrieved from a lookup table and returned as an estimate. This lookup table typically returns the fuel quantity value based on the determined pressure drop and rail pressure (measured by sensor 6).

[0040] Figure 2 (Prior art) is a graph of fuel rail pressure relative to an index, used for, for example Figure 1The diagram illustrates a known technique for estimating fuel quantity in a gasoline system. The graph demonstrates that, due to the highly stable rail pressure, the aforementioned mean / median-based technique performs satisfactorily for gasoline systems with low rail pressure values.

[0041] Figures 3(a) (Prior Art) and 3(b) (Prior Art) are curves of fuel rail pressure relative to the index under normal and low fuel quantity conditions in known techniques for fuel quantity estimation in diesel systems.

[0042] In diesel systems, where a significantly higher fuel rail pressure is involved compared to gasoline systems, the results are worse because: The higher rail pressure value produces more pressure fluctuations (see Figure 3(a): significant fluctuations are clearly visible in the curves in both the pre-injection section 302 and the post-injection section 306). Unlike gasoline injectors, diesel injectors exhibit static leakage (see Figure 3(b): apart from the significant fluctuations 304 in the pre-injection section 302 and 308 in the post-injection section 306, both sections show a decreasing trend over time due to static leakage). Due to the higher rail pressure, fuel temperature changes are more significant, and Low fuel quantity estimates are more important for good combustion (see Figure 3(b)).

[0043] In addition, alternative (non-mean / median based) techniques have been employed to attempt to address some of the aforementioned problems. For example, techniques using probability density functions have been proposed.

[0044] <Method of the Invention>

[0045] Figure 4 (a) is a graph of fuel rail pressure relative to an index, used to illustrate the fuel quantity estimation technique according to an embodiment of the present invention. Figure 4 (b) is Figure 4 (a) An enlarged view of the graph section, showing the possible locations of the predetermined time points. Figure 5 This is a flowchart of the fuel quantity estimation process according to an embodiment of the present invention.

[0046] Reference Figure 5 This describes the process by the processing circuit (e.g.) Figure 7 The process executed by the electronic controller 36) in the internal combustion engine (not shown) is used to estimate the amount of fuel injected by the fuel injector 2. For this purpose, through... Figure 7Pressure sensor 6 (configured to output the rail pressure of fuel common rail 1 during engine operation) acquires rail pressure data / values, with the acquisition time covering an analysis window for a given injection event. Fuel injector 2 is configured to selectively execute fuel injection events by injecting fuel in response to a drive pulse (or drive signal or command signal) applied to the injector, for example, a drive pulse generated by processing circuitry, which has a predetermined duration (referred to as pulse width).

[0047] ECU 36 is configured to process rail pressure data according to the method of the present invention. For simplicity, the terms rail pressure value or rail pressure data are used as synonyms. The rail pressure value represents the pressure in the fuel common rail 1 and may correspond to the direct reading of sensor 6, the absolute value, or any other value expressed based on a predetermined calculation method and with reference to a predetermined reference.

[0048] The process begins by receiving (step s602) multiple pre-injection rail pressure values ​​and multiple post-injection rail pressure values, for example, from pressure sensor 6. These values ​​correspond to rail pressure values ​​before (e.g., in pre-injection portion 302) and after (e.g., in post-injection portion 306), respectively. Figure 4 In the middle, corresponding to the injection cycle 100 ( Figure 1 ), duration is D P The spray event is specified as 500.

[0049] Each of the pre-injection rail pressure and post-injection rail pressure values ​​is preferably associated with a corresponding index value, which corresponds to the elapsed time since the initial point. This initial point may correspond to the end of the previous pumping operation by the fuel injector (point 0), or to a predetermined start point B1 for receiving the plurality of pre-injection rail pressure values ​​(see [link to relevant documentation]). Figure 4 The index value can correspond to the engine angular position (or the corresponding time). In other words, the pressure value is associated with a time base.

[0050] In the post-injection section 306, the last received post-injection rail pressure value may correspond to the start of the next pumping event of the fuel pump, or to E1, which is scheduled to end the reception of the plurality of post-injection rail pressure values.

[0051] exist Figure 4 In this context, B and E represent the start and end of the drive pulse 500 corresponding to the observed injection event, respectively. In one embodiment, the plurality of received post-injection rail pressure values ​​comprise a set of rail pressure values ​​received after a time margin TM from the end of the drive pulse. One advantage of using the time margin TM is that it can eliminate injection pressure fluctuations, thereby improving the accuracy of pressure drop calculations. Similarly, a pre-injection time margin can be applied, whereby the received pre-injection rail pressure values ​​comprise a set of rail pressure values ​​up to point B before the start of that time margin.

[0052] In one embodiment, the last of the plurality of pre-jet rail pressure values ​​received corresponds to the start B of the drive pulse 500. Alternatively or additionally, the first of the plurality of post-jet rail pressure values ​​received corresponds to the end E of the drive pulse, or to a time point L after a time margin TM has elapsed since the end of the drive pulse 500.

[0053] As mentioned earlier, in this case, time period 500 is the driving pulse, so point B can correspond to the moment when the injection begins (crankshaft angle) or point E can correspond to the moment when the injection ends; the time period between points B and E can correspond to the pulse width.

[0054] Alternatively, time period 500 can represent the hydraulic pulse of the fuel injector caused by the drive pulse. In this case, B would be the moment when the injector reaches the fully open position (i.e., the so-called opening delay moment), and point E would be the moment when the injector is stationary in the closed position (i.e., the so-called closing delay moment).

[0055] Back Figure 5 Step s602 is followed by step s604: The upper rail pressure value PU at a predetermined time point (or predetermined index value) within the drive pulse 500 is determined by extrapolating from the injection front rail pressure value. In one embodiment, this predetermined time point is the center M of the drive pulse 500 (see...). Figure 4 Alternatively, the predetermined time point can be any position between B and E in drive pulse 500.

[0056] For example, the predetermined time point is not the center M of the drive pulse 500, but can be a point located within a predetermined time interval S from the center M of the drive pulse. Preferably, the value of this predetermined time interval S is within the duration D of the drive pulse 500. P Within the range of 1% to 45%, on either side of M.

[0057] Back Figure 5 Step s604 is followed by step s606: by extrapolating from the injection rear rail pressure value, the lower rail pressure value at the index value at the predetermined time point (e.g., M) is determined. P L (For comparison, in) Figure 4 In the middle, the upper and lower pressure values ​​obtained using the old mean / median-based method are expressed as: O U and O L 。

[0058] In particular, determining the upper rail pressure value P U This includes deriving the injection front line from the received rail pressure value, and / or (ii) determining the lower rail pressure value. PL This includes deriving the post-injection curve. The idea is to have a curve that fits the pressure values ​​before and after injection, allowing for extrapolation over the time period of the injection event. Typically, such a curve can be determined by calculating the slope and y-intercept of these curves.

[0059] Preferably, the upper rail pressure value is determined. P U This includes calculating the mathematical regression of the received pre-jet rail pressure value in order to estimate the pre-jet regression of the received rail pressure value relative to the index value using the least squares method (in... Figure 4 The curve (represented by line RL1) in the graph is used as the injection front line. Similarly, the lower rail pressure value is determined. P L This includes calculating a mathematical regression of multiple received post-injection rail pressure values ​​in order to estimate the post-injection regression line RL2 as the post-injection line using the least squares method.

[0060] In particular, determining the upper rail pressure value P U This includes extrapolation before injection regression, i.e., along line RL1, where the upper rail pressure value... P U This is the pressure value corresponding to the index value at M. In the figure, this is represented by the intersection point IU of the extrapolated pre-injection regression line RL1 (e.g., indicated by the first extended arrow A1) and the straight line C passing through time point M. Furthermore, the lower rail pressure value is determined. P L This includes the extrapolation injection and subsequent return, i.e., along line RL2 (e.g., indicated by the second extended arrow A2), where the lower rail pressure value... P L This is the pressure value corresponding to the same index value (i.e., time point M). In the figure, this is represented as the intersection point IL of the extrapolated post-injection regression line and the straight line C passing through the index value M.

[0061] In one embodiment, extrapolation along the pre-jet return line RL1 includes the last one received from the plurality of pre-jet rail pressure values ​​(corresponding to...). Figure 4 Extrapolation is performed at point B in the equation. As used herein, the term "finally," in relation to pre-ejection, refers to the rail pressure close to the start of the injection event. In one embodiment, extrapolation along the pre-ejection regression line RL1 includes extrapolation from its lower end. In one embodiment, the lower end of the pre-ejection regression line RL1 corresponds to the start of drive pulse 500 at point B.

[0062] In one embodiment, extrapolation along the post-jet return line RL2 includes (i) the first one received from the plurality of post-jet rail pressure values ​​(corresponding to) Figure 4 Extrapolate from point E in the time margin TM, or (ii) from the first rail pressure value in the group of rail pressure values ​​after the time margin TM has elapsed (corresponding to Figure 4Extrapolation is performed along the post-injection regression line RL2. As used herein, the term "firstly," in relation to post-injection data, refers to the pressure value near the end of the injection event. In one embodiment, extrapolation along the post-injection regression line RL2 includes extrapolation from its apex. In one embodiment, the apex of the post-injection regression line corresponds to the end of the drive pulse E, or to the time point L after the time margin TM has elapsed since the end of drive pulse 500.

[0063] Back Figure 5 Step s606 is followed by step s608: Determine the pressure drop Δ P As the upper rail pressure value P U With lower rail pressure value P L The difference between them. For example Figure 4 As shown, Δ P It is less than (and more accurately than) the pressure difference between OU and OL obtained by means / medians.

[0064] Finally, refer to Figure 5 Step s608 is followed by step s610: from the determined pressure drop Δ P The amount of fuel injected by the fuel injector is derived. Deriving the injected fuel amount may include using the determined pressure drop Δ. P Access a pre-stored lookup table to return the amount of injected fuel as an estimate, the mapping depending on at least one of fuel type, temperature, injector type, and system pressure.

[0065] Figure 6 These are graphs showing fuel rail pressure drop versus rail pressure, comparing known median-based techniques (upper graph 702) with a technique according to an embodiment of the present invention (lower graph 704). These are test results from an electrical test bench for a 6-cylinder diesel heavy-duty high-pressure system. These graphs demonstrate the results of the improved technique of the present invention—considering static leakage at low fuel injection rates (e.g., 2 mg). It can be seen that the lower graph 704 using the technique of the present invention is flatter than the upper graph 702, indicating that the pressure drop measurement is less affected by rail pressure increases and reduces or eliminates the effects of static leakage.

[0066] Although the implementation has been described with reference to an embodiment of a measuring device having various components, it should be understood that other implementations may utilize other combinations and arrangements of these and other components.

Claims

1. A method executed by processing circuitry for estimating the amount of fuel injected by a fuel injector of an internal combustion engine, the processing circuitry being coupled to one or more pressure sensors configured to output the rail pressure of a common fuel rail supplying fuel to the fuel injector during use, the fuel injector being configured to selectively execute injection events, in which fuel is injected in response to receiving each of one or more drive pulses having a predetermined duration, the method comprising: Receive multiple pre-injection rail pressure values ​​and multiple post-injection rail pressure values, which correspond to the rail pressure values ​​before and after the time window corresponding to the timing of the injection event, respectively; The upper rail pressure value at a predetermined time point within the time period corresponding to the injection event is determined by extrapolating from the pre-injection rail pressure value. The lower rail pressure value at the predetermined time point is determined by extrapolating from the injection rear rail pressure value. The pressure drop is determined as the difference between the upper rail pressure value and the lower rail pressure value; as well as The amount of fuel injected by the fuel injector is derived from the determined pressure drop.

2. The method according to claim 1, wherein, The predetermined time point within the time window is (i) the center of the time window, or (ii) located within a predetermined time interval from the center of the time window.

3. The method according to claim 2, wherein, The value of the predetermined time interval is in the range of 1% to 40% of the duration of the time window.

4. The method according to claim 1, 2 or 3, wherein, Each of the pre-jet rail pressure value and the post-jet rail pressure value is associated with a corresponding index value, the index value corresponding to the elapsed time since the initial point, and wherein (i) determining the upper rail pressure value includes deriving the front jet line from the pre-jet rail pressure value, and / or (ii) determining the lower rail pressure value includes deriving the rear jet line from the post-jet rail pressure value.

5. The method according to claim 4, wherein, (i) The injection front line is derived by calculating the mathematical regression of the received injection front rail pressure values ​​so as to estimate the injection front regression line as the injection front line by least squares method, and / or (ii) the injection back line is derived by calculating the mathematical regression of multiple received injection back rail pressure values ​​so as to estimate the injection back regression line as the injection back line by least squares method.

6. The method according to any one of the preceding claims, wherein, The time window corresponds to the timing of the drive pulse of the corresponding injection event, or the timing of the hydraulic pulse of the corresponding injection event.

7. The method according to any one of the preceding claims, wherein, The plurality of received post-injection rail pressure values ​​include a set of rail pressure values ​​received after a time margin from the end of the injection event; and / or the plurality of received pre-injection rail pressure values ​​include a set of rail pressure values ​​received before the time margin prior to the injection event.

8. The method according to any one of the preceding claims, wherein, (i) Determining the upper rail pressure value includes extrapolating along the injection front line, wherein the upper rail pressure value is the pressure value at the predetermined time point, and (ii) Determining the lower rail pressure value includes extrapolating along the injection back line, wherein the lower rail pressure value is the pressure value at the predetermined time point.

9. The method according to claim 8, wherein, Extrapolation along the injection front line includes extrapolating the injection front rail pressure value received last among the plurality of injection front rail pressure values.

10. The method according to claim 8 or 9, wherein, Extrapolation along the injection post-line includes (i) extrapolating from the first injection post-rail pressure value received from the plurality of injection post-rail pressure values, or (ii) extrapolating from the first rail pressure value in the group of rail pressure values ​​after the time margin has elapsed.

11. The method according to claim 7, wherein, Pushing outward along the front spray line includes pushing outward from its lower end, and / or pushing outward along the rear spray line includes pushing outward from its top end.

12. The method according to any one of the preceding claims, wherein, (i) The last received injection front rail pressure value among the lower end of the injection front line or the plurality of injection front rail pressure values ​​corresponds to the start of the injection event pulse or to the time point at which a time margin begins before the start of the injection event; and / or (ii) The first received injection rear rail pressure value among the upper end of the injection rear line or the plurality of injection rear rail pressure values ​​corresponds to the end of the drive pulse or to the time point after a time margin has elapsed after the end of the injection event.

13. The method according to any one of the preceding claims, wherein, Derivation of the injected fuel quantity involves accessing a pre-stored lookup table using the determined pressure drop to return the injected fuel quantity as an estimate based on at least one of fuel type, temperature, injector type, and system pressure.

14. The method according to any one of the preceding claims, wherein, The initial point corresponds to the end of a previous pumping event before the fuel pump, or to the start of receiving the plurality of injection front rail pressure values.

15. The method according to any one of the preceding claims, wherein, The lower end of the injection rail corresponds to the start of the next pumping event of the fuel pump, or to the end of receiving the plurality of injection rail pressure values.

16. A method of operating a fuel injection system for an internal combustion engine, said fuel injection system comprising at least one fuel injector associated with a combustion chamber and coupled to a common fuel rail including a pressure sensor, wherein, Injection events are performed by applying a drive signal of a predetermined length to the injector; and wherein the method according to any one of the preceding claims is performed to determine the amount of fuel injected during the corresponding fuel injection event.

17. An engine control unit for estimating the amount of fuel injected by a fuel injector of an internal combustion engine, the control unit including processing circuitry configured to perform the method according to any one of the preceding claims.

18. A vehicle comprising an engine control unit according to claim 17.

19. A computer program product comprising instructions that, when executed by a processing circuit, cause the method according to any one of claims 1 to 16 to be performed.

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