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A system for estimating an auxiliary-injected fuel quantity includes a fuel injector for injecting fuel into an engine, a fuel pump supplying fuel to a fuel collection unit that then supplies fuel to the fuel injector, and a control circuit that generates an auxiliary-injected fuel quantity estimati

A system for estimating an auxiliary-injected fuel quantity includes a fuel injector for injecting fuel into an engine, a fuel pump supplying fuel to a fuel collection unit that then supplies fuel to the fuel injector, and a control circuit that generates an auxiliary-injected fuel quantity estimation model by disabling the fuel pump prior to fuel injection, and enabling the fuel pump to resume fuel pumping following fuel injection, by the fuel injector, determines a first pressure in the fuel collection unit after stabilization of the fuel pressure therein following disablement of the fuel pump and prior to the fuel injection, determines a second pressure in the fuel collection unit after the fuel injection and prior to resuming pumping of fuel by the fuel pump, and forms the model as a function of the first and second pressures and an injector on-time for a number of different engine operating conditions.

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1. System for estimating an auxiliary-injected fuel quantity injected into an internal combustion engine separate from a main-injected fuel quantity, comprising:a fuel injector responsive to an injector on-time signal, having separate main-injection and auxiliary-injection on-times, to inject fuel i

1. System for estimating an auxiliary-injected fuel quantity injected into an internal combustion engine separate from a main-injected fuel quantity, comprising:a fuel injector responsive to an injector on-time signal, having separate main-injection and auxiliary-injection on-times, to inject fuel into the engine;a fuel collection unit supplying fuel to the fuel injector;a fuel pump supplying pressurized fuel to the fuel collection unit;a pressure sensor in fluid communication with the fuel collection unit and producing a pressure signal indicative of fuel pressure therein; anda control circuit periodically generating an auxiliary-injected fuel quantity model by disabling the fuel pump prior to fuel injection, and enabling the fuel pump to resume fuel pumping following fuel injection, by the fuel injector, determining based on the pressure signal a first pressure in the fuel collection unit after stabilization of the fuel pressure therein following disablement of the fuel pump and prior to the fuel injection, determining based on the pressure signal a second pressure in the fuel collection unit after the fuel injection and prior to resuming pumping of fuel by the fuel pump, and forming the auxiliary-injected fuel quantity model as a function of the first and second pressures and the injector on-time signal for a number of different engine operating conditions, the control circuit estimating the auxiliary-injected fuel quantity according to the auxiliary-injected fuel quantity model. 2. The system of claim 1 wherein the control circuit is configured to estimate for each of the number of different engine operating conditions a total injected fuel quantity, corresponding to a sum of the main-injected fuel quantity and the auxiliary-injected fuel quantity, as a function of the first and second pressures and of the injector on-time signal, the main-injected fuel quantity according to a main-injected fuel quantity model, and an auxiliary-injected fuel quantity value as a difference between the total injected fuel quantity and the main-injected fuel quantity, the control circuit forming the auxiliary-injected fuel quantity model as a function of the auxiliary-injected fuel quantity values for each of the number of different engine operating conditions. 3. The system of claim 2 wherein the auxiliary-injected fuel quantity corresponds to a post-injected fuel quantity injected into the engine following injection of the main-injected fuel quantity, the auxiliary-injected fuel quantity values correspond to post-injected fuel quantity values, the auxiliary-injection on-time corresponds to a post-injection on-time, and the auxiliary-injected fuel quantity model corresponds to a post-injected fuel quantity model. 4. The system of claim 3 wherein the control circuit is responsive to the pressure signal to estimate a bulk modulus of the pressurized fuel;and wherein the control circuit is configured to estimate the total injected fuel quantity further as a function of the bulk modulus of the pressurized fuel. 5. The system of claim 3 wherein the control circuit is configured to estimate a control flow leakage value as a function of the first and second pressures and of the injector on-time signal;and wherein the control circuit is configured to estimate the total injected fuel quantity further as a function of the control flow leakage value. 6. The system of claim 5 further including means for determining an operating temperature of the engine and producing an engine temperature signal corresponding thereto;and wherein the control circuit is configured to estimate a parasitic flow leakage value as a function of the first and second pressures and of the engine temperature signal;and wherein the control circuit is configured to estimate the total injected fuel quantity further as a function of the parasitic flow leakage value. 7. The system of claim 6 wherein the means for determining an operating temperature of the engine is a temperature senso r producing a fuel temperature signal indicative of a temperature of the pressurized fuel;and wherein the engine temperature signal in the estimate of the parasitic flow leakage value corresponds to the fuel temperature signal. 8. The system of claim 6 wherein the means for determining an operating temperature of the engine is a temperature sensor producing a coolant temperature signal indicative of a temperature of engine coolant fluid;and wherein the engine temperature signal in the estimate of the parasitic flow leakage value corresponds to the coolant temperature signal. 9. The system of claim 6 wherein the control circuit is responsive to the pressure signal to estimate a bulk modulus of the pressurized fuel;and wherein the control circuit is configured to estimate the total injected fuel quantity further as a function of the bulk modulus of the pressurized fuel. 10. The system of claim 3 wherein the injection on-time signal further includes a separate pilot-injection on-time for injecting a pilot-injected quantity of fuel into the engine prior to injection of the main-injected fuel quantity;and wherein the control circuit is configured to further disable for each of the number of engine operating conditions the pilot-injection on-time prior to the fuel injection, and enable the pilot-injection on-time following the fuel injection, by the fuel injector. 11. The system of claim 3 wherein the control circuit is configured to generate the main-injected fuel quantity model by periodically disabling the fuel pump and the post-injection on-time prior to fuel injection, and enabling the fuel pump to resume pumping and the post-injection on-time following fuel injection, by the fuel injector, determining based on the pressure signal a third pressure in the fuel collection unit after stabilization of the fuel pressure therein following disablement of the fuel pump and prior to fuel injection by the fuel injector, determining based on the pressure signal a fourth pressure in the fuel collection unit after fuel injection by the fuel injector and prior to resuming pumping of fuel by the fuel pump, and forming the main-injected fuel quantity model as a function of the third and fourth pressures and of the injector on-time signal for a plurality of different engine operating conditions. 12. The system of claim 11 wherein the control circuit is configured to estimate for each of the plurality of different engine operating conditions a main-injected fuel quantity value as a function of the third and fourth pressures and of the injector on-time signal, the control circuit forming the main-injected fuel quantity model as a function of the main-injected fuel quantity values for each of the plurality of different engine operating conditions. 13. The system of claim 12 wherein the control circuit is responsive to the pressure signal to estimate a bulk modulus of the pressurized fuel;and wherein the control circuit is configured to estimate for each of the plurality of different engine operating conditions the main-injected fuel quantity value further as a function of the bulk modulus of the pressurized fuel. 14. The system of claim 12 wherein the control circuit is configured to estimate for each of the plurality of different engine operating conditions a control flow leakage value as a function of corresponding ones of the third and fourth pressures and injector on-time signals;and wherein the control circuit is configured to estimate each of the plurality of main-injected fuel quantity values further as a function of a corresponding one of the plurality of control flow leakage values. 15. The system of claim 14 further including means for determining an operating temperature of the engine and producing an engine temperature signal corresponding thereto;and wherein the control circuit is configured to estimate for each of the plurality of different engine operating condition values a parasitic flow leakage value as a function of correspondin g ones of the third and fourth pressures and of the engine temperature signal;and wherein the control circuit is configured to estimate each of the plurality of main-injected fuel quantity values further as a function of a corresponding one of the parasitic flow leakage value. 16. The system of claim 15 wherein the means for determining an operating temperature of the engine is a temperature sensor producing a fuel temperature signal indicative of a temperature of the pressurized fuel;and wherein the engine temperature signal in each of the plurality of estimates of the parasitic flow leakage value corresponds to the fuel temperature signal. 17. The system of claim 15 wherein the means for determining an operating temperature of the engine is a temperature sensor producing a coolant temperature signal indicative of a temperature of engine coolant fluid;and wherein the engine temperature signal in each of the plurality of estimates of the parasitic flow leakage value corresponds to the coolant temperature signal. 18. The system of claim 15 wherein the control circuit is responsive to the pressure signal to estimate a bulk modulus of the pressurized fuel;and wherein the control circuit is configured to estimate for each of the plurality of different engine operating conditions the main-injected fuel quantity value further as a function of the bulk modulus of the pressurized fuel. 19. The system of claim 11 wherein the injection on-time signal further includes a separate pilot-injection on-time for injecting a pilot-injected quantity of fuel into the engine prior to injection of the main-injected fuel quantity;and wherein the control circuit is configured to further disable for each of the plurality of engine operating conditions the pilot-injection on-time prior to the fuel injection, and enable the pilot-injection on-time following the fuel injection, by the fuel injector. 20. The system of claim 3 wherein the control circuit is configured to determine a post-injected fuel quantity error as a difference between the post-injected fuel quantity and a commanded post-injected fuel quantity, and to adjust the post-injection on-time to minimize the post-injection fueling quantity error. 21. The system of claim 2 wherein the auxiliary-injected fuel quantity corresponds to a pilot-injected fuel quantity injected into the engine prior injection of the main-injected fuel quantity, the auxiliary-injected fuel quantity values correspond to pilot-injected fuel quantity values, the auxiliary-injection on-time corresponds to a pilot-injection on-time, and the auxiliary-injected fuel quantity model corresponds to a pilot-injected fuel quantity model. 22. The system of claim 21 wherein the control circuit is responsive to the pressure signal to estimate a bulk modulus of the pressurized fuel;and wherein the control circuit is configured to estimate the total injected fuel quantity further as a function of the bulk modulus of the pressurized fuel. 23. The system of claim 21 wherein the control circuit is configured to estimate a control flow leakage value as a function of the first and second pressures and of the injector on-time signal;and wherein the control circuit is configured to estimate the total injected fuel quantity further as a function of the control flow leakage value. 24. The system of claim 23 further including means for determining an operating temperature of the engine and producing an engine temperature signal corresponding thereto;and wherein the control circuit is configured to estimate a parasitic flow leakage value as a function of the first and second pressures and of the engine temperature signal;and wherein the control circuit is configured to estimate the total injected fuel quantity further as a function of the parasitic flow leakage value. 25. The system of claim 24 wherein the means for determining an operating temperature of the engine is a temperature sensor producing a fuel temperature signal indicative of a tempe rature of the pressurized fuel;and wherein the engine temperature signal in the estimate of the parasitic flow leakage value corresponds to the fuel temperature signal. 26. The system of claim 24 wherein the means for determining an operating temperature of the engine is a temperature sensor producing a coolant temperature signal indicative of a temperature of engine coolant fluid;and wherein the engine temperature signal in the estimate of the parasitic flow leakage value corresponds to the coolant temperature signal. 27. The system of claim 24 wherein the control circuit is responsive to the pressure signal to estimate a bulk modulus of the pressurized fuel;and wherein the control circuit is configured to estimate the total injected fuel quantity further as a function of the bulk modulus of the pressurized fuel. 28. The system of claim 21 wherein the injection on-time signal further includes a separate post-injection on-time for injecting a post-injected quantity of fuel into the engine following injection of the main-injected fuel quantity;and wherein the control circuit is configured to further disable for each of the number of engine operating conditions the post-injection on-time prior to the fuel injection, and enable the post-injection on-time following the fuel injection, by the fuel injector. 29. The system of claim 21 wherein the control circuit is configured to generate the main-injected fuel quantity model by periodically disabling the fuel pump and the pilot-injection on-time prior to fuel injection, and enabling the fuel pump to resume pumping and the pilot-injection on-time following fuel injection, by the fuel injector, determining based on the pressure signal a third pressure in the fuel collection unit after stabilization of the fuel pressure therein following disablement of the fuel pump and prior to fuel injection by the fuel injector, determining based on the pressure signal a fourth pressure in the fuel collection unit after fuel injection by the fuel injector and prior to resuming pumping of fuel by the fuel pump, and forming the main-injected fuel quantity model as a function of the third and fourth pressures and of the injector on-time signal for a plurality of different engine operating conditions. 30. The system of claim 29 wherein the control circuit is configured to estimate for each of the plurality of different engine operating conditions a main-injected fuel quantity value as a function of the third and fourth pressures and of the injector on-time signal, the control circuit forming the main-injected fuel quantity model as a function of the main-injected fuel quantity values for each of the plurality of different engine operating conditions. 31. The system of claim 30 wherein the control circuit is responsive to the pressure signal to estimate a bulk modulus of the pressurized fuel;and wherein the control circuit is configured to estimate for each of the plurality of different engine operating conditions the main-injected fuel quantity value further as a function of the bulk modulus of the pressurized fuel. 32. The system of claim 30 wherein the control circuit is configured to estimate for each of the plurality of different engine operating conditions a control flow leakage value as a function of corresponding ones of the third and fourth pressures and injector on-time signals;and wherein the control circuit is configured to estimate each of the plurality of main-injected fuel quantity values further as a function of a corresponding one of the plurality of control flow leakage values. 33. The system of claim 32 further including means for determining an operating temperature of the engine and producing an engine temperature signal corresponding thereto;and wherein the control circuit is configured to estimate for each of the plurality of different engine operating condition values a parasitic flow leakage value as a function of corresponding ones of the third and fourth pressures and of the en gine temperature signal;and wherein the control circuit is configured to estimate each of the plurality of main-injected fuel quantity values further as a function of a corresponding one of the parasitic flow leakage value. 34. The system of claim 33 wherein the means for determining an operating temperature of the engine is a temperature sensor producing a fuel temperature signal indicative of a temperature of the pressurized fuel;and wherein the engine temperature signal in each of the plurality of estimates of the parasitic flow leakage value corresponds to the fuel temperature signal. 35. The system of claim 33 wherein the means for determining an operating temperature of the engine is a temperature sensor producing a coolant temperature signal indicative of a temperature of engine coolant fluid;and wherein the engine temperature signal in each of the plurality of estimates of the parasitic flow leakage value corresponds to the coolant temperature signal. 36. The system of claim 33 wherein the control circuit is responsive to the pressure signal to estimate a bulk modulus of the pressurized fuel;and wherein the control circuit is configured to estimate for each of the plurality of different engine operating conditions the main-injected fuel quantity value further as a function of the bulk modulus of the pressurized fuel. 37. The system of claim 29 wherein the injection on-time signal further includes a separate post-injection on-time for injecting a pilot-injected quantity of fuel into the engine prior to injection of the main-injected fuel quantity;and wherein the control circuit is configured to further disable for each of the plurality of engine operating conditions the post-injection on-time prior to the fuel injection, and enable the pilot-injection on-time following the fuel injection, by the fuel injector. 38. The system of claim 21 wherein the control circuit is configured to determine a pilot-injected fuel quantity error as a difference between the pilot-injected fuel quantity and a commanded pilot-injected fuel quantity, and to adjust the pilot-injection on-time to minimize the pilot-injection fueling quantity error. 39. A method of estimating an auxiliary-injected fuel quantity injected into an internal combustion engine having a fuel injector responsive to an injector on-time signal to inject fuel into the engine, wherein the injector on-time signal includes separate main-injection and auxiliary-injection on-times, a fuel collection unit supplying fuel to the fuel injector, and a fuel pump supplying pressurized fuel to the fuel collection unit, the method comprising the steps of:disabling the fuel pump prior to fuel injection by the fuel injector;determining a first pressure corresponding to fuel pressure within the fuel collection unit after stabilization of the fuel pressure therein following the disabling step and prior to the fuel injection;determining a second pressure corresponding to fuel pressure within the fuel collection unit after the fuel injection;enabling the fuel pump to resume fuel pumping following determination of the second pressure;repeating the disabling step, both determining steps and the enabling step to determine the first and second pressures for a number of different engine operating conditions;determining an auxiliary-injected fuel quantity model as a function of the first and second pressures and the injector on-time signal for each of the number of different engine operating conditions; andestimating the auxiliary-injected fuel quantity according to the auxiliary-injected fuel quantity model. 40. The method of claim 39 wherein the step of determining an auxiliary-injected fuel quantity model includes:estimating for each of the number of different engine operating conditions a total injected fuel quantity, corresponding to a sum of a main-injected fuel quantity and the auxiliary-injected fuel quantity, as a function of the first and second pressures and of the injector on-time signa l;estimating for each of the number of different engine operating conditions the corresponding main-injected fuel quantity according to a main-injected fuel quantity model;estimating for each of the number of different engine operating conditions an auxiliary-injected fuel quantity value as a difference between corresponding ones of the total injected fuel quantities and the main-injected fuel quantities; andforming the auxiliary-injected fuel quantity model as a function of the auxiliary-injected fuel quantity values for each of the number of different engine operating conditions. 41. The method of claim 40 wherein the auxiliary-injected fuel quantity corresponds to a post-injected fuel quantity injected into the engine following injection of the main-injected fuel quantity, the auxiliary-injected fuel quantity values correspond to post-injected fuel quantity values, the auxiliary-injection on-time corresponds to a post-injection on-time, and the auxiliary-injected fuel quantity model corresponds to a post-injected fuel quantity model. 42. The method of claim 41 wherein the injection on-time signal further includes a separate pilot-injection on-time for injecting a pilot-injected quantity of fuel into the engine prior to injection of the main-injected fuel quantity;and wherein the disabling step further includes disabling for each of the number of engine operating conditions the pilot-injection on-time prior to the fuel injection, and enabling the pilot-injection on-time following the fuel injection, by the fuel injector. 43. The method of claim 41 wherein the step of estimating for each of the number of different engine operating conditions the corresponding main-injected fuel quantity according to a main-injected fuel quantity model includes generating the main-injected fuel quantity model. 44. The method of claim 43 wherein the step of generating the main-injected fuel quantity model includes:disabling the fuel pump and the post-injection on-time prior to fuel injection, and enabling the fuel pump to resume pumping and the post-injection on-time following fuel injection, by the fuel injector;determining based on the pressure signal a third pressure in the fuel collection unit after stabilization of the fuel pressure therein following disablement of the fuel pump and prior to fuel injection by the fuel injector;determining based on the pressure signal a fourth pressure in the fuel collection unit after fuel injection by the fuel injector and prior to resuming pumping of fuel by the fuel pump; andforming the main-injected fuel quantity model as a function of the third and fourth pressures and of the injector on-time signal for a plurality of different engine operating conditions. 45. The method of claim 44 wherein the injection on-time signal further includes a separate pilot-injection on-time for injecting a pilot-injected quantity of fuel into the engine prior to injection of the main-injected fuel quantity;and wherein the step of disabling the fuel pump and the post-injection on-time further includes disabling for each of the plurality of engine operating conditions the pilot-injection on-time prior to the fuel injection, and enabling the pilot-injection on-time following the fuel injection, by the fuel injector. 46. The method of claim 41 further including the steps of:determining a post-injected fuel quantity error as a difference between the post-injected fuel quantity and a commanded post-injected fuel quantity; andadjusting the post-injection on-time to minimize the post-injection fueling quantity error. 47. The method of claim 40 wherein the auxiliary-injected fuel quantity corresponds to a pilot-injected fuel quantity injected into the engine prior to injection of the main-injected fuel quantity, the auxiliary-injected fuel quantity values correspond to pilot-injected fuel quantity values, the auxiliary-injection on-time corresponds to a pilot-injection on-time, and the auxiliary-injected fuel quantity model corres ponds to a pilot-injected fuel quantity model. 48. The method of claim 47 wherein the injection on-time signal further includes a separate post-injection on-time for injecting a pilot-injected quantity of fuel into the engine following injection of the main-injected fuel quantity;and wherein the disabling step further includes disabling for each of the number of engine operating conditions the post-injection on-time prior to the fuel injection, and enabling the pilot-injection on-time following the fuel injection, by the fuel injector. 49. The method of claim 47 wherein the step of estimating for each of the number of different engine operating conditions the corresponding main-injected fuel quantity according to a main-injected fuel quantity model includes generating the main-injected fuel quantity model. 50. The method of claim 49 wherein the step of generating the main-injected fuel quantity model includes:disabling the fuel pump and the pilot-injection on-time prior to fuel injection, and enabling the fuel pump to resume pumping and the pilot-injection on-time following fuel injection, by the fuel injector;determining based on the pressure signal a third pressure in the fuel collection unit after stabilization of the fuel pressure therein following disablement of the fuel pump and prior to fuel injection by the fuel injector;determining based on the pressure signal a fourth pressure in the fuel collection unit after fuel injection by the fuel injector and prior to resuming pumping of fuel by the fuel pump; andforming the main-injected fuel quantity model as a function of the third and fourth pressures and of the injector on-time signal for a plurality of different engine operating conditions. 51. The method of claim 50 wherein the injection on-time signal further includes a separate post-injection on-time for injecting a post-injected quantity of fuel into the engine following injection of the main-injected fuel quantity;and wherein the step of disabling the fuel pump and the pilot-injection on-time further includes disabling for each of the plurality of engine operating conditions the post-injection on-time prior to the fuel injection, and enabling the post-injection on-time following the fuel injection, by the fuel injector. 52. The method of claim 47 further including the steps of:determining a pilot-injected fuel quantity error as a difference between the pilot-injected fuel quantity and a commanded pilot-injected fuel quantity; andadjusting the pilot-injection on-time to minimize the pilot-injection fueling quantity error. 53. System for minimizing post-injected fueling variations in an internal combustion engine, comprising:a number of fuel injectors each responsive to one of a corresponding number of injector on-time signals to supply fuel to the engine, each of the injector on-time signals having separate main-injection and post-injection on-times;a fuel collection unit supplying fuel to each of the number of fuel injectors;a fuel pump supplying pressurized fuel to the fuel collection unit;a pressure sensor in fluid communication with the fuel collection unit and producing a pressure signal indicative of fuel pressure therein; anda control circuit periodically disabling the fuel pump prior to fuel injection, and enabling the fuel pump to resume fuel pumping following fuel injection, by a selected one of the number of fuel injectors, the control circuit responsive to the pressure signal to determine a first pressure in the fuel collection unit after stabilization of the fuel pressure therein following disablement of the fuel pump and prior to fuel injection by the selected one of the number of fuel injectors, and to determine a second pressure in the fuel collection unit after fuel injection by the selected one of the number of fuel injectors and prior to resuming pumping of fuel by the fuel pump, the control circuit periodically determining the first and second pressures for remaining ones of the number of fuel inj ectors, the control circuit adjusting one or more of the post-injection on-times as a function of the first and second pressures for each of the number of fuel injectors to minimize post-injection fueling variations between the number of fuel injectors. 54. The system of claim 53 wherein the control circuit is configured to determine for each of the number of fuel injectors a pressure difference value as a difference between corresponding ones of the first and second pressures;and wherein the control circuit is configured to minimize post-injection fueling variations between the number of fuel injectors by adjusting the one or more of the post-injection on-times to minimize differences between the number of pressure difference values. 55. The system of claim 53 wherein the control circuit is configured to estimate for each of the number of fuel injectors a total injected fuel quantity as a function of corresponding ones of the first and second pressures, and a post-injected fuel quantity as a difference between the total injected fuel quantity and of a corresponding one of a number of commanded main fuel injection quantities;and wherein the control circuit is configured to minimize post-injection fueling variations between the number of fuel injectors by adjusting the one or more of the post-injection on-times to minimize differences between the number of post-injected fuel quantities. 56. The system of claim 55 wherein the control circuit is responsive to the pressure signal to estimate a bulk modulus of the pressurized fuel;and wherein the control circuit is configured to estimate each of the number of total injected fuel quantities further as a function of the bulk modulus of the pressurized fuel. 57. The system of claim 55 wherein the control circuit is configured to estimate for each of the number of fuel injectors a control flow leakage value as a function of corresponding ones of the first and second pressures and of corresponding ones of the number of injector on-time signals;and wherein the control circuit is configured to estimate for each of the number of fuel injectors the total injected fuel quantity further as a function of a corresponding one of the control flow leakage values. 58. The system of claim 57 further including means for determining an operating temperature of the engine and producing an engine temperature signal corresponding thereto;and wherein the control circuit is configured to estimate for each of the number of fuel injectors a parasitic flow leakage value as a function of corresponding ones of the first and second pressures and of the engine temperature signal;and wherein the control circuit is configured to estimate for each of the number of fuel injectors the total injected fuel quantity further as a function of a corresponding one of the parasitic flow leakage values. 59. The system of claim 58 wherein the means for determining an operating temperature of the engine is a temperature sensor producing a fuel temperature signal indicative of a temperature of the pressurized fuel;and wherein the engine temperature signal in the estimates of each of the number of parasitic flow leakage values corresponds to the fuel temperature signal. 60. The system of claim 58 wherein the means for determining an operating temperature of the engine is a temperature sensor producing a coolant temperature signal indicative of a temperature of engine coolant fluid;and wherein the engine temperature signal in the estimates of each of the number of parasitic flow leakage values corresponds to the coolant temperature signal. 61. The system of claim 58 wherein the control circuit is responsive to the pressure signal to estimate a bulk modulus of the pressurized fuel;and wherein the control circuit is configured to estimate each of the number of total injected fuel quantities further as a function of the bulk modulus of the pressurized fuel.