System and method for estimating a state vector associated with a battery

BACKGROUND OF THE INVENTION

0001Batteries are used in a wide variety of electronic and electrical devices. It is desirable to be able to estimate the internal state of a battery, including state-of-charge (SOC). The SOC is a value that indicates the present available capacity of the battery that may be used to do work. A battery monitoring system may measure a history of electrical current input to a battery and an output voltage from the battery to provide an estimate of a battery state.

0002A battery generally discharges over a time interval when it is electrically unloaded and a state of the battery changes during this time interval. A battery monitoring system, however, interrupts its history of measurements and calculations during this time interval. A disadvantage of this system is that it cannot accurately determine the state of the battery at a time when a battery is electrically coupled to a load circuit after it has been electrically decoupled from the load circuit for the time interval.

0003Thus, the inventor herein has recognized a need for a system and a method for estimating a state vector associated with a battery at a time when a battery is electrically coupled to a load circuit, after it has been electrically decoupled from the load circuit for the time interval.

BRIEF DESCRIPTION OF THE INVENTION

0004A method for estimating a state vector associated with a battery in accordance with an exemplary embodiment is provided. The method includes determining a time interval that the battery has been electrically decoupled from a load circuit. The time interval starts at a first time. The method further includes obtaining a first state vector associated with the battery from a memory. The first state vector is determined prior to the first time. The method further includes calculating a second predicted state vector associated with the battery based on the first state vector and the time interval. The method further includes measuring a battery voltage output by the battery to obtain a first battery voltage value after the first time interval when the battery is electrically re-coupled to the load circuit. The method further includes estimating a second battery voltage value associated with the battery based on the second predicted state vector. The method further includes calculating a voltage error value based on the first battery voltage value and the second battery voltage value. The method further includes calculating a third estimated state vector associated with the battery based on the second predicted state vector and the voltage error value.

0005A system for estimating a state vector associated with a battery in accordance with another exemplary embodiment is provided. The system includes a voltage sensor configured to measure a voltage output from the battery. The further includes a computer operably coupled to the voltage sensor. The computer is configured to determine a time interval that the battery has been electrically decoupled from a load circuit. The time interval starts at a first time. The computer is further configured to obtain a first state vector associated with the battery from a memory. The first state vector is determined prior to the first time. The computer is further configured to calculate a second predicted state vector associated with the battery based on the first state vector and the time interval. The computer is further configured to induce the voltage sensor to measure the voltage output from the battery to obtain a first battery voltage value after the first time interval when the battery is electrically coupled to the load circuit. The computer is further configured to estimate a second battery voltage value associated with the battery based on the second predicted state vector. The computer is further configured to calculate a voltage error value based on the first battery voltage value and the second battery voltage value. The computer is further configured to calculate a third estimated state vector associated with the battery based on the second predicted state vector and the voltage error value.

0006An article of manufacture in accordance with another exemplary embodiment is provided. The article of manufacture includes a computer storage medium having a computer program encoded therein for estimating a state vector associated with a battery. The computer storage medium includes code for determining a time interval that the battery has been electrically decoupled from a load circuit. The time interval starts at a first time. The computer storage medium further includes code for obtaining a first state vector associated with the battery from a memory. The first state vector is determined prior to the first time. The computer storage medium further includes code for calculating a second predicted state vector associated with the battery based on the first state vector and the time interval. The computer storage medium further includes code for measuring a battery voltage output from the battery to obtain a first battery voltage value after the first time interval when the battery is electrically coupled to the load circuit. The computer storage medium further includes code for estimating a second battery voltage value associated with the battery based on the second predicted state vector. The computer storage medium further includes code for calculating a voltage error value based on the first battery voltage value and the second battery voltage value. The computer storage medium further includes code for calculating a third estimated state vector associated with the battery based on the second predicted state vector and the voltage error value.

0007Other systems and/or methods according to the embodiments will become or are apparent to one with skill in the art upon review of the following drawings and detailed description. It is intended that all such additional systems and methods be within the scope of the present invention, and be protected by the accompanying claims.

BRIEF DESCRIPTION OF THE DRAWINGS

0008<figref idref="DRAWINGS">FIG. 1</figref> is a schematic of a system for estimating a state vector associated with a battery in accordance with an exemplary embodiment;

0009<figref idref="DRAWINGS">FIGS. 2-3</figref> are flowcharts of a method for estimating a state vector associated with a battery in accordance with another exemplary embodiment; and

0010<figref idref="DRAWINGS">FIGS. 4-5</figref> are flowcharts of a method for estimating a state vector associated with a battery in accordance with another exemplary embodiment.

DETAILED DESCRIPTION OF THE INVENTION

0011Referring to <figref idref="DRAWINGS">FIG. 1</figref>, a system <b>10</b> for estimating a state vector associated with a battery <b>12</b> is illustrated. The battery <b>12</b> includes at least a battery cell <b>14</b>. Of course, the battery <b>12</b> can include a plurality of additional battery cells. The system <b>10</b> includes one or more voltage sensors <b>20</b>, a load circuit <b>26</b>, and a computational unit such as a computer <b>28</b>, and may also include one or more of a temperature sensor <b>22</b>, and a current sensor <b>24</b>.

0012The voltage sensor <b>20</b> is provided to generate a first output signal indicative of the voltage produced by one or more of the battery cells of the battery <b>12</b>. The voltage sensor <b>20</b> is electrically coupled between the I/O interface <b>46</b> of the computer <b>28</b> and the battery <b>12</b>. The voltage sensor <b>20</b> transfers the first output signal to the computer <b>28</b>. For clarity of presentation, a single voltage sensor will be described herein. However, it should be noted that in an alternate embodiment of system <b>10</b> a plurality of voltage sensors (e.g., one voltage sensor per battery cell) are utilized in system <b>10</b>.

0013The temperature sensor <b>22</b> is provided to generate a second output signal indicative of one or more temperatures of the battery <b>12</b>. The temperature sensor <b>22</b> is disposed proximate the battery <b>12</b> and is electrically coupled to the I/O interface <b>46</b> of the computer <b>28</b>. The temperature sensor <b>22</b> transfers the second output signal to the computer <b>28</b>. For clarity of presentation, a single temperature sensor will be described herein. However, it should be noted that in an alternate embodiment of system <b>10</b> a plurality of temperature sensors (e.g., one temperature sensor per battery cell) are utilized in system <b>10</b>.

0014The current sensor <b>24</b> is provided to generate a third output signal indicative of a current sourced or sunk by the battery cells of the battery <b>12</b>. The current sensor <b>24</b> is electrically coupled between the battery <b>12</b> and the load circuit <b>26</b>. The current sensor <b>24</b> is further electrically coupled to the I/O interface <b>46</b> of the computer <b>28</b>. The current sensor <b>24</b> transfers the third output signal to the computer <b>28</b>.

0015The load circuit <b>26</b> is electrically coupled to the current sensor <b>24</b> and sinks or sources a current from the battery <b>12</b>. The load circuit <b>26</b> comprises any electrical device that can be electrically coupled to the battery <b>12</b>.

0016The computer <b>28</b> is provided for determining a state vector associated with the battery <b>12</b>, as will be explained in greater detail below. The computer <b>28</b> includes a central processing unit (CPU) <b>40</b>, a read-only memory (ROM) <b>44</b>, a volatile memory such as a random access memory (RAM) <b>45</b> and an input/output (I/O) interface <b>46</b>. The CPU <b>40</b> operably communicates with the ROM <b>44</b>, the RAM <b>45</b>, and the I/O interface <b>46</b>. The CPU <b>40</b> includes a clock <b>42</b>. The computer readable media including ROM <b>44</b> and RAM <b>46</b> may be implemented using any of a number of known memory devices such as PROMs, EPROMs, EEPROMS, flash memory or any other electric, magnetic, optical or combination memory device capable of storing data, some of which represent executable instructions used by the CPU <b>40</b>.

0017Before providing a detailed discussion of the methodologies for determining a state vector associated with the battery <b>12</b>, a general overview will be provided. The state vector includes at least a state of charge (SOC) value associated with the battery <b>12</b>. The SOC value is a value from 0-100 percent, that indicates a present available capacity of the battery <b>12</b> that may be used to do work. The estimated state vector is determined when the load circuit <b>26</b> is energized utilizing the following parameters: (i) measured battery voltage (ii) a stored prior estimated state vector (including an SOC value); and (iii) a time interval that the load circuit <b>12</b> was de-energized or electrically de-coupled from the batter <b>12</b>. These parameters are utilized in a mathematical model of battery cell behavior in order to compute an improved estimate of the state vector of the battery <b>12</b> including possibly compensation for hysteresis effects, voltage polarization effects, and self-discharge. The duration of time that the device was de-energized may be measured using the clock <b>42</b> of the computer <b>28</b>.

0018It is assumed that a mathematical model of the battery cell dynamics is known, and may be expressed using a discrete-time state-space model comprising a state equation and an output equation, as will be described below.

0019The state equation utilized to determine the state vector associated with the battery <b>12</b> is as follows: <br /><i>x</i>_k<i>=f</i>(<i>x</i>_k−1<i>,u</i>_k−1<i>,w</i>_k−1<i>,k−</i>1<i>,k</i>) <br /> wherein, <br /> x_kis the state vector associated with the battery <b>12</b> at time index k; <br /> u_kis a variable representing a known/deterministic input to the battery <b>12</b>; <br /> w_kis a process noise or disturbance that models some unmeasured input which affects the state of the system; and <br /> f(x_k−1,u_k−1,w_k−1,k−1,k) is a state transition function. <br /> The state vector x_kincludes a SOC value therein. Further, the known/deterministic input u_kincludes at least one of: (i) an electrical current presently sourced or sunk by the battery <b>12</b>, and (ii) a temperature of the battery <b>12</b>.

0020An output vector associated with the battery <b>12</b> is determined utilizing the following equation: <br /><i>y</i>_k=h(<i>x</i>_k<i>,u</i>_k<i>,v</i>_k<i>,k</i>) <br /> wherein, <br /> h(x_k,u_k,v_k,k) is a measurement function; and <br /> v_kis sensor noise that affects the measurement of the output of battery <b>12</b> in a memory-less mode, but does not affect the state vector of battery <b>12</b>.

0021The following system utilizes probabilistic inference to determine an estimated state vector {circumflex over (x)}_kof the state vector x_kgiven all observations Y_k={y₀,y₁, . . . ,y_k}. A frequently used estimator is the conditional mean: <maths id="MATH-US-00001" num="1"><math overflow="scroll"><mrow><msub><mover><mi>x</mi><mo>^</mo></mover><mi>k</mi></msub><mo>=</mo><mrow><mrow><mi>E</mi><mo>⁡</mo><mrow><mo>[</mo><mrow><msub><mi>x</mi><mi>k</mi></msub><mo>⁢</mo><mstyle><mtext>|</mtext></mstyle><mo>⁢</mo><msub><mi>Y</mi><mi>k</mi></msub></mrow><mo>]</mo></mrow></mrow><mo>=</mo><mrow><msub><mo>∫</mo><msub><mi>R</mi><msub><mi>x</mi><mi>k</mi></msub></msub></msub><mo>⁢</mo><mrow><msub><mi>x</mi><mi>k</mi></msub><mo>⁢</mo><mrow><mi>p</mi><mo>⁡</mo><mrow><mo>(</mo><mrow><msub><mi>x</mi><mi>k</mi></msub><mo>⁢</mo><mstyle><mtext>|</mtext></mstyle><mo>⁢</mo><msub><mi>Y</mi><mi>k</mi></msub></mrow><mo>)</mo></mrow></mrow><mo>⁢</mo><mrow><mo>ⅆ</mo><msub><mi>x</mi><mi>k</mi></msub></mrow></mrow></mrow></mrow></mrow></math></maths><br /> where R_x_{<sub2>k </sub2>}is the range of x_k, and E[ ] is the statistical expectation operator. The foregoing equation computes a posterior probability density p(x_k|Y_k) recursively. Because the foregoing equation is difficult to solve, numerical methods have been utilized to approximate the equation to calculate the estimated state vector {circumflex over (x)}_k, as will be explained in greater detail below.

0022For purposes of understanding, the notation utilized in the equations of the following methods will be described. The circumflex symbol indicates an estimated quantity (e.g., {circle around (x)} indicates an estimate of the true quantity x). The superscript symbol “−” indicates an a priori estimate (i.e., a prediction of a quantity's present value based on past data). The superscript symbol “+” indicates an a posteriori estimate (e.g., {circle around (x)}_k⁺ is the estimate of true quantity x at time index k based on all measurements taken up to and including time k). The tilde symbol indicates the error of an estimated quantity (e.g., {tilde over (x)}_k⁻=x_k−{circumflex over (x)}_k⁻ and {tilde over (x)}_k⁺=x_k−{circumflex over (x)}_k⁺). The symbol Σ_xy=E[xy^T] indicates the correlation or cross correlation of the variables in its subscript (the quantities described herein are zero-mean, so the correlations are identical to covariances). The symbol Σ_Xindicates the same quantity as Σ_xx. The superscript “T” is a matrix/vector transpose operator.

0023Referring to <figref idref="DRAWINGS">FIGS. 2-3</figref>, a method for calculating the estimated state vector {circumflex over (x)}_kutilizing a general sequential probabilistic inference methodology will be explained.

0024At step <b>60</b>, the computer <b>28</b> determines a time interval that the battery <b>12</b> has been electrically decoupled from the load circuit <b>26</b>. The time interval starts at a first time.

0025At step <b>62</b>, the computer <b>28</b> obtains a first state vector x_k−1associated with the battery <b>12</b> from a memory <b>46</b>. The first state vector x_k−1is determined prior to the first time.

0026At step <b>64</b>, the computer <b>28</b> calculates a second predicted state vector {circumflex over (x)}_k⁻ associated with the battery <b>12</b> based on the first state vector x_k−1and the time interval, utilizing the equation: {circumflex over (x)}_k⁻=E[f(x_k−1, u_k−1, w_k−1, k−1)|Y_k−1].

0027At step <b>66</b>, the computer <b>28</b> calculates a first covariance value Σ_{{tilde over (x)},k}⁻ associated with the second predicted state vector {circumflex over (x)}_k⁻, utilizing the equation: <br />Σ_{{tilde over (x)},k}⁻<i>=E</i>[({tilde over (x)}_k⁻)({tilde over (x)}_k⁻)^T].

0028At step <b>68</b>, the computer <b>28</b> induces a voltage sensor <b>20</b> to measure a battery voltage output by the battery <b>12</b> to obtain a first battery voltage value after the first time interval when the battery <b>12</b> is electrically coupled to the load circuit <b>26</b>.

0029At step <b>70</b>, the computer <b>28</b> estimates a second battery voltage value associated with the battery <b>12</b> based on the second predicted state vector {circumflex over (x)}_k⁻, utilizing the equation: <br />ŷ_k<i>=E[h</i>(<i>x</i>_k<i>,u</i>_k,v_k<i>,k</i>)|<i>Y</i>_k].

0030At step <b>72</b>, the computer <b>28</b> calculates a voltage error value based on the first battery voltage value and the second battery voltage value.

0031At step <b>74</b>, the computer <b>28</b> calculates a third predicted state vector {tilde over (x)}_k⁺ associated with the battery <b>12</b> based on the second predicted state vector {circumflex over (x)}_k⁻ and the voltage error value y_k−ŷ_k, utilizing the equation: {tilde over (x)}_k⁺={tilde over (x)}_k⁻+L_k[y_k−{tilde over (y)}_k]. where the value L_kis determined utilizing the equation: <br /><i>L</i>_k<i>=E[</i>({tilde over (x)}_k⁻){tilde over (y)}_k)^T](<i>E[</i>({tilde over (y)}_k)({tilde over (y)}_k)^T])⁻¹<br /> The third predicted state vector {circumflex over (x)}_k⁺ is the most accurate estimate of the true state of the battery <b>12</b> produced by the foregoing method.

0032At step <b>76</b>, the computer <b>28</b> calculates a second covariance value Σ_{{tilde over (x)},k}⁺ associated with the third predicted state vector {circumflex over (x)}_k⁺, utilizing the equation:

0000Σ_{{tilde over (x)},k}⁺=Σ_{{tilde over (x)},k}⁻−L_kΣ_{{tilde over (y)},k}L_k^T. After step <b>76</b>, the method is exited.

0033It should be noted that there are many methods for approximating the third predicted state vector {circumflex over (x)}_k⁺, described above. For example, one method utilizes a linear Kalman filter, another method utilizes a nonlinear extended Kalman filter, another method utilizes a nonlinear sigma-point Kalman filter. These methods utilize different levels of computational effort and produce different degrees of accuracy in the resulting state vector.

0034For example, referring to <figref idref="DRAWINGS">FIGS. 4-5</figref>, a method for calculating the estimated state vector {circumflex over (x)}_kutilizing a non-linear extended Kalman filter will be explained. The following definitions are utilized in the equations of the method: <maths id="MATH-US-00002" num="2"><math overflow="scroll"><mtable><mtr><mtd><mrow><msub><mover><mi>A</mi><mo>^</mo></mover><mi>k</mi></msub><mo>=</mo><mrow><mfrac><mrow><mo>∂</mo><mrow><mi>f</mi><mo>⁡</mo><mrow><mo>(</mo><mrow><msub><mi>x</mi><mi>k</mi></msub><mo>,</mo><msub><mi>u</mi><mi>k</mi></msub><mo>,</mo><msub><mi>w</mi><mi>k</mi></msub><mo>,</mo><mi>k</mi></mrow><mo>)</mo></mrow></mrow></mrow><mrow><mo>∂</mo><msub><mi>x</mi><mi>k</mi></msub></mrow></mfrac><mo>⁢</mo><msub><mo>❘</mo><mrow><msub><mi>x</mi><mi>k</mi></msub><mo>=</mo><msubsup><mover><mi>x</mi><mo>^</mo></mover><mi>k</mi><mo>+</mo></msubsup></mrow></msub></mrow></mrow></mtd><mtd><mrow><msub><mover><mi>B</mi><mo>^</mo></mover><mi>k</mi></msub><mo>=</mo><mrow><mfrac><mrow><mo>∂</mo><mrow><mi>f</mi><mo>⁡</mo><mrow><mo>(</mo><mrow><msub><mi>x</mi><mi>k</mi></msub><mo>,</mo><msub><mi>u</mi><mi>k</mi></msub><mo>,</mo><msub><mi>w</mi><mi>k</mi></msub><mo>,</mo><mi>k</mi></mrow><mo>)</mo></mrow></mrow></mrow><mrow><mo>∂</mo><msub><mi>w</mi><mi>k</mi></msub></mrow></mfrac><mo>⁢</mo><msub><mo>❘</mo><mrow><msub><mi>w</mi><mi>k</mi></msub><mo>=</mo><msub><mover><mi>w</mi><mi>_</mi></mover><mi>k</mi></msub></mrow></msub></mrow></mrow></mtd></mtr><mtr><mtd><mrow><msub><mover><mi>C</mi><mo>^</mo></mover><mi>k</mi></msub><mo>=</mo><mrow><mfrac><mrow><mo>∂</mo><mrow><mi>h</mi><mo>⁡</mo><mrow><mo>(</mo><mrow><msub><mi>x</mi><mi>k</mi></msub><mo>,</mo><msub><mi>u</mi><mi>k</mi></msub><mo>,</mo><msub><mi>v</mi><mi>k</mi></msub><mo>,</mo><mi>k</mi></mrow><mo>)</mo></mrow></mrow></mrow><mrow><mo>∂</mo><msub><mi>x</mi><mi>k</mi></msub></mrow></mfrac><mo>⁢</mo><msub><mo>❘</mo><mrow><msub><mi>x</mi><mi>k</mi></msub><mo>=</mo><msubsup><mover><mi>x</mi><mo>^</mo></mover><mi>k</mi><mo>-</mo></msubsup></mrow></msub></mrow></mrow></mtd><mtd><mrow><msub><mover><mi>D</mi><mo>^</mo></mover><mi>k</mi></msub><mo>=</mo><mrow><mfrac><mrow><mo>∂</mo><mrow><mi>h</mi><mo>⁡</mo><mrow><mo>(</mo><mrow><msub><mi>x</mi><mi>k</mi></msub><mo>,</mo><msub><mi>u</mi><mi>k</mi></msub><mo>,</mo><msub><mi>v</mi><mi>k</mi></msub><mo>,</mo><mi>k</mi></mrow><mo>)</mo></mrow></mrow></mrow><mrow><mo>∂</mo><msub><mi>v</mi><mi>k</mi></msub></mrow></mfrac><mo>⁢</mo><msub><mo>❘</mo><mrow><msub><mi>v</mi><mi>k</mi></msub><mo>=</mo><msub><mover><mi>v</mi><mi>_</mi></mover><mi>k</mi></msub></mrow></msub></mrow></mrow></mtd></mtr></mtable></math></maths>

0035At step <b>80</b>, the computer <b>28</b> determines a time interval that a battery <b>12</b> has been electrically decoupled from a load circuit <b>26</b>. The time interval starts at a first time.

0036At step <b>82</b>, the computer <b>28</b> obtains a first state vector {circumflex over (x)}_k−1⁺ associated with the battery <b>12</b> from the memory <b>46</b>. The first state vector {circumflex over (x)}_k−1⁺ is determined prior to the first time.

0037At step <b>84</b>, the computer <b>28</b> calculates a second predicted state vector {circumflex over (x)}_k⁻ associated with the battery <b>12</b> based on the first state vector {circumflex over (x)}_k−1⁺ and the time interval, utilizing the equation: {circumflex over (x)}_k⁻=f({circumflex over (x)}_k−1⁺,u_k−1, <o ostyle="single">w</o>_k−1,k−1,k).

0038At step <b>86</b>, the computer <b>28</b> calculates a first covariance value Σ_{{tilde over (x)},k}⁻ associated with the second predicted state vector {circumflex over (x)}_k⁻, utilizing the equation: <br />Σ_{{tilde over (x)},k}⁻<i>=Â</i>_k−1Σ_{{tilde over (x)},k−1}⁺<i>Â</i>_k−1^T<i>+{circumflex over (B)}k−<b>1</b></i>Σ_w<i>{circumflex over (B)}</i>_k−1^T.

0039At step <b>88</b>, the computer <b>28</b> induces the voltage sensor <b>20</b> to measure a battery voltage output by the battery <b>12</b> to obtain a first battery voltage value after the first time interval when the battery <b>12</b> is electrically coupled to the load circuit <b>26</b>.

0040At step <b>90</b>, the computer <b>28</b> estimates a second battery voltage value associated with the battery <b>12</b> based on the second predicted state vector {tilde over (x)}_k⁻, utilizing the equation: <br />ŷ_k<i>=h</i>({circumflex over (x)}_k⁻<i>,u</i>_k<i>,{tilde over (v)}</i>_k<i>,k</i>).

0041At step <b>92</b>, the computer <b>28</b> calculates a voltage error value based on the first battery voltage value and the second battery voltage value.

0042At step <b>94</b>, the computer <b>28</b> calculates a third predicted state vector {circumflex over (x)}_k⁺ associated with the battery <b>12</b> based on the second predicted state vector {circumflex over (x)}_k⁻ and the voltage error value, utilizing the equation: {circumflex over (x)}_k⁺={circumflex over (x)}_k⁻+L_k[y_k−ŷ_k]. where the value L_kis determined utilizing the equation: <br /><i>L</i>_k=Σ_{{tilde over (x)},k}⁻<i>Ĉ</i>_k^T<i>[Ĉ</i>_kΣ_{{tilde over (x)},k}<i>Ĉ</i>_k^T<i>+{circumflex over (D)}</i>_kΣ_v<i>{circumflex over (D)}</i>_k^T]⁻¹.

0043At step <b>96</b>, the computer <b>28</b> calculates a second covariance value Σ_{{tilde over (x)},k}⁺ associated with the third predicted state vector {circumflex over (x)}_k⁺, utilizing the equation:

0000Σ_{{circumflex over (x)},k}⁺=(I−L_kĈ_k)Σ_{{tilde over (x)},k}⁻. After step <b>96</b>, the method is exited.

0044It should be noted that in alternate embodiments, the estimated state vector {circumflex over (x)}_kof the battery <b>12</b> can be calculated utilizing a linear Kalman filter, a nonlinear sigma-point Kalman filter, a square-root linear Kalman filter, a square-root extended Kalman filter, a square-root sigma-point Kalman filter, a particle filter, and the like.

0045The system and methods for estimating a state vector associated with a battery provide a substantial advantage over other systems and methods. In particular, the system and methods provide a technical effect of accurately estimating a state vector associated with the battery at a time when a battery is electrically coupled to a load circuit, after it has been electrically decoupled from the load circuit for the time interval.

0046The above-described methods can be embodied in the form of computer program code containing instructions embodied in tangible media, such as floppy diskettes, CD ROMs, hard drives, or any other computer-readable storage medium, wherein, when the computer program code is loaded into and executed by a computer, the computer becomes an apparatus for practicing the invention. The above-described methods can also be embodied in the form of computer program code, for example, whether stored in a storage medium, loaded into and/or executed by a computer, or transmitted over some transmission medium, loaded into and/or executed by a computer, or transmitted over some transmission medium, such as over electrical wiring or cabling, through fiber optics, or via electromagnetic radiation, wherein, when the computer program code is loaded into an executed by a computer, the computer becomes an apparatus for practicing the methods. When implemented on a general-purpose microprocessor, the computer program code segments configure the microprocessor to create specific logic circuits.

0047While the invention is described with reference to the exemplary embodiments, it will be understood by those skilled in the art that various changes may be made an equivalence may be substituted for elements thereof without departing from the scope of the invention. In addition, many modifications may be made to the teachings of the invention to adapt to a particular situation without departing from the scope thereof. Therefore, is intended that the invention not be limited the embodiment disclosed for carrying out this invention, but that the invention includes all embodiments falling with the scope of the intended claims. Moreover, the use of the term's first, second, etc. does not denote any order of importance, but rather the term's first, second, etc. are used to distinguish one element from another.