Method for estimating an exhaust gas temperature

1. A method for estimating a temperature of an exhaust gas in an exhaust line of an internal combustion engine, the exhaust line comprising a NO x sensor that comprises an heater, the method comprising:

determining, with an electronic control unit (ECU), a value of a parameter indicative of an heat released by the heater of the NO x sensor; and

calculating, with the electronic control unit (ECU), a value of the temperature of the exhaust gas as a function of the value of the parameter,

wherein the parameter is an electrical power supplied to the heater of the NOx sensor, and wherein the value of the parameter is calculated according to:

P

el

=

dc

·

V

batt

2

R

H

,

wherein, P el is the value of the electrical power supplied to the heater of the NO x sensor,

wherein V batt is a value of a voltage supplied by an electrical battery connected to the heater of the NO x sensor,

wherein dc is a duty cycle of a PWM electrical signal generated with the electrical battery and supplied to the heater of the NO x sensor, and

wherein R H is a value of an electrical resistance of the heater of the NO x sensor.

2. The method according to claim 1 , wherein the temperature of the exhaust gas is calculated according to:

T exh =T s −R s ·P el ,

wherein T exh is the value of the temperature of the exhaust gas,

wherein T s is a value of a target operating temperature of the NO x sensor, and

wherein R s is a value of a conversion parameter correlating the electrical power to the temperature of the NO x sensor.

3. The method according to claim 2 , wherein R s is determined on a basis of a value of an exhaust gas flow rate in the exhaust line.

4. The method according to claim 1 , further comprising performing a dynamic correction of the value of the temperature of the exhaust gas.

5. A non-transitory computer readable medium containing a computer program product with computer instructions stored therein for causing a computer processor to perform:

an estimation program for estimating a temperature of an exhaust gas in an exhaust line of an internal combustion engine, the exhaust line comprising a NO x sensor that comprises a heater program, the estimation program configured to:

determine a value of a parameter indicative of an heat released by a heater of the NO x sensor; and

calculate a value of the temperature of the exhaust gas as a function of the value of the parameter,

wherein the parameter is an electrical power supplied to the heater of the NOx sensor, and wherein the value of the temperature of the exhaust gas is calculated according to:

T exh =T s −R s ·P el ,

wherein T exh is the value of the temperature of the exhaust gas,

wherein P el is the value of the electrical power supplied to the heater of the NO x sensor,

wherein T s is a value of a target operating temperature of the NO x sensor, and

wherein R s is a value of a conversion parameter correlating the electrical power to a temperature of the NO x sensor.

6. The non-transitory computer readable medium embodying the computer program product according to claim 5 , wherein the value of the parameter is calculated according to:

P

el

=

dc

·

V

batt

2

R

H

,

wherein V batt is a value of a voltage supplied by an electrical battery connected to the heater of the NO x sensor,

wherein dc is a duty cycle of a PWM electrical signal generated by with the electrical battery and supplied to the heater of the NO x sensor, and

wherein R H is a value of an electrical resistance of the heater of the NO x sensor.

7. The non-transitory computer readable medium embodying the computer program product according to claim 5 , wherein R s is determined on a basis of a value of an exhaust gas flow rate in the exhaust line.

8. The non-transitory computer readable medium embodying the computer program product according to claim 5 , the estimation program further configured to perform a dynamic correction of the value of the temperature of the exhaust gas.

9. An estimating apparatus for an internal combustion engine, comprising:

an exhaust line;

a NO x sensor;

a heater for the NO x sensor; and

a controller configured to:

determine a value of a parameter that is indicative of heat released by the heater of the NOx sensor, and

calculate a value of the temperature of an exhaust gas in the exhaust line as a function of the value of the parameter,

wherein the parameter is an electrical power supplied to the heater of the NOx sensor, and wherein the value of the parameter is calculated according to:

P

el

=

dc

·

V

batt

2

R

H

,

wherein, Pel is the value of the electrical power supplied to the heater of the NO x sensor,

wherein V batt is a value of a voltage supplied by an electrical battery connected to the heater of the NO x sensor,

wherein dc is a duty cycle of a PWM electrical signal generated with the electrical battery and supplied to the heater of the NO x sensor, and

wherein R H is a value of an electrical resistance of the heater of the NO x sensor.

10. The estimating apparatus according to claim 8 , wherein the value of the temperature of the exhaust gas is calculated according to:

T exh =T s −R s ·P el ,

wherein T exh is the value of the temperature of the exhaust gas,

wherein T s is a value of a target operating temperature of the NO x sensor, and

wherein R s is a value of a conversion parameter correlating the electrical power to a temperature of the NO x sensor.

11. The estimating apparatus according to claim 10 , wherein R s is determined on a basis of a value of an exhaust gas flow rate in the exhaust line.

12. The estimating apparatus according to claim 9 , the estimating apparatus further configured to perform a dynamic correction of the value of the temperature of the exhaust gas.