Abstract:
An adaptive battery estimation control system includes a fixed and adaptive battery estimators effective for a battery parameter estimations across a wide range of dynamic battery operational conditions.

Description:
TECHNICAL FIELD 
     The present invention relates to estimation of battery dynamics. 
     BACKGROUND 
     Accurate estimates of battery dynamics may be used to improve many vehicle control systems, such as a control system associated with regenerative brake blending, and in vehicles including increased electrical content. For example, battery dynamics estimation may enable enhanced prognostics and battery controls. To provide increased vehicle system control, a greater number of sensors are being included with a vehicle. Including a greater number of sensors may increase the burden on the electrical system of a vehicle, of which the battery is a major component. 
     Several methods exist and are known in the art for estimating battery dynamics. However, existing methods relate primarily to “slow” battery dynamics and are typically limited to the battery state-of-charge (SOC). A battery also includes “fast” battery dynamics, which may include the battery voltage and the battery current. The “fast” battery dynamics may fluctuate at a rate much greater than the battery state-of-charge, thereby rendering estimations of state-of-charge unable to accurately reflect all battery dynamics. 
     SUMMARY 
     A method of adaptively estimating battery dynamics using an adaptive battery control system in operative communication with at least one battery includes estimating a battery terminal voltage, internal resistance, and current from a desired power request and from a plurality of battery dynamics inputs. Further, predicted battery terminal voltage and current, and an updated estimated battery internal resistance based on the estimated battery terminal voltage, the estimated battery internal resistance, and the estimated battery current are determined. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       One or more embodiments will now be described, by way of example, with reference to the accompanying drawings, in which: 
         FIG. 1  is a schematic illustration of a vehicle battery control module in signal communication with a vehicle battery in accordance with the present disclosure; 
         FIG. 2  is a flow chart illustrating a method of adaptively estimating battery dynamics using an adaptive battery control system in accordance with the present disclosure; 
         FIG. 3  is a flow-chart illustrating a method of adaptively estimating battery dynamics using an adaptive battery control system in accordance with the present disclosure; and 
         FIG. 4  is a flow-chart illustrating a method of adaptively estimating battery dynamics using an adaptive battery control system in accordance with the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Disclosed herein is an adaptive battery estimation control system, and a method of using the adaptive battery estimation control system in a vehicle having a battery, a vehicle electrical system, and a vehicle battery control module. The vehicle battery control module may comprise any combination of hardware, including but not limited to: microprocessors and computer memory devices; and software, the software operating to control the operation of the hardware and the vehicle battery. 
     As defined herein, a battery may be any device or combination of devices operating to receive, store, and discharge an electrical charge. 
     The adaptive battery estimation control system uses a plurality of sensors in signal communication with the vehicle battery control module to estimate ether or both battery voltage and battery current when the vehicle electrical system is placed under load or receives a charge. 
     The adaptive battery estimator includes a plurality of modules that cooperate to process input signals received from a plurality of sensors associated with a vehicle and a vehicle electrical system. The adaptive battery estimator operates to evaluate the received input signals to determine the battery parameters including, but not limited to: battery voltage, battery state-of-charge, battery power, and battery rated capacity. As used herein the term “module” or “modules” is defined as one or more units capable of processing or evaluating signals input into or stored within the vehicle battery control module including a fixed battery estimator and an adaptive battery estimator. Each module may be a stand-alone unit or a plurality of units comprising hardware or software or a combination thereof. 
     More particularly, in an embodiment, each of the plurality of sensors electronically communicates a battery voltage signal to a vehicle battery control module. The vehicle battery control module also electronically receives a power request. The power request may be any electrical load placed upon a vehicle electrical system and may be made by a vehicle user or a vehicle system. 
     The vehicle battery control module may also electronically receive an actual or reported and estimated state-of-charge signal used to estimate open circuit voltage of the battery from the battery state-of-charge sensor. The control module  14 , using estimated open circuit voltage of the battery and the power request, determines an estimated and a predicted voltage; an estimated and a predicted current; and an estimated internal resistance, or any combination thereof. 
       FIG. 1  illustrates an adaptive battery estimation control system  10  in a vehicle (not shown) having a vehicle battery control module  14  in bi-directional communication with a plurality of sensors, including a battery terminal voltage sensor  16 A, provided to communicate signals from a number of vehicle systems and in particular from a battery  18  to the vehicle battery control module  14 . 
     More particularly, the control module  14  includes a fixed battery estimator  32  used to determine an estimated battery terminal voltage, an estimated battery internal resistance, and an estimated battery current based on a measured or estimated terminal voltage and a desired power request. Control module  14  also includes an adaptive battery estimator  34  used to determine a predicted battery terminal voltage, a predicted battery current, and an estimated battery internal resistance based on the measured battery terminal voltage, the estimated battery internal resistance, and the estimated battery current input into the adaptive battery estimator  34  from the fixed battery estimator. 
     In an embodiment, when an open circuit voltage of the battery is a function of the battery&#39;s SOC, the vehicle battery control module  14  is placed in electrical and signal communication with a SOC estimator module  22 . The SOC estimator module  22  operates to provide the vehicle battery control module  14  with an estimated SOC, or an estimated open-circuit voltage (estimated V oc ). 
     In one embodiment, the adaptive battery estimation control system  10  estimates and predicts battery dynamics including an estimated battery terminal voltage in response to changing vehicle electrical system conditions based on battery SOC and a desired power request. 
     In an embodiment, shown in  FIG. 1 , the fixed battery estimator  32  includes a SOC estimator  22 , an a priori battery resistance estimator  23 , a battery current estimator  25 , and a battery terminal voltage estimator  37 . The fixed battery estimator  32  is in signal communication with the battery  18 , with a desired power request signal  17 A, and with the adaptive battery estimator  34  when the battery  18  is not in a low battery power state or condition, and thus, when SW 1  and SW 2  are closed. 
     In an embodiment when the battery  18  is not in a low battery state, the fixed battery estimator  32  receives a desired power request, P* b (k) at a time sample k via desired power signal  17 A, from a remote location, a state-of-charge signal  17 B from the battery  18  and outputs both an estimated battery terminal voltage {circumflex over (V)} b   0 (k) via estimated battery terminal voltage signal  27 A and an estimated internal battery resistance {circumflex over (R)} b   o (k) via estimated internal battery resistance signal  27 B to the adaptive battery estimator  34 . 
     In an embodiment when the battery  18  is not in a low power state, the state-of-charge signal  17 B is input into the state-of-charge estimator  22  to estimate an open circuit voltage {circumflex over (V)} oc (k) via estimated open circuit voltage signal  17 F, wherein the open circuit voltage {circumflex over (V)} oc (k) is a function of the battery state-of-charge, wherein the state-of-charge signal  17 B is based on an estimated state-of-charge or a reported state-of-charge. The open circuit voltage signal  17 F, an internal battery resistance signal  17 E, and the desired power request signal  17 A are input into the fixed battery terminal estimator  37  to determine the estimated battery terminal voltage {circumflex over (V)} b   0 (k). 
     In an embodiment, the estimated battery terminal voltage {circumflex over (V)} b   0 (k) is output via an estimated battery terminal signal  27 A to both the adaptive battery estimator  34  and back to the fixed battery estimator  32  via a feedback control loop  35 A, which includes signals  27 A,  29 A, and  17 E. 
     The feedback control loop  35 A inputs the estimated battery terminal voltage signal  27 A from the last time sample (k−1) into the battery current estimator  25 , wherein the battery current estimator  25  determines an estimated current Î b (k) via an estimated battery current signal  29 A. The estimated battery current signal  29 A is input into the a priori internal battery resistance estimator  23  to determine an estimated internal battery resistance {circumflex over (R)} b   o (k) via an estimated internal battery resistance signal  17 E, which is then input into the fixed battery terminal voltage estimator  37  and from there also to the adaptive battery estimator  34  via line  27 B. 
     More particularly, the battery current estimator  25  determines an estimated battery current signal  29 A based on both the desired power request signal  17 A, and the estimated battery terminal voltage signal  27 A from the last time sample (k−1). The feedback control loop  35 A operates to continuously update and estimate the internal battery resistance {circumflex over (R)} b   o (k). 
     With additional reference to  FIGS. 2-4  which illustrate various methods in accordance with the present disclosure, bracketed reference numerals (#) correspond to portions of such methods. In an embodiment, a method ( 60 ) for adaptively estimating and predicting battery dynamics is shown in  FIG. 2 . More particularly, the control module  14  includes a fixed battery estimator  32  ( 36 ) used to determine an estimated battery terminal voltage, an estimated battery internal resistance, and an estimated battery current based on an estimated open circuit voltage and a desired power request, and then uses an adaptive battery estimator  34  to determine a predicted battery terminal voltage, a predicted battery current, and an estimated battery internal resistance based on the estimated battery terminal voltage, the estimated battery internal resistance, and the estimated battery current input into the adaptive battery estimator  34  ( 70 ) from the fixed battery estimator  32  ( 36 ). 
     Initially, the battery open circuit voltage ({circumflex over (V)} oc (k)) is determined ( 24 ) by the vehicle battery control module  14  as a function of the SOC. The SOC may be either estimated or reported. In an embodiment wherein the SOC is reported, the SOC may be reported as information, which is typically collected at the battery cell during battery cell characterization. In an embodiment where the SOC is estimated, the SOC may be estimated by a variety of statistical estimation methods, as is known in the art. 
     Determination of {circumflex over (V)} oc (k) (24) may be made using Equation (1):
 
 {circumflex over (V)}   oc ( k )= f (SOC( k ))  (1)
 
wherein {circumflex over (V)} oc  is the determined open circuit voltage of the battery, k represents a discrete time sample and comprises an integer, and SOC is the state-of-charge. The sampling rate T (not shown) may vary. In one embodiment, the time sampling rate T is 8 milliseconds.
 
     Once {circumflex over (V)} oc  is determined, as illustrated in  FIG. 2 , a preliminary estimation of battery current is determined ( 26 ) by the battery current estimator  25  using Equation (2):
 
 Î   b ( k )= P*   b ( k )/ {circumflex over (V)}   b ( k− 1)  (2)
 
wherein Î b  is the preliminary estimation of battery current, k is the time sample as disclosed in Equation (1), P* b  is desired power request representing power flowing out of the battery  18 , and {circumflex over (V)} b  is the estimated battery terminal voltage of the battery  18 .
 
     The determined preliminary estimate of battery current (Î b ) ( 26 ) is then used to compute the battery internal resistance ({circumflex over (R)} b   o ) ( 28 ) using Equation (3): 
                         R   ^     b   o     ⁡     (   k   )       =     {             KeHVBR_R   ⁢   _HVBatResistanceDisChg     ,               if     ⁢           ⁢         I   ^     b     ⁡     (   k   )         &gt;   0                 KeHVBR_R   ⁢   _HVBatResistanceChg     ,               if     ⁢           ⁢         I   ⋒     b     ⁡     (   k   )         ≤   0                     (   3   )               
wherein {circumflex over (R)} b   o  is the battery internal resistance, k is the time sample and comprises an integer, KeHVBR_R_HVBatResistanceDisChg is a variable corresponding to the battery  18  being in a discharge state if Î b (k)&gt;0 as determined in Equation (2), and KeHVBR_R_HVBatResistanceChg is a software functionality module corresponding to the battery  18  being in a charging state if Î b (k) is a value that is less than zero.
 
     Next, as illustrated in  FIG. 2 , each of the battery circuit open voltage ({circumflex over (V)} oc (k)), the preliminary estimate of battery current (Î b ), and the battery internal resistance ({circumflex over (R)} b   o ) parameters are used to estimate the battery terminal voltage ( 30 ) through a relationship derived from Equations (1) through (3), wherein the relationship defines estimated battery terminal voltage {circumflex over (V)} be   0 (k) determined by the fixed battery estimator  32 . The fixed battery estimator determines a linear battery terminal voltage using Equation (4): 
                         V   ^     b   0     ⁢           e     ⁢     (   k   )         =             V   ^     oc     ⁡     (   k   )       +             V   ^     oc   2     ⁡     (   k   )       -     4   ⁢         R   ^     b   0     ⁡     (   k   )       ⁢       P   b   *     ⁡     (   k   )               2             (   4   )               
wherein each of the variables are defined in Equations (1)-(3).
 
     Once determined, {circumflex over (V)} be   0 (k) and other estimated signals are input ( 68 ) into the adaptive battery estimator  34 . A predicted voltage value {circumflex over (V)} bp   0 (k) via predicted battery terminal voltage signal  33 A is determined by the non-linear adaptive battery estimator  34  ( 70 ), enabling the vehicle battery control module  14  to track, estimate, and predict battery dynamics online. 
     In an embodiment, the non-linear adaptive battery estimator  34  uses logic to determine the predicted voltage value {circumflex over (V)} bp   0 (k) using the estimated battery terminal voltage {circumflex over (V)} b     e     0 (k) derived from the fixed battery estimator  32  as determined in Equation (4), as represented in Equation (5): 
                           V   ^     b     ⁢           p     ⁢     (   k   )         ≅           V   ^     b   0     ⁢           e     ⁢     (   k   )         +       ∂     V   b         ∂     R   b             ⁢     ❘       R   b     =         R   ^     b   0     ⁡     (   k   )           ⁢     ×   d   ⁢           ⁢         R   ^     b     ⁡     (   k   )                 (   5   )               
wherein R b  is an updated estimated internal battery resistance of the battery  18  determined by the fixed battery estimator  32  and d{circumflex over (R)} b (k) is a change in the estimated internal battery resistance as determined by the adaptive battery estimator in Equation (8) below, and wherein
 
                 ∂     V   b         ∂     R   b         ⁢     ❘       R   b     =         R   ^     b   0     ⁡     (   k   )                 
is a change in the estimated battery terminal voltage with respect to a change in the estimated internal battery resistance.
 
     More particularly, Equation (5) calculates 
                 ∂     V   b         ∂     R   b         ⁢     ❘       R   b     =         R   ^     b   0     ⁡     (   k   )                 
as follows:
 
     
       
         
           
             
               
                 
                   
                     
                       
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     In one embodiment, 
                 ∂     V   b         ∂     R   b         ⁢     ❘       R   b     =         R   ^     b   0     ⁡     (   k   )                 
represents a statistical sensitivity factor determined ( 38 ) in Equation (6a):
 
                     ϕ   ⁡     (   k   )       =         ∂     V   b         ∂     R   b         ⁢     ❘       R   b     =         R   ^     b   0     ⁡     (   k   )                     (     6   ⁢   b     )               
wherein φ represents the statistical sensitivity factor and k represents a time sample and comprises an integer.
 
     Using φ determined in Equation (6b), the adaptive battery estimator  34  then determines a covariance P(k) ( 40 ), wherein the covariance is determined using Equation (7): 
                     P   ⁡     (   k   )       =       1   α     ⁡     [       P   ⁡     (     k   -   1     )       -           P   2     ⁡     (     k   -   1     )       ⁢       ϕ   2     ⁡     (   k   )           α   +       P   ⁡     (     k   -   1     )       ⁢       ϕ   2     ⁡     (   k   )               ]               (   7   )               
wherein α is a fixed variable.
 
     After updating the covariance, the adaptive battery estimator  34  calculates an update to the battery internal resistance ({circumflex over (R)} b   o ) (42) using Equation (8): 
                     d   ⁢           ⁢         R   ^     b     ⁡     (   k   )         =       d   ⁢           ⁢         R   ^     b     ⁡     (     k   -   1     )         +       1     α   +       P   ⁡     (     k   -   1     )       ⁢       ϕ   2     ⁡     (   k   )             ⁢     P   ⁡     (     k   -   1     )       ⁢     ϕ   ⁡     (   k   )       ⁢     (         V   b     ⁡     (   k   )       -         V   ^     b     ⁡     (     k   -   1   -   d     )         )                 (   8   )               
wherein d represents a corrective factor that may provide tuning or correction of measurement and of lag in measurement. Additionally, the corrective factor d may provide correction for other battery or system parameters, the tuning of which would provide an optimization of the function of the adaptive battery control module  14 .
 
     In an embodiment, the value of 
               ϕ   ⁡     (   k   )       =         ∂     V   b         ∂     R   b         ⁢     ❘       R   b     =         R   ^     b   0     ⁡     (   k   )                   
is substituted in Equation (5) with φ(k) derived from Equations (6a) and (6b) to determine the predicted battery terminal voltage as {circumflex over (V)} b     p   (k) ( 44 ) defined in Equation (9):
   {circumflex over (V)}   b     p   ( k )≅ {circumflex over (V)}   b   0 ( k )+φ( k )* d{circumflex over (R)}   b ( k )  (9) 
     During use of a vehicle including a battery  18 , the internal resistance, interchangeably referred to herein as impedance, of the battery  18  may change, depending upon the operating condition of the battery  18 . The operating conditions of the battery  18  may include the battery  18  being charged by a power source, the battery  18  being discharged to a load, or the battery  18  maintaining a given charge. To account for variations in battery impedance, another embodiment is provided, wherein an adaptive battery estimator  46  is provided to account for differences in battery impedance caused by differing battery operating conditions. 
     In an embodiment illustrated in  FIG. 3 , a method ( 84 ) operates to adaptively estimate and predict battery dynamics. Initially, a fixed battery estimator  66  ( 36 ) operates to estimate the battery dynamics in the same manner as the fixed battery estimator  32  as shown in  FIG. 2 . The updated estimated internal battery resistance reflecting a change in the internal battery resistance is calculated by an adaptive battery estimator  46  depending on whether the battery is in a charging or a discharging state ( 48 ), ( 49 A), ( 49 B). The adaptive battery estimator  46  determines the statistical sensitivity factor φ(k) ( 38 ) as disclosed in Equations (6a) and (6b), and the covariance P(k) ( 40 ) as disclosed in Equation (7). However, unlike the adaptive battery estimator  34  ( 70 ), the adaptive battery estimator  46  ( 72 ) substitutes Equation (8) with Equations (10a) and (10b) as follows to determine d{circumflex over (R)} b (k). The selected d{circumflex over (R)} b (k) is then used to calculate the predicted battery terminal voltage {circumflex over (V)} b     p   (k) as disclosed in Equation (9) and determines whether the battery is in a discharging state wherein the power P*(k) is greater than zero or a charging state wherein P*(k) is less than or equal to zero ( 48 ) and includes the following process, to be used by adaptive battery estimator  46 , according to the value of P*(k), as shown in Equations (10a) and (10b): 
                   If                               P   *     (   k   )       &lt;   0     ,           (     10   ⁢   a     )               then                             d   ⁢           ⁢         R   ^       b   ,   chg       ⁡     (   k   )         =       d   ⁢           ⁢         R   ^       b   ,   chg       ⁡     (     k   -   1     )         +       1     a   +       P   ⁡     (     k   -   1     )       ⁢       ϕ   2     ⁡     (   k   )             ⁢     P   ⁡     (     k   -   1     )       ⁢     ϕ   ⁡     (   k   )       ⁢     (         V   b     ⁡     (   k   )       -         V   ^     b     ⁡     (     k   -   1   -   d     )         )                                 wherein                             d   ⁢           ⁢         R   ⋒     b     ⁡     (   k   )         =     d   ⁢           ⁢           R   ^       b   ,   chg       ⁡     (   k   )       .                               If                             P   *     (   k   )       ≥   0           (     10   ⁢   b     )                 d   ⁢           ⁢         R   ^       b   ,   dischg       ⁡     (   k   )         =       d   ⁢           ⁢         R   ^       b   ,   dischg       ⁡     (     k   -   1     )         +       1     a   +       P   ⁡     (     k   -   1     )       ⁢       ϕ   2     ⁡     (   k   )             ⁢     P   ⁡     (     k   -   1     )       ⁢     ϕ   ⁡     (   k   )       ⁢     (         V   b     ⁡     (   k   )       -         V   ^     b     ⁡     (     k   -   1   -   d     )         )                                 
wherein d{circumflex over (R)} b (k)=d{circumflex over (R)} b,dischg (k). In Equations (10a) and (10b), d{circumflex over (R)} b,chg  is the impedance of the battery  18  when the battery  18  is in a charging operating condition and d{circumflex over (R)} b,dischg  is the impedance of the battery  18  when the battery  18  is in a discharging operating condition.
 
     In an embodiment, the adaptive battery estimator  46  may switch between d{circumflex over (R)} b,dischg  ( 49 A) and d{circumflex over (R)} b,chg  ( 49 B) of Equations (10a) and (10b), using a battery impedance corresponding to a discharge state of operation of the battery  18 , or a battery impedance corresponding to a charging state of the battery  18 , represented by d{circumflex over (R)} b,dischg  and d{circumflex over (R)} b,chg , respectively, in the above equations and illustrated in  FIG. 3 . 
     In another embodiment a method ( 90 ) of adaptively estimating and predicting battery dynamics is shown in  FIG. 4 . Adaptive battery estimator  80  estimates and predicts battery dynamics including an estimated battery terminal voltage in response to changing vehicle electrical system conditions based on a measured battery terminal voltage, a maximum battery rated capacity (E o ) and a desired power request when the battery  18  is in a low power state or condition. 
     In another embodiment, the adaptive battery estimator  80  determines an estimate of battery dynamics without requiring an estimate of the V oc  of the battery  18  when the battery is in a low power condition. The battery terminal voltage V b  is not estimated using the fixed battery estimator  66 , but rather is determined from a measured battery terminal voltage V(k) and a maximum rated capacity of the battery E o  representing a nominal energy storage capacity of the battery. In the low battery power condition embodiment, SW 1  and SW 2  are opened, thereby bypassing the fixed battery estimator for determining an open circuit voltage. Instead, SW 3  and SW 4  are closed to input voltage and battery capacity signals  17 C and  17 D, respectively, into the adaptive battery estimator  80  to generate predicted battery terminal voltage signal  33 A. A feedback control loop  35 B, formed between the adaptive battery estimator  80 , the battery current estimator  25  and the a priori battery resistance estimator  23  is used to update the internal battery resistance {circumflex over (R)} b,chg  in a similar manner as described with respect to feedback control loop  35 A, except that the predicted battery terminal voltage in feedback control loop  35 B is input into the battery current estimator  25  from a predicted battery voltage signal  33 A instead of signal line  27 A to update and input both the estimated battery resistance and the estimated battery current into the adaptive battery estimator  80 . 
     In an embodiment, the vehicle battery control module  14  samples and holds measured battery voltage during periods of low battery power ( 52 ). The vehicle battery control module  14  then operates to determine a rate limit ( 54 ) based upon the maximum rated capacity E o  of the battery  18 . The vehicle battery control module  14  then inputs the measured terminal voltage from the battery terminal voltage signal  17 C and the estimated battery capacity E o  from the estimated battery capacity signal  17 D into the adaptive battery estimator  80  to generate a first estimated battery terminal voltage {circumflex over (V)} oc (k) when k equals 1 and a predicted battery terminal voltage when k is greater than 1 ( 55 ). The estimated or predicted battery voltage signal  33 A is then input into feedback control loop  35 B. The adaptive battery estimator  80  operates to adaptively estimate battery dynamics using Equations (11a)-(11c):
 
If | P *( k )|&lt; P {circumflex over (V)}   oc ( k )= V ( k )  (11a)
 
If  P *( k )&gt;0 then,  {circumflex over (V)}   oc ( k )=Rate —   lim[{circumflex over (V)}   oc ( k− 1)− dV ( k )]  (11b)
 
If  P *( k )&lt;0  {circumflex over (V)}   oc ( k )=Rate —   lim[{circumflex over (V)}   oc ( k− 1)+ dV ( k )]  (11c)
 
     Instead of using V oc  for battery dynamics estimation, as is disclosed in  FIGS. 2-4 , another embodiment determines a rate limit of the change in battery voltage ( 54 ). The rate limit is formed as a function of the measured battery voltage and the maximum battery rated capacity E o  communicated to the adaptive battery estimator  80  during when the battery is operating in a low battery condition. The change in measured battery voltage may be incremental and is determined using Equation (12): 
                         dSOC   est     ⁡     (   k   )       =       -   P     ×     (   k   )     ⁢     dT   /     E   0           ⁢     
     ⁢       dV   ⁡     (   k   )       =         ∂   V       ∂   SOC       ⁢     ❘       SOC   est     ⁡     (   k   )         ⁢     ×       dSOC   est     ⁡     (   k   )                     (   12   )               
wherein SOC est  is the estimated state-of-charge, E 0  is the maximum battery rated capacity, and k is the time sample comprising an integer.
 
     The estimated battery terminal voltage V oc  from the last time sample (k−1) is then input ( 68 ) into feedback control loop  35 B to determine an estimated battery current ( 26 ) and to update the internal battery resistance ( 28 ) as disclosed in Equations (2) and (3). For each time sample where k is greater than 1, the estimated voltage {circumflex over (V)} oc (k) from the last time sample becomes the predicted voltage. In the embodiment where the battery is in a low power state, SW 1  and SW 2  are opened, and SW 3 , SW 4 , and SW 5  are closed. The adaptive battery estimator  80  adaptively predicts battery dynamics and uses battery dynamics inputs and equations (11a)-(11c) and (12) to determine a sensitivity factor ( 38 ), a covariance ( 40 ), an estimated or a predicted battery terminal voltage  33 A ( 44 ). 
     The disclosure has described certain preferred embodiments and modifications thereto. Further modifications and alterations may occur to others upon reading and understanding the specification. Therefore, it is intended that the disclosure not be limited to the particular embodiment(s) disclosed as the best mode contemplated for carrying out this disclosure, but that the disclosure will include all embodiments falling within the scope of the appended claims.