System and method for recursively estimating battery cell total capacity

1. A method for estimating a battery cell total capacity indicative of a total capacity of a battery cell, comprising:

receiving a first battery cell state-of-charge estimate at a first time and receiving a second battery cell state-of-charge estimate at a second time subsequent to the first time;

measuring an integrated battery cell current value indicative of an integrated battery cell current between the first time and the second time;

updating at least one recursive parameter based on the first battery cell state-of-charge estimate, the second battery cell state-of-charge estimate, and the integrated battery cell current value;

estimating, by using a computer, the battery cell total capacity based on said at least one recursive parameter; and

storing a value corresponding to the estimated battery cell total capacity in a memory.

2. The method of claim 1 , wherein updating at least one recursive parameter based on the first battery cell state-of-charge estimate, the second battery cell state-of-charge estimate, and the integrated battery cell current value comprises:

computing a state-of-charge difference by subtracting the first battery cell state-of-charge estimate from the second battery cell state-of-charge estimate;

updating a first recursive parameter by multiplying a prior value of the first recursive parameter by a first scaling factor between 0 and 1 (inclusive);

further updating the first recursive parameter by adding the square of the state-of-charge difference and by subtracting the square of the integrated battery cell current value;

updating a second recursive parameter by multiplying its prior value by a second scaling factor between 0 and 1 (inclusive); and

further updating the second recursive parameter by adding the product of the state-of-charge difference and the integrated battery cell current value.

3. The method of claim 2 , wherein the step of updating the second recursive parameter uses the relationship s 2 =s 2 +(z(t 2 )−z(t 1 ))y.

4. The method of claim 1 , wherein estimating a battery cell total capacity based on at least one recursive parameter comprises:

receiving a first recursive parameter and a second recursive parameter; and solving a quadratic equation involving the first recursive parameter and the second recursive parameter to determine the estimated battery cell total capacity.

5. The method of claim 4 , wherein the step of estimating the battery cell total capacity is governed by the equation

C

=

-

s

1

+

s

1

2

+

4

⁢

s

2

2

2

⁢

s

2

.

6. The method of claim 4 , wherein the first recursive parameter is governed by the equation s 1 =αs 1 +x 2 −y 2 , and the second recursive parameter is governed by the equation s 2 =βs 2 +xy, where 0<α<1 and 0<β<1.

7. The method of claim 1 , wherein determining the estimated battery cell total capacity based on at least one recursive parameter comprises:

receiving a first recursive parameter and a second recursive parameter;

solving a quadratic equation involving the first recursive parameter and the second recursive parameter to determine an initial battery cell total capacity estimate;

determining a filtered battery cell total capacity estimate based on at least one of an initial battery cell total capacity estimate corresponding to a present or prior time and a filtered battery cell total capacity estimate corresponding to a prior time; and

determining an estimated battery cell total capacity based on the filtered battery cell total capacity estimate.

8. The method of claim 1 where measuring an integrated battery cell current value indicative of the integrated battery cell current between the first time and the second time comprises:

measuring an initial integrated battery cell current value indicative of the integrated battery cell current between the first time and the second time; and

computing the integrated battery cell current by multiplying the initial integrated battery cell current value by a scaling constant.

9. The method of claim 1 , wherein the step of measuring an integrated battery cell current value indicative of the integrated battery cell current between the first time and the second time uses the relationship

y

=

∫

t

1

t

2

⁢

η

⁢

⁢

i

⁡

(

t

)

⁢

⁢

ⅆ

t

.

10. The method of claim 1 , wherein the step of updating at least one recursive parameter based on the first battery cell state-of-charge estimate, the second battery cell state-of-charge estimate, and the integrated battery cell current value uses the relationship s 1 =s 1 +(z(t 2 )−z(t 1 )) 2 −y 2 .

11. A system for estimating a battery cell total capacity indicative of a total capacity of a battery cell, comprising:

a computer configured to receive a first state-of-charge estimate at a first time;

the computer configured to receive a second state-of-charge estimate at a second time, subsequent to the first time;

a current sensor electrically coupled to the battery cell, the current sensor configured to generate a signal indicative of integrated battery cell current between the first and second times;

the computer configured to receive the first state-of-charge estimate, the second state-of-charge estimate, and the integrated battery cell current, the computer is further configured to update at least one recursive parameter based on the first state-of-charge estimate, the second state-of-charge estimate, and the integrated battery cell current, and to estimate the battery cell total capacity based on said at least one recursive parameter, the computer further configured to store a value corresponding to the estimated battery cell total capacity in a memory.

12. A non-transitory computer readable medium having computer-executable instructions for performing a method for estimating a battery cell total capacity indicative of a total capacity of a battery cell, the method comprising:

receiving a first battery cell state-of-charge estimate at a first time and receiving a second battery cell state-of-charge estimate at a second time subsequent to the first time;

measuring an integrated battery cell current value indicative of an integrated battery cell current between the first time and the second time;

updating at least one recursive parameter based on the first battery cell state-of-charge estimate, the second battery cell state-of-charge estimate, and the integrated battery cell current value;

estimating the battery cell total capacity based on said at least one recursive parameter; and

storing a value corresponding to the estimated battery cell total capacity in a memory.