Abstract:
A system and method for determining the state of health of a starter motor to notify a vehicle driver of a potential starter motor failure before the failure actually occurs. The starter motor includes an armature and motor brushes each providing a resistance, and an armature coil providing an armature inductance. Further, the starter motor has a back EMF because of the starter motor being coupled to a flywheel and the vehicle engine. The system and method monitor the combined resistance of the armature and the motor brushes, the inductance of the armature and a back EMF constant of the motor, and provide a signal indicating a potential starter motor failure if any of these three values significantly deviates from nominal values. In one embodiment, the analysis of the motor resistance, armature inductance and back EMF constant is provided by a regression model to determine estimated motor parameters.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of the priority date of U.S. Provisional Patent Application Ser. No. 61/061,880, titled Method and Apparatus for Starter Motor Diagnosis and Prognosis Using Parameter Estimation Algorithm, filed Jun. 16, 2008. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates generally to a system and method for determining the state of health of a starter motor in a vehicle and, more particularly, to a system and method for determining the state of health of a starter motor in an internal combustion engine vehicle that employs a parameter estimation algorithm for determining starter motor resistance, inductance and back electro-motive force (EMF). 
     2. Discussion of the Related Art 
     As is well understood in the art, internal combustion engines typically employ a starter motor that is electrically coupled to a vehicle battery. When the ignition switch is turned on, battery power is provided to the starter motor, which rotates a motor shaft that rotates a flywheel. The flywheel rotates an engine shaft that in combination with fuel being provided to the engine causes the engine to be started so that operation of the engine can be sustained. The starter motor includes many components, including a motor armature, a motor stator, motor brushes, and other electrical components that define the motor. One or more of these components could fail as a result of many different situations where the starter motor will not operate properly, and thus, the vehicle may not start. For example, motor operation may be degraded or the motor may fail as a result of a dirty or bad brush, a short circuit of the armature coil, a weakened motor magnetic field as a result of the degradation of a permanent magnet in the motor, etc. Therefore, it is desirable to predict starter motor failure in advance of the actual failure so remedial actions can be taken before the vehicle driver is unable to start the vehicle. 
     SUMMARY OF THE INVENTION 
     In accordance with the teachings of the present invention, a system and method are disclosed for determining the state of health of a starter motor in an internal combustion engine vehicle so that the vehicle driver can be notified of a potential starter motor failure before the failure actually occurs. The starter motor includes an armature and motor brushes each providing a resistance, and an armature coil providing an armature inductance. Further, the starter motor has a back EMF because of the starter motor being coupled to a flywheel and the vehicle engine. The system and method monitor the combined resistance of the armature and the motor brushes, the inductance of the armature and a back EMF constant of the motor, and provide a signal indicating a potential starter motor failure if any of these three values significantly deviates from nominal values. In one embodiment, the analysis of the motor resistance, armature inductance and back EMF constant is provided by a regression model to determine estimated motor parameters. The regression model can employ a recursive least squares algorithm or a batch least squares algorithm. 
     Additional features of the present invention will become apparent from the following description and appended claims, taken in conjunction with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic block diagram of a vehicle starting system including a starter motor and a controller for determining starter motor state of health; 
         FIG. 2  is a schematic diagram of the electrical circuit of the starter motor shown in  FIG. 1 ; 
         FIG. 3  is a flow chart diagram showing a process for determining starter motor diagnosis and prognosis to determine the starter motor state of health that uses a recursive least squares regression model; and 
         FIG. 4  is a flow chart diagram showing a process for determining starter motor diagnosis and prognosis to determine the starter motor state of health that uses a batch least squares regression model. 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     The following discussion of the embodiments of the invention directed to a system and method for determining the state of health of a starter motor in an internal combustion engine vehicle is merely exemplary in nature and is no way intended to limit the invention or its applications or uses. 
       FIG. 1  is a schematic block diagram of a starting system  10  for a vehicle. The starting system  10  includes a vehicle engine  12 , a battery  14  and a starter motor  16 , such as a permanent magnet starter motor of the type well known to those skilled in the art. The starter motor  16  is coupled to a flywheel  18  by a rotatable motor shaft  20  and the flywheel  18  is coupled to the engine  12  by a rotatable engine shaft  22 . A voltage sensor  24  measures the voltage V m  across the starter motor  16  and a current sensor  26  measures the current flow I a  from the battery  14  to the starter motor  16 . Also, a temperature sensor  28  measures the temperature T of the starter motor  16 . As will be discussed in detail below, the system  10  includes a diagnosis and prognosis controller  30  that receives the starter current signal I a  from the current sensor  26 , the starter voltage signal V m  from the voltage sensor  24 , an engine speed signal ω E  from the engine  12  and the temperature signal T from the temperature sensor  28 , and provides an indication of the state of health of the starter motor  16 . 
       FIG. 2  is schematic diagram of an equivalent electrical circuit  32  of the starter motor  16 . The armature current I a  from the starter motor  16  flows from a positive terminal to a negative terminal through the electrical components in the circuit  32 . The electrical circuit  32  includes a resistance R b  that is the electrical resistance of the brushes of the starter motor  16 . The circuit  32  also includes a resistance R a  that is the resistance of the armature coil within the starter motor  16 . Further, the circuit  32  includes an inductance L a  that is the inductance of the armature coil in the motor  16 . Also, the circuit  32  includes a back EMF represented by voltage E b  that is a function of the rotational speed of the shaft  20 . The starter motor  16  may fail as a result of a dirty or bad brush, which will change the resistance R b , or a short circuit of the armature coil, which will decrease the inductance L a  and decrease a back EMF motor constant K m , or a degradation of the permanent magnet in the starter motor  16  will produce a weakened magnetic field, which will decrease the back EMF motor constant K m . 
     As will be discussed below, the state of health of the starter motor  16  will be determined based on these three values, particularly, a resistance value R m , the inductance L a  and the back EMF E b  defined as:
 
 R   m =( R   a   +R   b )  (1)
 
L m =L a   (2)
 
E b =K m T S ω E   (3)
 
Where K m  is the back EMF motor constant, T S  is the gear ratio between the rotation of the shaft  20  and the shaft  22  and ω E  is the rotational speed of the shaft  22 , and where ω S =T E ω E , where ω S  is the rotational speed of the shaft  20 .
 
     The starter motor current and voltage behavior can be defined by a continuous time model as: 
     
       
         
           
             
               
                 
                   
                     
                       L 
                       m 
                     
                     ⁢ 
                     
                       
                         ⅆ 
                         
                           I 
                           a 
                         
                       
                       
                         ⅆ 
                         t 
                       
                     
                   
                   = 
                   
                     
                       
                         - 
                         
                           R 
                           m 
                         
                       
                       ⁢ 
                       
                         I 
                         a 
                       
                     
                     + 
                     
                       V 
                       m 
                     
                     - 
                     
                       
                         K 
                         m 
                       
                       ⁢ 
                       
                         T 
                         S 
                       
                       ⁢ 
                       
                         ω 
                         E 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     This voltage/current relationship can be discretized for a fixed sampling time Δt as: 
     
       
         
           
             
               
                 
                   
                     
                       I 
                       a 
                     
                     ( 
                     
                         
                     
                     ⁢ 
                     k 
                     ) 
                   
                   = 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         ( 
                         
                           1 
                           - 
                           
                               
                           
                           ⁢ 
                           
                             
                               Δ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 tR 
                                 m 
                               
                             
                             
                               L 
                               m 
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           I 
                           a 
                         
                         ( 
                         
                             
                         
                         ⁢ 
                         
                           k 
                           - 
                           
                               
                           
                           ⁢ 
                           1 
                         
                         ) 
                       
                     
                     + 
                     
                         
                     
                     ⁢ 
                     
                       
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           t 
                         
                         
                           L 
                           m 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           V 
                           m 
                         
                         ( 
                         
                             
                         
                         ⁢ 
                         
                           k 
                           - 
                           
                               
                           
                           ⁢ 
                           1 
                         
                         ) 
                       
                     
                     - 
                     
                         
                     
                     ⁢ 
                     
                       
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           t 
                         
                         
                           L 
                           m 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         K 
                         m 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         T 
                         S 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           ω 
                           E 
                         
                         ( 
                         
                             
                         
                         ⁢ 
                         
                           k 
                           ⁢ 
                           
                               
                           
                           - 
                           
                               
                           
                           ⁢ 
                           1 
                         
                         ⁢ 
                         
                             
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     From this, the following model parameters p 1 ,p 2  and p 3  can be defined, and can be given nominal values from which a determination of the starter motor health can be provided. 
     
       
         
           
             
               
                 
                   
                     p 
                     1 
                   
                   = 
                   
                     ( 
                     
                       1 
                       - 
                       
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             tR 
                             m 
                           
                         
                         
                           L 
                           m 
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
             
               
                 
                   
                     p 
                     2 
                   
                   = 
                   
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       t 
                     
                     
                       L 
                       m 
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
             
               
                 
                   
                     p 
                     3 
                   
                   = 
                   
                     
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         t 
                       
                       
                         L 
                         m 
                       
                     
                     ⁢ 
                     
                       K 
                       m 
                     
                     ⁢ 
                     
                       T 
                       S 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     The model parameters p 1 ,p 2  and p 3  can be estimated from the starter current I a , the starter voltage V m  and the engine RPM ω E . 
     As will be discussed below, motor parameters are estimated to determine the state of health of the starter motor  16 . In one embodiment a regression model is first defined as: 
     
       
         
           
             
               
                 
                   
                     y 
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         φ 
                         T 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     ⁢ 
                     θ 
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
             
               
                 
                   Where 
                   , 
                   
                       
                   
                   ⁢ 
                   
                     
                       y 
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     = 
                     
                       
                         I 
                         a 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       φ 
                       T 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           I 
                           a 
                         
                         ⁡ 
                         
                           ( 
                           
                             k 
                             - 
                             1 
                           
                           ) 
                         
                       
                       , 
                       
                         
                           V 
                           m 
                         
                         ⁡ 
                         
                           ( 
                           
                             k 
                             - 
                             1 
                           
                           ) 
                         
                       
                       , 
                       
                         - 
                         
                           
                             ω 
                             E 
                           
                           ⁡ 
                           
                             ( 
                             
                               k 
                               - 
                               1 
                             
                             ) 
                           
                         
                       
                     
                     } 
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
             
               
                 
                   θ 
                   = 
                   
                     { 
                     
                       
                         
                           
                             p 
                             1 
                           
                         
                       
                       
                         
                           
                             p 
                             2 
                           
                         
                       
                       
                         
                           
                             p 
                             3 
                           
                         
                       
                     
                     } 
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     From the regression model of equations (9), (10) and (11), a recursive least square algorithm with exponential forgetting can be defined as: 
     
       
         
           
             
               
                 
                   
                     
                       θ 
                       ^ 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         θ 
                         ^ 
                       
                       ⁡ 
                       
                         ( 
                         
                           k 
                           - 
                           1 
                         
                         ) 
                       
                     
                     + 
                     
                       
                         P 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       ⁢ 
                       
                         φ 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             y 
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           - 
                           
                             
                               
                                 φ 
                                 T 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                             ⁢ 
                             
                               
                                 θ 
                                 ^ 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   k 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
             
               
                 
                   
                     P 
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       λ 
                     
                     [ 
                     
                       
                         P 
                         ⁡ 
                         
                           ( 
                           
                             k 
                             - 
                             1 
                           
                           ) 
                         
                       
                       - 
                       
                         
                           
                             P 
                             ⁡ 
                             
                               ( 
                               
                                 K 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                           ⁢ 
                           
                             φ 
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           ⁢ 
                           
                             
                               φ 
                               T 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           ⁢ 
                           
                             P 
                             ⁡ 
                             
                               ( 
                               
                                 k 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                         
                           λ 
                           + 
                           
                             
                               
                                 φ 
                                 T 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                             ⁢ 
                             
                               P 
                               ⁡ 
                               
                                 ( 
                                 
                                   k 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                             ⁢ 
                             
                               φ 
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     According to another embodiment of the present invention, the regression model is defined in matrix form as:
 
Y=Φθ  (15)
 
     The vector and matrix of this regression model can be defined as: 
     
       
         
           
             
               
                 
                   Y 
                   = 
                   
                     
                       { 
                       
                         
                           
                             
                               
                                 I 
                                 a 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   t 
                                   2 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 I 
                                 a 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   t 
                                   3 
                                 
                                 ) 
                               
                             
                           
                         
                         
                           
                             ⋮ 
                           
                         
                         
                           
                             
                               
                                 I 
                                 a 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   t 
                                   n 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       } 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       Φ 
                       ⁡ 
                       
                         [ 
                         
                           
                             
                               
                                 
                                   I 
                                   a 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     t 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                             
                               
                                 
                                   V 
                                   m 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     t 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                             
                               
                                 - 
                                 
                                   
                                     ω 
                                     E 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       t 
                                       1 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   I 
                                   a 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     t 
                                     2 
                                   
                                   ) 
                                 
                               
                             
                             
                               
                                 
                                   V 
                                   m 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     t 
                                     2 
                                   
                                   ) 
                                 
                               
                             
                             
                               
                                 - 
                                 
                                   
                                     ω 
                                     E 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       t 
                                       2 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               ⋮ 
                             
                             
                               ⋮ 
                             
                             
                               ⋮ 
                             
                           
                           
                             
                               
                                 
                                   I 
                                   a 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     t 
                                     
                                       n 
                                       - 
                                       1 
                                     
                                   
                                   ) 
                                 
                               
                             
                             
                               
                                 
                                   V 
                                   m 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     t 
                                     
                                       n 
                                       - 
                                       1 
                                     
                                   
                                   ) 
                                 
                               
                             
                             
                               
                                 - 
                                 
                                   
                                     ω 
                                     E 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       t 
                                       
                                         n 
                                         - 
                                         1 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     This regression model can be solved using a batch least squares algorithm as:
 
{circumflex over (θ)}=[Φ T Φ] −1 Φ T   Y   (17)
 
     From either of the regression models referred to above, motor parameters R m , K m  and L m  can be estimated as: 
     
       
         
           
             
               
                 
                   
                     R 
                     m 
                   
                   = 
                   
                     
                       
                         p 
                         1 
                       
                       - 
                       1 
                     
                     
                       p 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
             
               
                 
                   
                     K 
                     m 
                   
                   = 
                   
                     
                       p 
                       3 
                     
                     
                       p 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
             
               
                 
                   
                     L 
                     m 
                   
                   = 
                   
                     
                       p 
                       2 
                     
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       t 
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     In one embodiment, the motor parameters R m , K m  and L m  are stored in a memory in the form of a temperature based look-up table as R m   o (T), K m   o (T) and L m   o (T). 
     From the motor parameters R m , K m  and L m , an error e can be defined as: 
                   e   =           ⁢     max   ⁢     {         w   R     ⁢                R   ^     m     -       K   m   O     ⁡     (   T   )             R   m   O     ⁡     (   T   )                ,       w   K     ⁢                K   ⋒     m     -       K   m   O     ⁡     (   T   )             K   ⋒     m              ,       w   L     ⁢           L   ^     m     -       L   m   O     ⁡     (   T   )             L   ^     m           }               (   21   )               
Where, w R  is a weighting factor for the resistance motor parameter R m , w K  is a weighting factor for the back EMF constant motor parameter K m  and w L  is a weighting factor for the inductance motor parameter L m , where the weighting factor is given an optimal result.
 
     Thus, any changes in the motor resistance R m , the motor constant K m  and the inductance I m  is captured in the error equation (21). By establishing an error threshold e Th , a warning signal can be given to the vehicle driver, such as a light on the dashboard, telling the vehicle driver that the state of health of the starter motor  16  is reduced, which may cause it to fail in the future. Equation (22) below gives the state of health SOH starter  of the starter motor  16  based on the error signal e as a percentage. This value is output from the controller  30 . 
     
       
         
           
             
               
                 
                   
                     S 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     O 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       H 
                       Starter 
                     
                   
                   = 
                   
                     
                       
                         
                           e 
                           TH 
                         
                         - 
                         e 
                       
                       
                         e 
                         TH 
                       
                     
                     × 
                     100 
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
       FIG. 3  is a flow chart diagram  40  showing one process for determining the state of health of the starter motor  16  using the recursive least squares algorithm, discussed above. The starter motor  16  is operational when the ignition starter is turned on and the motor  16  is cranked, so that is the time when signals are available from the starter motor  16 . The algorithm determines whether the starter motor  16  has started cranking at box  42 , and then reads the starter motor temperature T at box  44 . The algorithm then reads the starter voltage V m , the starter current I a  and the engine RPM ω E  at box  46 . The algorithm then uses the regression model of equations (9)-(12) and the recursive least squares algorithm of equations (13) and (14) at box  48 . Once the algorithm has determined the regression model and recursive least squares algorithm, it determines whether the cranking has ended at decision diamond  50 , and if not, returns to the box  46  to read the starter voltage V m , the starter current I a  and the engine RPM ω E . If the starter motor  16  has finished being cranked and the engine has started, then the algorithm calculates the motor parameters of equations (18), (19) and (20) at box  52 , and calculates the motor error e using equation (21) at box  54 . The algorithm then calculates the state of health value SOH starter  using equation (22) at box  56  and informs the vehicle driver of the starter motor SOH and whether service is required at box  58 . The algorithm then waits until the next ignition cycle at box  60 . 
       FIG. 4  is a flow chart diagram  70  showing a process for determining the state of health of the starter motor  16  using the batch least squares algorithm. The algorithm determines whether starter motor cranking has begun at box  72 , and if so, sets a sample k=1 at box  74 , and then reads the starter motor temperature T at box  68 . The algorithm measures the starter voltage V m , the starter current I a  and the engine RPM ω E  at box  76 , and then sets these values to the sample k at box  78 . The algorithm then determines whether the starter motor cranking has ended at decision diamond  80 , if not, adds one to the sample k at box  82  and returns to reading the starter voltage V m , the starter current I a  and the engine RPM ω E  at the box  76 . If the starter motor cranking has ended at the decision diamond  80 , then the algorithm determines the matrixes Y,φ and θ for the batch least squares algorithm using equations (15), (16) and (17) at box  84 . As above, the algorithm calculates the motor parameters at box  86 , the motor error e at box  88 , the starter motor state of health SOH starter  at box  90 , and informs the driver of the starter state of health at box  92 . The algorithm then waits until the next ignition cycle at box  94  to begin the process over. 
     The foregoing discussion discloses and describes merely exemplary embodiments of the present invention. One skilled in the art will readily recognize from such discussion and from the accompanying drawings and claims that various changes, modifications and variations can be made therein without departing from the spirit and scope of the invention as defined in the following claims.