Method and control unit for estimating an injected amount of fuel

Abstract

A method carried out by processing circuitry (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. The processing circuitry being coupled to one or more pressure sensors configured to output a rail pressure of a fuel rail supplying, in use, fuel to the fuel injector. 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 being of predetermined duration. The method comprises receiving a plurality of pre-injection rail pressure values and a plurality of post-injection rail pressure values, corresponding, respectively, to rail pressure values prior to and after a drive pulse. Then, by extrapolation from the pre-injection rail pressure values, an upper rail pressure value corresponding to an index value at a predetermined timepoint within the drive pulse is determined. Similarly, by extrapolation from the post-injection rail pressure values, a lower rail pressure value corresponding to the index value at the predetermined timepoint is determined. The upper and lower rail pressure values are preferably obtained by estimating pre-injection and post-injection regression lines based on the rail pressure values by least squares method; and the pressure drop is preferably obtained by determining the difference between the upper and lower rail pressure values at the centre of the drive pulse. The amount of fuel injected by the fuel injector is then derived from the determined pressure drop. A control unit and a vehicle incorporating it are also disclosed.

Description

METHOD AND CONTROL UNIT FOR ESTIMATING AN INJECTED AMOUNT OF FUELTechnical field

[0001] The present invention generally relates to internal combustion engines, and to fuel injectors therefor. The invention more particularly relates to an improved method and control unit for estimating an amount of fuel injected by a fuel injector.Background Art

[0002] It is known to estimate an amount of fuel injected by a fuel injector by pressure drop analysis (PDA), whereby one or more sensors measure a rail pressure drop on a fuel rail supplying fuel to the injector(s) - between pressure before and after fuel injection, and the pressure drop is then used to calculate the amount of fuel. A common PDA strategy is disclosed in GB 2533104 A. This type of estimation is useful as the amount can be compared with a calculated / desired amount of fuel, e.g., based upon current torque requirements of the engine in which the fuel injector is used, to log discrepancies or alert when a discrepancy exceeds a threshold.

[0003] Typically, drive pulses are supplied to the injector (e.g., via power electronics) under the control of a control unit, such as the electronic control unit (ECU) of a vehicle, and a drive pulse whose timing and duration is determined by the control unit causes the fuel injector to operate to inject fuel.

[0004] As discussed in further detail below, averaging or other techniques are used in known methods to determine the pre-injection and post-injection rail pressures.Technical problem

[0005] A problem is that, with known techniques, the estimation is sub-optimal for for low fuel injection quantities, particularly in the case of high-pressure systems, such as diesel and gasoline direct injection engines, and hydrogen propulsion systems. Further, the techniques do not adequately deal with variations in (fuel) temperature and injector seat wear, and are susceptible to the effects of static leaks.

[0006] It is an object of the present invention to avoid the foregoing issue and to provide a method and control unit that take into account the actual injector static leaks in the pressure drop calculation at the time of PDA analysis, especially in high- pressure systems.General Description of the Invention

[0007] In order to overcome the above-mentioned issue, the present invention provides a method according to claim 1 .

[0008] The inventive method is to be carried out by processing circuitry (resp. by a control unit), for estimating an 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 a rail pressure of a fuel rail supplying, in use, fuel to the fuel injector, the fuel injector being configured to inject fuel in response to receiving each of one or more drive pulses, the drive pulses being of predetermined duration, the method comprising: receiving a plurality of pre-injection rail pressure values and a plurality of post-injection rail pressure values, corresponding, respectively, to rail pressure values prior to and after a time window corresponding to the timing of an injection event; determining, by extrapolation from the pre-injection rail pressure values, an upper rail pressure value at a predetermined timepoint within a time period corresponding to the injection event; determining, by extrapolation from the post-injection rail pressure values, a lower rail pressure value at the predetermined timepoint; determining a pressure drop as the difference between the upper rail pressure value and the lower rail pressure value; and deriving the amount of fuel injected by the fuel injector from the determined pressure drop.

[0009] The inventive method provides an improved PDA strategy, which relies on processing of rail pressure data before and after the respective injection event. Advantageously, the pre- and post-injection pressure data / values are fitted by regression analysis and upper and lower rail pressure values are determined by extrapolation within the time period spanning the duration of the injection event. Thepresent method is more reliable than state of the art strategies to take into account static leaks.

[0010] The inventive method has been developed for application in diesel engines, where fuel injectors typically have a static leak due to injector design (causing a decrease in rail pressure). However, the inventive method may also find application with other types of fuel systems, in particular in fuel delivery systems for gaseous fuel (H2 or CNG), where there is a continuous filing of the fuel rail (here rather causing an increase in rail pressure). In other words, the inventive method may find application in fuel delivery systems where the fuel rail pressure is subject to a continuous trend of variation (increase or decrease) due to system design.

[0011] The present method can be generally implemented in a method of controlling an internal combustion engine, wherein the obtained amount of fuel injected by the fuel injector is used for fuel injection control. In particular, the obtained fuel amounts can be used to develop injector-specific correction parameters used to build the command signals applied to the respective injectors.

[0012] In the process, the pressure drop is determined based on extrapolated pre- and post-injection values located within the time period corresponding to the injection event. The begin and end timings of this time period can correspond to those of the drive (or command) pulse applied to the injector, or to those of the corresponding hydraulic pulse. The term hydraulic pulse here refers to the duration during which the injector is actually open.

[0013] In embodiments, the predetermined timepoint within the time window (i) is the centre of the time window or (ii) lies within a predetermined time spacing from the centre of the time window. Preferably, the predetermined time spacing has a value in the range 1 % to 40 % of the duration of the time window.

[0014] Preferably, (i) determining the upper rail pressure value comprises deriving a pre-injection line from the pre-injection rail pressure values, and / or (ii) determining the lower rail pressure value comprises deriving a post-injection line from the postinjection rail pressure values .

[0015] The received pressure values may be “associated with a respective index value corresponding to elapsed time since an initial point”, which essentially meansthat the values can be associated with a corresponding timing, which can be expressed in time (e.g. s or ms) or in crank angle degrees.

[0016] In practice, deriving a pre-injection line from the pre I post rail pressure values may imply computing the parameters of a line, i.e. the slope and y-intercept.

[0017] Preferably, (i) the pre-injection line is derived by calculating the mathematical regression of the received pre-injection rail pressure values so as to estimate a pre-injection regression line on a plot of the received rail pressure value versus index value as the pre-injection line by least squares method, and / or (ii) the post-injection line is derived by calculating the mathematical regression of a plurality of the received post-injection rail pressure values so as to estimate a post-injection regression line on the plot as the post-injection line by least squares method.

[0018] Preferably, the plurality of the received post-injection rail pressure values comprises a set of the rail pressure values received after the elapse of a time margin since the end of the drive pulse.

[0019] Preferably, (i) determining the upper rail pressure value comprises extrapolating along the pre-injection line, whereby the upper rail pressure value is the pressure value at the intersection of the extrapolated pre-injection line with a line through the index value at the predetermined timepoint, and / or (ii) determining the lower rail pressure value comprises extrapolating along the post-injection line, whereby the lower rail pressure value is the pressure value at the intersection of the extrapolated post-injection line with the line through the index value at the predetermined timepoint.

[0020] In an embodiment, extrapolating along the pre-injection line comprises extrapolating from the last-received one of the plurality of pre-injection rail pressure values.

[0021] In an embodiment, extrapolating along the post-injection line comprises (i) extrapolating from the first-received one of the plurality of post-injection rail pressure values or (ii) extrapolating from the first rail pressure value in the set of the rail pressure values after the elapse of a time margin.

[0022] In an embodiment, extrapolating along the pre-injection line comprises extrapolating from the lower end thereof, and / or extrapolating along the postinjection line comprises extrapolating from the upper end thereof.

[0023] Preferably, (i) the lower end of the pre-injection line or the last-received one of the plurality of pre-injection rail pressure values corresponds to the start of the drive pulse and / or (ii) the upper end of the post-injection line or the first-received one of the plurality of post-injection rail pressure values corresponds to the end of the drive pulse or to a time point corresponding to the elapse of a time margin after the end of the drive pulse.

[0024] Preferably, deriving the amount of fuel injected comprises using a relationship between a rail pressure drop and injected fuel quantity, which preferably depends on at least one of fuel type, temperature, injector type and system pressure. For example, the deriving the amount of fuel injected comprises accessing a pre-stored look-up table using the determined pressure drop to return the amount of fuel injected as an estimate, preferably based on one or more of these parameters

[0025] Preferably, the initial point corresponds to the end of the previous pumping by the fuel injector or to the beginning of the receipt of the plurality of pre-injection rail pressure values.

[0026] Preferably, the lower end of the post-injection line corresponds to the beginning of the next pumping by the fuel injector or to the end of the receipt of the plurality of post-injection rail pressure values.

[0027] Preferably, the index value corresponds to engine angular position.

[0028] The present method may typically be implemented by software (program code / instructions) implemented by a computer, such as an engine control unit, or a module thereof.

[0029] According to another aspect of the present invention, there is provided an engine control unit, for estimating an amount of fuel injected by a fuel injector of an internal combustion engine, the control unit comprising the processing circuitry configured to carry out the method of any of claims 1 to 13 of the appended claims.

[0030] According to another aspect of the present invention, there is provided a vehicle incorporating the engine control unit of the previous paragraph.

[0031] According to another aspect of the present invention, there is provided a computer program product comprising instructions which, when executed by processing circuitry, cause the method of any of claims 1 to 16 of the appended claims to be performed.

[0032] An advantage of the invention is to more accurately estimate fuel injection quantities, so as to take into account the actual injector static leaks, especially in high-pressure systems.Brief Description of the Drawings

[0033] Further details and advantages of the present invention will be apparent from the following detailed description of a non-limiting embodiment with reference to the attached drawings, wherein:Figure 1 (PRIOR ART) is a plot of fuel rail pressure vs engine angle, as used in known techniques for fuel quantity estimation in a gasoline system;Figure 2 (PRIOR ART) is a plot of fuel rail pressure vs index, as used in known techniques for fuel quantity estimation in a gasoline system as in Fig. 1 ;Figure 3(a) (PRIOR ART) and Figure 3(b) (PRIOR ART) are, respectively, plots of fuel rail pressure vs index for regular and low fuel quantities, as used in known techniques for fuel quantity estimation in a diesel system;Figure 4 is a is a plot of fuel rail pressure vs index, as used to illustrate techniques according to embodiments of the invention for fuel quantity estimation;Figure 5 is a flowchart of a process for fuel quantity estimation according to embodiments of the invention;Figure 6 are plots of fuel rail pressure drop vs rail pressure, comparing the known median-based techniques (upper plots) and the techniques according to embodiments of the invention (lower plots); andFigure 7 is a schematic diagram of a fuel system for a vehicle, in which the techniques according to embodiments of the invention may be used.Description of Preferred Embodiments

[0034] In the following, like reference numerals denote like parts, and any element, design feature or method step of any embodiment may be used in combination with an element, design feature or method step of any other embodiment unless stated otherwise herein.

[0035] Initially, reference is made to Fig. 7, which is a schematic diagram of a fuel system 10 for a vehicle, in which the techniques according to embodiments of the invention may be used. Such fuel system is well known and will only be briefly described.

[0036] Fuel system 10 comprises a common fuel rail 1 (or accumulator) fluidly connecting the fuel therein to a series of injectors 2 (e.g. of solenoid actuated fuel injectors). The circuit typically includes an in-tank electrical fuel pump 3, a fuel filter 4, and a high-pressure pump 5. A high-pressure sensor 6 is located on the common rail 1 as shown in order to measure the fuel pressure inside the common rail 1. A high-pressure valve 8 is provided on the common rail 1 , which is a safety valve that opens when the pressure exceeds a preset value (which may be passive or controllable). Reference sign 7 indicates a backleak circuit including a backleak regulator and injector return line, which is typically present in diesel fuel injection systems. Such backleak circuit 7 is typically used for indirectly controlled fuel injectors (Diesel injectors include a solenoid-controlled valve that hydraulically controls the needle), but is not required for injectors where the pintle is directly controlled via the solenoid, typically via an armature coupled to the pintle, as in gasoline or gaseous fuel injectors. The fuel system 10 also includes an electronic controller 36 such as an engine control unit (ECU) connected to the 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, inter alia, to control fuel injection. The controller 36 is configured to operate the present method via hardware and / or software.

[0037] Returning now to Fig. 1 (PRIOR ART) is a plot of fuel rail pressure vs. engine angle, as used in known techniques for fuel quantity estimation in a gasoline system. Fuel quantity estimation is performed by processing the rail pressure signal (e.g., from pressure sensor 6), cleaning it and analysing the level before the injectionand after the injection. The injection (period) is designated 100, and has a duration essentially corresponding to that of a drive (or command) pulse (e.g., from controller 36), i.e., Dp.

[0038] The rail pressure drop AP - used to calculate the fuel injected by the injector - is evaluated by processing as follows: the mean (or the median) of the pressure level 102 before the injection (see “Max Pressure” in Fig. 1 ) is calculated, the mean (or the median) of the pressure level 104 after the injection (see “Min Pressure” in Fig. 1 ) is calculated, and the amount of fuel injected is obtained by accessing a look-up table using the determined pressure drop AP to return the amount of fuel injected as an estimate. Such look-up table typically return values of fuel amount in function of the determined pressure drop and rail pressure (measured by sensor 6).

[0039] Figure 2 (PRIOR ART) is a plot of fuel rail pressure vs index, as used in known techniques for fuel quantity estimation in a gasoline system as in Fig. 1. This plot illustrates that the aforementioned mean / median-based technique works satisfactorily for gasoline systems with low rail pressure values as rail pressure is very stable.

[0040] Figure 3(a) (PRIOR ART) and Figure 3(b) (PRIOR ART) are, respectively, plots of fuel rail pressure vs index for regular and low fuel quantities, as used in known techniques for fuel quantity estimation in a diesel system.

[0041] In a diesel system, i.e., involving significantly higher fuel rail pressures compared to gasoline systems, the results are poorer because:• there are more pressure waves due to higher rail pressures values (see Fig. 3(a): in each of a pre-injection part 302 and the post-injection part 306 significant waves are apparent in the plot),• diesel injectors have static leaks, unlike gasoline injectors (see Fig. 3(b): as well as having significant waves 304 in the pre-injection part 302 and waves 308 the post-injection part 306 of the plot, both of those parts trend downwards with time due to the static leaks),• fuel temperature variations are more important due to higher rail pressure, and• low fuel quantity estimation is more important for a good combustion (see Fig. 3(b)).

[0042] In addition, alternative (non mean / median-based) techniques have been employed to seek to address some of the aforementioned issues. For example, techniques using a Probability Density Function (PDF) have been proposed. clnventive method>

[0043] Figure 4(a) is a is a plot of fuel rail pressure vs index, as used to illustrate techniques according to embodiments of the invention for fuel quantity estimation, and Fig. 4(b) is an enlarged view of part of the plot of Fig. 4(a), indicating possible positions of the predetermined timepoint. Figure 5 is a flowchart of a process for fuel quantity estimation according to embodiments of the invention.

[0044] Referring to Fig. 5, this illustrates a process carried out by processing circuitry (such as the electronic controller 36 of Fig. 7), for estimating an amount of fuel injected by a fuel injector 2 of an internal combustion engine (not shown). For this purpose, rail pressure data / values are acquired by means of pressure sensor 6 in Fig. 7 (configured to output the rail pressure of the fuel rail 1 during engine operation), during an analysis window encompassing the given injection event. The fuel injector 2 is configured to selectively perform fuel injection events, by which fuel is injected in response to a drive pulses (or drive signal or command signal) applied to the injector, e.g., generated by the processing circuitry, the drive pulses being of predetermined duration (known as pulse width).

[0045] The ECU 36 is configured to process the rail pressure data in accordance with the present method. For the sake of simplification, the term rail pressure values or rail pressure data are used as synonyms, the rail pressure values are representative of the pressure in the fuel rail 1 and may correspond to a direct reading of the sensor 6, to an absolute value or to any other value reflecting the pressure expressed with respect to a predetermined reference or based on a predetermined calculation method.

[0046] The process begins with receiving (step s602) a plurality of pre-injection rail pressure values and a plurality of post-injection rail pressure values, e.g., from the pressure sensor 6. These values correspond, respectively, to rail pressurevalues prior to (e.g., in pre-injection part 302) and after (e.g., in post-injection part 306) a an injection event. In Fig. 4, the injection event, of duration Dp, and generally corresponding to the injection period 100 (Fig. 1 ), is designated 500.

[0047] Each of the pre-injection rail pressure values and the post-injection rail pressure values is preferably associated with a respective index value corresponding to elapsed time since an initial point. The initial point may correspond to the end 0 of the previous pumping by the fuel injector or to the predetermined beginning B1 of the receipt of the plurality of pre-injection rail pressure values (see Fig. 4). The index values may correspond to engine angular position (or corresponding timing). In other words, the pressure values are associated with a time reference.

[0048] In the post-injection part 306, the last-received post-injection rail pressure value may correspond to the beginning of the next pumping event by the fuel pump or to the predefined end E1 of the receipt of the plurality of post-injection rail pressure values.

[0049] In Fig. 4, B and E denote the start and end of the drive pulse 500 corresponding to the observed injection event, respectively. In an embodiment, the plurality of the received post-injection rail pressure values comprises the set of the rail pressure values received after the elapse of a time margin TM since the end of the drive pulse. An advantage of the use of the time margin TM is that the injection pressure waves may be removed, thereby enhancing accuracy of pressure drop calculation. Similarly, a pre-injection time margin may be applied before, whereby the received pre-injection rail pressure values comprises the set of the rail pressure values received until the beginning of this time margin before point B.

[0050] In an embodiment, the last-received one of the plurality of pre-injection rail pressure values corresponds to the start B of the drive pulse 500. Alternatively or additionally, the first-received one of the plurality of post-injection rail pressure values corresponds to the end E of the drive pulse or to a time point L corresponding to the elapse of a time margin TM after the end of the drive pulse 500.

[0051] As indicated, in the present case the time period 500 is the drive pulse and hence point B may correspond to a timing (crank angle) of start of injection or pointE may correspond to a timing of end of injection; and the time period between point B and E may correspond to the pulse width.

[0052] Alternatively, the time period 500 may represent the hydraulic pulse of the fuel injector caused by the drive pulse. In such case B would be the timing at which the injectors comes to the fully open position (i.e. timing of the so-called Opening delay) and point E is the moment the injector comes at rest in the closed position (timing of the so-called closing delay).

[0053] Returning to Fig. 5, step s602 is followed by the step of determ ining (s604), by extrapolation from the pre-injection rail pressure values, an upper rail pressure value Pu corresponding to a predetermined timepoint (or a predetermined index value) within the drive pulse 500. In an embodiment, the predetermined timepoint is the centre M of the drive pulse 500 (see Fig. 4). Alternatively, this predetermined timepoint may be anywhere between B and E in the drive pulse 500.

[0054] For example, the predetermined timepoint is not the centre M of the drive pulse 500 but may be a point lying within a predetermined time spacing S from the centre M of the drive pulse. Preferably, the predetermined time spacing S has a value in the range 1 % to 45 % of the duration Dp of the drive pulse 500, on either side or M.

[0055] Returning to Fig. 5, step s604 is followed by the step of determ ining (s606), by extrapolation from the post-injection rail pressure values, a lower rail pressure value PL corresponding to the index value at the predetermined timepoint (e.g., M). (For comparison in Fig. 4, the upper and lower pressure values obtained by the old, mean / median based method are indicated as Ou and C )

[0056] In particular, determining the upper rail pressure value Pu comprises deriving a pre-injection line from the received rail pressure value, and / or (ii) determining the lower rail pressure value PL comprises deriving a post-injection line. The idea is to have a line that fits the pre / post injection pressure values, to extrapolate within the time period of the injection event. Typically, such line can be determined by calculating the slope and y-intercept of those lines.

[0057] Preferably, determining the upper rail pressure value Pu comprises calculating the mathematical regression of the received pre-injection rail pressurevalues so as to estimate a pre-injection regression (illustrated by line RL1 in the plot of Fig. 4) of the received rail pressure value versus index value by least squares method as the pre-injection line. Similarly, determining the lower rail pressure value PL comprises calculating the mathematical regression of a plurality of the received post-injection rail pressure values so as to estimate a post-injection regression line RL2 by least squares method as the post-injection line.

[0058] In particular, determining the upper rail pressure value Pu comprises extrapolating the pre-injection regression, i.e. along line RL1 , whereby the upper rail pressure value Pu is the pressure value corresponding to the index value at M. In the figure, this is represented as the intersection III of the extrapolated pre-injection regression line RL1 (e.g., indicated by first extension arrow A1 ) with a line C through the timepoint M. Additionally, determining the lower rail pressure value PL comprises extrapolating the post-injection regression, i.e. along line RL2 (e.g., indicated by second extension arrow A2), whereby the lower rail pressure value PL is the pressure value corresponding to the same index value, ii.e. timepoint M. In the figure, this is represented as the intersection IL of the extrapolated post-injection regression line with the line C through the index value M.

[0059] In an embodiment, extrapolating along the pre-injection regression line RL1 comprises extrapolating from the last-received one (corresponding to point B in Fig. 4) of the plurality of pre-injection rail pressure values. As used herein, the term ‘last’, in relation to pre-injection, refers to rail pressures close to the start of the injection event. In an embodiment, extrapolating along the pre-injection regression line RL1 comprises extrapolating from the lower end thereof. In an embodiment, the lower end of the pre-injection regression line RL1 corresponds to the start B of the drive pulse 500.

[0060] In an embodiment, extrapolating along the post-injection regression line RL2 comprises (i) extrapolating from the first-received one of the plurality of postinjection rail pressure values (corresponding to point E in Fig. 4) or (ii) extrapolating from the first rail pressure value (corresponding to point L in Fig. 4) in the set of the rail pressure values after the elapse of a time margin TM. As used herein, the term ‘first’ in relation to post-injection data, refers to pressure values close to the end of the injection event. In an embodiment, extrapolating along the post-injectionregression line RL2 comprises extrapolating from the upper end thereof. In an embodiment, the upper end of the post-injection regression line corresponds to the end E of the drive pulse or to a time point L corresponding to the elapse of a time margin TM after the end of the drive pulse 500.

[0061] Returning to Fig. 5, step s606 is followed by the step of determining (s608) a pressure drop AP as the difference between the upper rail pressure value Pu and the lower rail pressure value PL. AS can be seen in Fig. 4, AP is smaller (and more accurate) than the pressure difference between OU and OL obtained by the mean / median based method.

[0062] Finally, referring to Fig. 5, step s608 is followed by the step of deriving (s610) the amount of fuel injected by the fuel injector from the determined pressure drop AP. Deriving the amount of fuel injected may comprise accessing a pre-stored look-up table using the determined pressure drop AP to return the amount of fuel injected as an estimate, the mapping being e.g. dependent on at least one of fuel type, temperature, injector type and system pressure.

[0063] Figure 6 are plots of fuel rail pressure drop vs rail pressure, comparing the known median-based techniques (upper plots 702) and the techniques according to embodiments of the invention (lower plots 704). These are the result of tests on an electrical bench with a 6-cylinder diesel heavy-duty high-pressure system. The plots indicate the improved results of the techniques according to the invention - to take into account the static leaks on a low fuel quantity injection (e.g., 2mg). It can be seen that the lower plots 704 using techniques are flatter than upper plots 702, indicating that pressure drop measurement is less influenced by rising rail pressure, and reduces or eliminates the effect of static leaks.

[0064] While embodiments have been described by reference to embodiments of survey devices having various components in their respective implementations, it will be appreciated that other embodiments make use of other combinations and permutations of these and other components.

Claims

Claims1. A method carried out by processing circuitry, for estimating an 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 a rail pressure of a fuel rail supplying, in use, fuel to the fuel injector, the fuel injector being configured to selectively perform injection events by which fuel is injected in response to receiving each of one or more drive pulses, the drive pulses being of predetermined duration, the method comprising: receiving a plurality of pre-injection rail pressure values and a plurality of post-injection rail pressure values, corresponding, respectively, to rail pressure values prior to and after a time window corresponding to the timing of an injection event; determining, by extrapolation from the pre-injection rail pressure values, an upper rail pressure value at a predetermined timepoint within a time period corresponding to the injection event; determining, by extrapolation from the post-injection rail pressure values, a lower rail pressure value at the predetermined timepoint; determining a pressure drop as the difference between the upper rail pressure value and the lower rail pressure value; and deriving the amount of fuel injected by the fuel injector from the determined pressure drop.

2. The method of claim 1 , wherein the predetermined timepoint within the time window (i) is the centre of the time window or (ii) lies within a predetermined time spacing from the centre of the time window.

3. The method of claim 2, wherein the predetermined time spacing has a value in the range 1 % to 40 % of the duration of the time window.

4. The method of claim 1 , 2 or 3, wherein each of the pre-injection rail pressure values and the post-injection rail pressure values is associated with a respective index value corresponding to elapsed time since an initial point, and wherein (i) determining the upper rail pressure value comprises deriving a pre-injection line from the pre-injection rail pressure values, and / or (ii) determining the lower rail pressure value comprises deriving a post-injection line from the post-injection rail pressure values.

5. The method of claim 4, wherein (i) the pre-injection line is derived by calculating the mathematical regression of the received pre-injection rail pressure values so as to estimate a pre-injection regression line as the pre- injection line by least squares method, and / or (ii) the post-injection line is derived by calculating the mathematical regression of a plurality of the received post-injection rail pressure values so as to estimate a post-injection regression line as the post-injection line by least squares method.

6. The method of any of the preceding claims, wherein said time window corresponding to the timing of a drive pulse of the respective injection event, or to the timing of its hydraulic pulse.

7. The method of any of the preceding claims, wherein the plurality of the received post-injection rail pressure values comprises a set of the rail pressure values received after the elapse of a time margin since the end of the injection event; and / or the plurality of the received pre-injection rail pressure values comprises a set of the rail pressure values received before the time margin preceding the injection event.

8. The method of any of the preceding claims, wherein (i) determining the upper rail pressure value comprises extrapolating along the pre-injection line, whereby the upper rail pressure value is the pressure value at said predetermined timepoint, and (ii) determining the lower rail pressure value comprises extrapolating along the post-injection line, whereby the lower rail pressure value is the pressure value at said predetermined timepoint.

9. The method of claim 8, wherein extrapolating along the pre-injection line comprises extrapolating from the last-received one of the plurality of pre- injection rail pressure values.

10. The method of claim 8 or 9, wherein extrapolating along the post-injection line comprises (i) extrapolating from the first-received one of the plurality of postinjection rail pressure values or (ii) extrapolating from the first rail pressure value in the set of the rail pressure values after the elapse of the time margin.11 . The method of claim 7, wherein extrapolating along the pre-injection line comprises extrapolating from the lower end thereof, and / or extrapolating along the post-injection line comprises extrapolating from the upper end thereof.

12. The method of any of the preceding claims, wherein (i) the lower end of the pre-injection line or the last-received one of the plurality of pre-injection rail pressure values corresponds to the start of the injection event pulse or a time point corresponding to the beginning of a time margin vefore the beginning of the injection event; and / or (ii) the upper end of the post-injection line or the first-received one of the plurality of post-injection rail pressure values corresponds to the end of the drive pulse or to a time point corresponding to the elapse of a time margin after the end of the injection event.

13. The method of any of the preceding claims, wherein deriving the amount of fuel injected comprises accessing a pre-stored look-up table using the determined pressure drop to return the amount of fuel injected as an estimate based on at least one of fuel type, temperature, injector type and system pressure.

14. The method of any of the preceding claims, wherein the initial point corresponds to the end of the previous pumping event of a fuel pump or to the beginning of the receipt of the plurality of pre-injection rail pressure values.

15. The method of any of the preceding claims, wherein the lower end of the postinjection line corresponds to the beginning of the next pumping event by the fuel pump or to the end of the receipt of the plurality of post-injection rail pressure values.

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

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

18. A vehicle incorporating the engine control unit of claim 17.

19. A computer program product comprising instructions which, when executed by processing circuitry, cause the method of any of claims 1 to 16 to be performed.

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