Patent Publication Number: US-11656210-B2

Title: Gas sensing systems and methods of operation thereof

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a divisional application of U.S. patent application Ser. No. 16/852,035, filed on Apr. 17, 2020, which is a divisional application of U.S. patent application Ser. No. 15/663,711, filed on Jul. 29, 2017, now issued as U.S. Pat. No. 10,677,768, which applications are hereby incorporated herein by reference in their entirety. 
    
    
     TECHNICAL FIELD 
     The present invention relates generally to a sensing system, and, in particular embodiments, to gas sensing system structures and the methods of operation thereof. 
     BACKGROUND 
     Sensing systems including sensor devices such as resistive gas sensors can detect the presence of target analytes in an ambient environment. It may be important to design sensor devices with the ability to output detection events in real-time with high sensitivity. Sensor devices may also be designed for high accuracy and specificity with respect to a target analyte or group of target analytes. In the specific case of resistive gas sensors, detection events may be based on the change in resistance or capacitance of a semiconducting thin-film structure that is influenced by the adsorption of gas molecules. 
     As the sensitivity of a sensor device improves, the influence of external environmental factors on the sensor device may also increase. Such environmental factors may include temperature, humidity, composition and concentration of species in the ambient atmosphere, and electromagnetic interference, among others. High sensitivity to external environmental factors may decrease sensor accuracy. Therefore, sensor devices which compensate for external environmental influences may be desirable in order to provide both high sensitivity and high accuracy. 
     SUMMARY 
     In accordance with an embodiment of the invention, a method of sensing includes obtaining first sensor data points by a sensor, obtaining first reference data points, and determining a correlation between the first sensor data points and the first reference data points. The method of sensing further includes measuring second sensor data points by the sensor, obtaining second reference data points, and adjusting the second sensor data points using the correlation and the second reference data points to obtain corrected sensor data points. The method of sensing also includes determining sensed values from the corrected sensor data points and storing the sensed values. 
     In accordance with another embodiment of the invention, a method of sensing includes obtaining first sensor data points by a sensor and obtaining first reference data points. Obtaining the first sensor data points and the first reference data points is performed during a first time interval. The method of sensing further includes measuring second sensor data points by the sensor and generating corrected second sensor data points by correcting for baseline variation in the second sensor data points using a relationship between the first sensor data points and the first reference data points. The measuring the second sensor data points and generating the corrected second sensor data points is performed after the first time interval during a second time interval. The method of sensing also includes determining sensed values from the corrected second sensor data points. 
     In accordance with still another embodiment of the invention, a sensor device includes a gas sensor disposed on a first substrate. The gas sensor is configured to measure first sensor data points and second sensor data points. A heating element is disposed within the first substrate. The gas sensor overlaps the heating element. A processor is operatively coupled to the gas sensor and the heating element. The sensor device also includes a memory storing a program to be executed by the processor. The program includes instructions for recording first resistance values and second resistance values of the heating element. The program also includes instructions for adjusting the second sensor data points using the first sensor data points, the first resistance values, and the second resistance values to obtain corrected sensor data points. The program further includes instructions for determining sensed values from the corrected sensor data points. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the present invention, and the advantages thereof, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which: 
         FIGS.  1 A and  1 B  illustrate a method of sensing and a sensing system in accordance with an embodiment of the invention where  FIG.  1 A  illustrates the method of sensing and  FIG.  1 B  illustrates the sensing system; 
         FIG.  2    illustrates another method of sensing in which baseline variation is corrected based on correlation with reference data points in accordance with an embodiment of the invention; 
         FIG.  3    illustrates still another method of sensing in which baseline variation is corrected based on correlation with reference data points in accordance with an embodiment of the invention; 
         FIG.  4    illustrates a method of preprocessing sensing data in accordance with an embodiment of the invention; 
         FIG.  5    illustrates another method of preprocessing sensing data in accordance with an embodiment of the invention; 
         FIG.  6    illustrates a method of adjusting a baseline to correct baseline variation and normalizing sensor data points in accordance with an embodiment of the invention; 
         FIG.  7    illustrates an example sensor device including a substrate, a heating element, and a sensor in accordance with an embodiment of the invention; 
         FIG.  8    illustrates an example sensor device including a substrate, a heating element, a sensor, and an environmental sensor in accordance with an embodiment of the invention; 
         FIG.  9    illustrates an example sensor device including a substrate, a heating element, a sensor, and a reference sensor in accordance with an embodiment of the invention; 
         FIG.  10    illustrates an example sensor device including a substrate, a heating element, a sensor, an environmental sensor, and a reference sensor where the environmental sensor is located on the substrate in accordance with an embodiment of the invention; 
         FIG.  11    illustrates another example sensor device including a substrate, a heating element, a sensor, an environmental sensor, and a reference sensor where the environmental sensor is located on a second substrate in accordance with an embodiment of the invention; 
         FIG.  12    illustrates a top view of an example sensor device including multiple sensors and a reference sensor in accordance with an embodiment of the invention; 
         FIG.  13    illustrates a top view of an example sensor device including multiple sensors and multiple reference sensors in accordance with an embodiment of the invention; 
         FIG.  14    illustrates a top view of an example sensor device including multiple pairs of a sensor and a reference sensor in accordance with an embodiment of the invention; 
         FIG.  15    illustrates a top view of an example sensor device including multiple pairs of a sensor and a reference sensor and further including an environmental sensor in accordance with an embodiment of the invention; 
         FIG.  16    illustrates a top view of an example sensor device including multiple sensors, an environmental sensor, and a reference sensor where the environmental sensor is located on a second substrate in accordance with an embodiment of the invention; 
         FIG.  17    illustrates a top view of an example sensor device including multiple sensors, and environmental sensor, and multiple reference sensors where the environmental sensor is located on a second substrate in accordance with an embodiment of the invention; 
         FIG.  18    illustrates a top view of an example sensor device including multiple pairs of a sensor and a reference sensor and further including an environmental sensor where the environmental sensor is located on a second substrate in accordance with an embodiment of the invention; 
         FIGS.  19 A and  19 B  illustrate qualitative graphs of sensor resistance versus time and heating element resistance versus time with baseline variation due to sensor drift where  FIG.  19 A  illustrates resistance responses of a sensor and a heating element before correcting the baseline variation and  FIG.  19 B  illustrates resistance responses of the sensor and the heating element after correcting the baseline variation; and 
         FIGS.  20 A and  20 B  illustrate qualitative graphs of sensor resistance versus time with baseline variation due to sensor drift over multiple correction intervals where  FIG.  20 A  illustrates resistance responses of a sensor before correcting the baseline variation and  FIG.  20 B  illustrates resistance responses of the sensor after correcting the baseline variation. 
     
    
    
     Corresponding numerals and symbols in the different figures generally refer to corresponding parts unless otherwise indicated. The figures are drawn to clearly illustrate the relevant aspects of the embodiments and are not necessarily drawn to scale. The edges of features drawn in the figures do not necessarily indicate the termination of the extent of the feature. 
     DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS 
     The making and using of various embodiments are discussed in detail below. It should be appreciated, however, that the various embodiments described herein are applicable in a wide variety of specific contexts. The specific embodiments discussed are merely illustrative of specific ways to make and use various embodiments, and should not be construed in a limited scope. 
     Sensing systems may be designed to detect quantities of a target analyte by determining the deviation of a measured value from a baseline value. For example, in a gas sensing system, electrical resistance of a sensor may be used as a measured value to detect target gases. In this system, the baseline or reference resistance may be on the order of 1 kΩ, for example, when no target gases are present. Target gases may then be sensed by evaluating deviations of the sensor resistance from the value of 1 kΩ. However, external factors that are unrelated to the target gas such as environmental factors may affect the sensor. These external factors may cause the baseline value to vary over time which may negatively impact the accuracy of the sensing system. Therefore, a sensing system that corrects for baseline variation may be advantageous. 
     In various embodiments, a sensing system is implemented that includes a sensor device configured to correct for baseline variation by processing sensing data according to an algorithm to correlate sensor output with reference measurements. The algorithm may include the steps of obtaining sensor data points and reference data points, determining a correlation between the sensor data points and the reference data points, and adjusting the sensor data points to correct for baseline variation. The sensor device may be a gas sensor in various embodiments and is a graphene-based resistive gas sensor in one embodiment. The baseline variation may be caused by environmental factors such as temperature and/or humidity. 
     The sensor device may advantageously enable higher sensitivity by correcting for baseline variation caused by external environmental factors. Such baseline variation may be a time-varying change in the baseline of a sensor and may be referred to as sensor drift in some implementations. The contribution to the signal caused by baseline variation may be diminished or removed entirely in various embodiments which may advantageously enable higher sensitivity to target analytes. In the specific case of a gas sensor device, the correction of baseline variation may beneficially enable accurate detection of low concentrations of gas molecules on the scale of parts-per-million (ppm), parts-per-billion (ppb), or lower. 
     The sensor device may also have the benefit of correcting for baseline variation without requiring that the sensor device operate at a specific temperature value. For example, the sensor device may operate at any temperature and baseline variation due to temperature fluctuation may be corrected. Another possible benefit of the sensor device may be that materials that are sensitive to environmental factors such as graphene may be used in the structure of the sensor device. In contrast, a conventional sensor device without correction for baseline variation may be designed to be very insensitive to the environment which may limit possible materials, structure, and performance of the conventional sensor device. 
     The sensor device may also advantageously perform adaptive corrections for baseline variation. Adaptive correction may include correlating changes in the baseline with the cause of baseline variation in real-time or near-real-time which may result in more accurate correction for baseline variation. For example, the effects of the environment on the baseline of a sensor device may vary over time and may not be known prior to the sensing events. Adaptive corrections for baseline variation may determine correlations immediately before performing corrections which may improve accuracy of the corrections as well as being applicable to many different sensing environments. 
     Embodiments provided below describe various structures and methods of operating sensing systems, and in particular, sensing systems that compensate for baseline variation. The following description describes the embodiments. Several embodiment methods of sensing are described using  FIGS.  1 - 3   . Two embodiment methods of preprocessing data are described using  FIGS.  4  and  5   . An embodiment method of adjusting a baseline and normalizing data points is described using  FIG.  6   . Various embodiment sensor devices which may be included in sensing system implementations are described using  FIGS.  7 - 18   . Qualitative graphs of two baseline correction scenarios are described using  FIGS.  19  and  20   . 
       FIGS.  1 A and  1 B  illustrate a method of sensing and a sensing system in accordance with an embodiment of the invention where  FIG.  1 A  illustrates the method of sensing and  FIG.  1 B  illustrates the sensing system. 
     Referring to  FIGS.  1 A and  1 B , a method  100  of sensing includes the following steps which may be performed by a sensing system  105 . Step  101  includes obtaining sensing data and may be performed by a sensing array  90 . The step of obtaining sensing data may take various forms ranging from recording a single data point at an instant in time from a single sensor to recording multiple data points from a sensor array over a period time. For example, in one embodiment, step  101  includes obtaining sensing data by recording a single data point from a sensor and recording a single reference point from a reference sensor at an instant in time. In another embodiment, step  101  includes obtaining sensing data by recording four data points per second from each sensor in a sensor array and also from an environmental sensor over a period of ten seconds. Other variations may be apparent to those of ordinary skill in the art and may depend on a specific implementation of a sensor device. 
     The sensing array  90  may include only a single sensor or may include multiple sensors and types of sensors. For example, as shown in  FIG.  1 B , sensor array  90  includes a sensing sensor  92  and a reference sensor  93 . In various embodiments, the reference sensor  93  may be used to determine appropriate baseline values for sensing sensor  92 . 
     Step  102  includes preprocessing the sensing data. The step of preprocessing the sensing data may include processing steps that prepare the sensing data to be interpreted as sensing events. For example, if a sensor device includes multiple sensors in a sensor array, an averaging step may be performed while preprocessing the sensing data. As another example, preprocessing the sensor data may include detecting and removing outliers in the sensing data. Other possible preprocessing steps may include determining a baseline, correcting a baseline, normalizing data points, combining multiple types of data points, multiplying by scalar factors, removing data points from the beginning or end of a data set, and the like. 
     Step  103  includes post processing the sensing data. For example, the sensing data may include sensing events in the form of peaks or other identifiable features. The sensing events may be identified using criteria specific to the sensor implementation and sensed values may be determined from the sensing events. The processing steps  102  and  103  may be performed locally by a processor within a sensor device such as an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or a general purpose processor coupled to a memory storing a program, as examples. Alternatively, steps  102  and  103  may be performed externally by a computer that is connected to the sensor device such as a desktop computer, laptop computer, server, tablet computer, smart phone, and the like. 
     Steps  102  and  103  may be performed by a processor  94 . The processor may be operatively coupled to sensing array  90  as well as a memory  95 . In various embodiments, memory  95  may be used to store information obtained by preprocessing and post processing the sensing data. Memory  95  may also be used to store computer instructions that, when executed by processor  94 , may perform steps  102  and  103  among others. Memory  95  may be a non-volatile computer-readable storage medium such as a computer hard drive, random access memory, and the like. 
     Step  104  includes outputting the sensed values in a format understandable by a user or a connected device. Step  104  may be performed by a display  91  operatively coupled to sensing array  90 , processor  94 , and memory  95 . For example, the sensed values may be output to a digital display or formatted in a data file and stored on a computer-readable storage medium. In the specific case of a gas sensor, the sensed values may be output as a concentration such as parts-per-million (ppm) or parts-per-billion (ppb) to communicate a concentration of a sensed gas in an ambient environment. 
       FIG.  2    illustrates another method of sensing in which baseline variation is corrected based on correlation with reference data points in accordance with an embodiment of the invention. 
     Referring to  FIG.  2   , a method  200  of sensing includes the following steps. Step  211  includes obtaining sensor data points and step  221  includes obtaining reference data points. Steps  211  and  221  may be executed at the same time or at different times. In various embodiments, steps  211  and  221  are part of a step  101  of obtaining sensing data such as previously described in reference to  FIGS.  1 A and  1 B . Sensor data points may be obtained by recording measurements from sensors configured to respond to sensing events. Reference data points may be obtained by recording measurements from reference sensors that are configured to be used as a reference or that have an identifiable trait that may be used as a reference. Only as an illustration, a gas sensing system may comprise one reference sensor for providing the reference data and a plurality of sensors for measuring different type of target analytes so as to generate sensor data. For example, the sensor data may comprise detected concentration for each target analyte that is being measured. 
     Step  212  includes determining a correlation between the sensor data points and the reference data points. The correlation may be determined by comparing the sensor data points and reference data points. The existence of a correlation between the sensor data points and the reference data points may indicate the existence of an external influence that is unrelated to target analyte of the sensor. For example, the sensor data points may be obtained from a sensor that is sensitive to the presence of a target analyte while the reference data points may be obtained from a reference sensor that is not affected by the presence of the target analyte. A correlation between the sensor data points and the reference data points may then indicate that influences unrelated to the target analyte affect the sensor and the reference sensor in a similar manner. 
     In some embodiments, the reference data points may be measurements from an environmental sensor. The output of the environmental sensor may be chosen to be unrelated to the sensing target. For example, the environmental sensor may measure an environmental factor (e.g., temperature, humidity, pressure, and others) that is known to affect the performance of the sensing sensor. Accordingly, the environmental sensor may be a temperature sensor, a humidity sensor, or a pressure sensor, for example. In this way a correlation between the environmental factor and the sensor response of the sensing sensor can be determined by using the correlation between the sensor data points and the reference data points. 
     In other embodiments, the reference data points may be measurements from a structural reference sensor that has a similar structure as a sensing sensor, but is unresponsive to the sensing target. Since the output of the structural reference sensor is not affected by the sensing target, a correlation between the sensor output and the structural reference sensor output may be related to an external influence, which contributes to baseline variation. In some embodiments, the reference data points may be obtained from a combination of environmental sensor and structural reference sensor measurements. 
     Step  222  includes adjusting the sensor data points to correct for baseline variation. After the adjustment, the sensor data points may reflect a sensor output with a constant baseline. For example, an equation relating the correlation and the reference points to baseline values may be used to obtain a correction for each sensor data point. Possible equations include linear regression, multiple regression, n th  order polynomial fitting such as quadratic, cubic, quartic, etc., logarithmic fitting, and exponential fitting, as examples. As an illustration, the baseline used as a reference by the sensor data points is made constant using the reference data points. That is, background noise and/or baseline variation in the signal caused by external effects may be significantly reduced or removed from the sensor data points. 
     Step  232  includes normalizing the sensor data points. In some cases, the measured sensor response resulting in the set of sensor data points may need to be dimensionless to facilitate accurate post processing. For example, the sensor data points may be represented as a percentage or a ratio rather than in specific units of measure. 
     In various embodiments, step  232  is optional and may be omitted depending on specific post processing implementations. In some embodiments, steps  212 ,  222 , and  232  are part of a step  102  of preprocessing the sensing data such as previously described in reference to  FIGS.  1 A and  1 B . 
     Steps  211 ,  221 ,  212 ,  222 , and  232  may be repeated for a first period of time t 1 . For example, it may be advantageous in some implementations to gather a large amount to data before each post processing step in order to obtain accurate sensing events and sensed values. In this case, obtaining and preprocessing sensing data may be performed for a predetermined amount to time to accumulate a sufficient quantity of data points, and then the preprocessed data set can be sent for post processing. In some cases, first period of time t 1  may be referred to as a sampling time. 
     Still referring to  FIG.  2   , step  213  includes identifying and extracting features from the sensor data points. For example, a feature may be identified by determining that a value exceeds a predetermined threshold. Alternatively, the beginning and end of a feature may be identified by determining that a rate of change of the sensing data crosses a predetermined threshold. In addition to features, so-called regions of interest may also be identified. In some cases feature may be considered synonymous with region of interest, but this may depend on specific sensing implementations. The identification of regions of interest and/or features may include complex analysis of the shape of a curve defined by the sensing data. Following identification, the regions of interest and/or features may be extracted by removing remaining data points. 
     Step  223  includes classifying the extracted features using a set of predetermined criteria. Classification of the extracted features may be used to determine the most important features and/or remove features that do not contain sensing information. For example, removal of features may be performed in a dimensional reduction step. A set of features may be reduced to the most important features using dimensional analysis methods such as principal component analysis (PCA), Kernel PCA, linear discriminant analysis (LDA), Random forests, etc. Classification of the extracted features may be performed using a standard machine learning algorithm such as Naïve Bayes, logistic regression, decision trees, support vector machines, neural networks, K-nearest neighbors, etc. Once classified, the data can be cross referenced with stored calibration values (such as a look-up table) to extract sensed values. 
     After classifying the extracted features, step  233  includes determining sensed values from the classified features. In various embodiments, steps  213 ,  223 , and  233  are part of a step  103  of post processing the sensing data such as previously described in reference to  FIGS.  1 A and  1 B . Step  104  includes outputting sensed values and is as previously described. 
       FIG.  3    illustrates still another method of sensing in which baseline variation is corrected based on correlation with reference data points in accordance with an embodiment of the invention. 
     Referring to  FIG.  3   , the method  300  of sensing includes the following steps. Step  211  includes obtaining sensor data points and step  221  includes obtaining reference data points and may be as previously described with respect to  FIG.  2   . Additionally, steps  211  and  221  may be part of a step  101  of obtaining sensing data that may be repeated for a second period of time t 2  before the sensing data is processed in subsequent steps. In some applications, the second period of time t 2  may be referred to as a sampling time. 
     Step  212  includes determining a correlation between the sensor data points and the reference data points and may be part of a step  102  of preprocessing the sensing data that has been obtained in step  101 . Method  300  differs from method  200  in that the step  212  of determining the correlation is performed after the second period of time t 2  has passed rather than multiple times over a first period of time t 1  as in method  200 . 
     After sensing data has been obtained in step  101  and a correlation has been determined in step  212 , an additional set of sensing data may be obtained in a step  301  of obtaining additional sensing data. Step  301  includes a step  311  of obtaining additional sensor data points and a step  321  of obtaining additional reference data points similar to steps  211  and  221  as previously described. 
     The correlation determined in step  212  may then be used in conjunction with the additional sensing data for adjusting the additional sensor data points to correct for baseline variation in step  222 . An optional step  232  includes normalizing the additional sensor data points. Steps  222  and  232  of method  300  are similar to corresponding steps in method  200  and may be part of a step  302  of preprocessing additional sensing data. 
     Following preprocessing of the additional sensing data, a step  103  of post processing data and a step  104  of outputting sensed values is performed. Steps  103  and  104  may be as previously described. Steps  301 ,  302 ,  103  and  104  may be repeated for a third period of time t 3  during which the same correlation that is determined in step  212  may be used to correct any number of additional sensing data sets. Additionally, step  301  may be repeated for a sampling time similar to step  101 . 
     Any of the described steps may also be performed serially or in parallel. For example, a sensing system may acquire new data in steps  101  or  301  at the same time as previously acquired data is being processed in steps  102 ,  302 , and/or  103 . Similarly, output values may be display in step  104  while new sensing data sets are being obtained and processed. 
     In contrast to method  200 , in method  300  a first sensing data set is used to determine the correlation and subsequent sensing data sets are corrected using the correlation and the optionally normalized. For example, in one scenario, no sensing events may take place during the second period of time t 2 . This may advantageously improve the accuracy of the correlation that is determined between the sensor data points and the reference data points. During the third period of time t 3  sensing events may or may not occur, and the sensing system may output sensed values that are adjusted to correct for baseline variation using the correlation determined from sensing data with no detection events. 
     After a predetermined amount of time or in response to a determination that a new correlation should be determined, a step  305  of beginning the process anew at step  101  may be performed. In some embodiments, step  305  may be performed after determining that the sensed values that are output in step  104  have been below a threshold for a predetermined amount of time. In other embodiments, step  305  may be performed when the number of sensing events identified in step  103  is below a predetermined threshold. 
     As an example, second time t 2  may be 10 seconds, third period of time t 3  may be 30 seconds, and step  305  may be performed after each expiration of the third period of time t 3 . In this case a correlation is determined every 40 seconds after 10 seconds of obtaining sensing data. The correlation is then used to correct for baseline variation on additional sensing data that is continuously gathered for 30 seconds. In this example, sensed values are output for 75% of every cycle. During the 25% downtime, sensor system may be refreshed to improve the sensing accuracy during the 75% uptime. Any combination of values of the second and third period of time t 2  and t 3  is possible and may be chosen based on a potential tradeoff between accuracy of the correction to the baseline variation and the desired uptime of the sensor. In some embodiments, the values of the second and third periods of time t 2  and t 3  may be dynamic or manually adjustable. 
     As another example, the third period of time t 3  may extend until a predetermined amount of time without a sensing event has passed. Step  305  and optional step  306  may then be performed. The sensing data points and reference data points obtained during the time without a sensing event may be used in step  212  to determine a new correlation. In this example, sensor downtime may be advantageously reduced by only determining coefficients when no sensor events are occurring. 
     Optionally, step  101  may be omitted when performing step  305  which is shown as a dotted arrow  306  proceeding directly to step  102 . For example, the criteria to perform step  305  may coincide with the criteria to use a set of sensing data in step  212  enabling step  101  to be omitted in some or all iterations of method  300 . 
       FIG.  4    illustrates a method of preprocessing sensing data in accordance with an embodiment of the invention. 
     Referring to  FIG.  4   , a method  400  of preprocessing sensing data includes a step  412  of determining correlation coefficients using regression analysis. The regression analysis may be any suitable method in which a relationship between a dependent variable and one or more in independent variables. Possible regression analysis methods may include linear regression, ordinary least squares regression, polynomial regression, nonlinear regression, and the like. In one embodiment, the regression analysis used in step  412  is simple linear regression. 
     An example of using simple linear regression in step  412  to determine correlation coefficients is as follows. A sensing system may include a sensor with resistance R S  that is sensitive to fluctuations in temperature. The sensing system may include a heating element with a resistance R H  that is variable in time t. The temperature of the heating element may depend on the heating element resistance R H . In a previous step of obtaining sensing data, a set of sensor data points R S  and a set of reference data points R H  may be obtained over a period of time t 0 ≤t≤t f . Correlation coefficients C 0  and C 1  may then be determined from the first order polynomial equation below.
 
 R   S ( t )= C   1   R   H ( t )+ C   0  
 
     As another example of using simple linear regression in step  412 , a sensing system may include a sensor with resistance R S  that is sensitive to fluctuations in temperature. The sensing system may also include a heating element driven by a current that is regulated using a closed loop control such as pulse-width modulation (PWM) modes or proportional-integral-derivative (PID) control. The sensing system may also include a temperature sensor located near the sensor that measures the ambient temperature T. Since the current through the heating element is regulated, the baseline variation of the sensor may be primarily caused by fluctuations in ambient temperature. In a previous step of obtaining sensing data, a set of sensor data points R S  and a set of reference data points T may be obtained over a period of time t 0 ≤t≤t f . Correlation coefficients C 0  and C 1  may then be determined from the first order polynomial equation below.
 
 R   S ( t )= C   1   T ( t )+ C   0  
 
     As still another example, multiple linear regression may be used in step  412  as follows. A sensing system may include a sensor with resistance R S  that is sensitive to fluctuations in temperature and humidity. The sensing system may also include a heating element, a humidity sensor, and an array of temperature sensors located near both the heating element and the sensor. The array of temperature sensors may measure the temperature T at the sensor and the humidity sensor may measure the humidity RH at the sensor. In a previous step of obtaining sensing data, a set of sensor data points R S  and two sets of reference data points T, RH may be obtained over a period of time t 0 ≤t≤t f . Correlation coefficients C 0 , C 1 , and C 2  may then be determined from the equation below.
 
 R   S ( t )= C   2   RH ( t )+ C   1   T ( t )+ C   0  
 
     In other embodiments, such as when there is a nonlinear dependence on the reference data points, the regression analysis used in step  412  is polynomial regression. In still other embodiments, such as for very complex sensing systems where complete understanding may be difficult, regression analysis may be replaced with machine learning algorithms. 
     In various embodiments, step  412  may be performed for each sensor in an array of sensors resulting in a set of correlation coefficients for each sensor. Alternatively, step  412  may be performed using the average output of a sensor array or for the average output of subsets of a sensor array. 
     Following the determination of correlation coefficients in step  412 , the correlation coefficients may be stored in a computer-readable memory for future use in an optional step  442 . Alternatively, the correlation coefficients may be determined immediately prior to every use and not stored in a memory. The correlation coefficients that are stored in step  442  may overwrite previously stored correlation coefficients and/or may be appended to a history of stored correlation coefficients. The history of correlation coefficients may be used to ensure that the new correlation coefficients are reasonable and for potential troubleshooting of the sensor. The steps  412  and  442  may be part of a step  102  of preprocessing the sensing data as previously described. 
       FIG.  5    illustrates another method of preprocessing sensing data in accordance with an embodiment of the invention. 
     Referring to  FIG.  5   , a method  500  of preprocessing sensing data includes a step  412  of determining correlation coefficients using regression analysis and a step  442  which may be a previously described with respect to  FIG.  4   . In contrast to method  400 , method  500  includes a step  522  of quantifying the correlation between the sensor data points and the reference data points after step  412 . In various embodiments, the quantity determined in step  522  may be a coefficient of determination R 2 . The coefficient of determination R 2  may be used as an indicator of the level of correlation between the sensor data points and the reference data points. Other indicators such as the square of the Pearson correlation coefficient may also be used and may be apparent to those of ordinary skill in the art. 
     Step  532  includes a branching step that determines if the quantity determined in step  522  is higher than a predetermined threshold. For example, a sensing system may exhibit desired performance using the correlation coefficients determined in step  412  when the coefficient of determination R 2  is above 0.91. In this example, the predetermined threshold for step  522  may be 0.91. When the coefficient of determination R 2  is greater than 0.91, the correlation coefficients are stored in memory in step  442 . If the coefficient of determination R 2  is less than or equal to 0.91, a step  552  is performed which does not store the new correlation coefficients in memory and which continues on to a later step. In this way, an older set of correlation coefficients which meet the required correlation may be used instead of new set that is not sufficiently correlated. 
     As shown in  FIG.  5   , the steps  412 ,  522 ,  532 ,  552 , and  442  may be part of a step  102  of preprocessing the sensing data as previously described. 
       FIG.  6    illustrates a method of adjusting a baseline to correct baseline variation and normalizing sensor data points in accordance with an embodiment of the invention. The method illustrated in  FIG.  6    may be incorporated as appropriate into the methods of any of the previously described embodiments. 
     Referring to  FIG.  6   , a method  600  of adjusting a baseline to correct baseline variation and normalizing sensor data points includes a step  612  of using stored correlation coefficients to determine instantaneous baseline values at each of the sensor data points. For example, in the first scenario given in reference to  FIG.  4   , an equation is used to determine a set of correlation coefficients C 0  and C 1 . The same equation may be used to determine the instantaneous baseline values R S,baseline (t) for each time t using the stored correlation coefficients C 0  and C 1  and a new reference data point R H,new (t) corresponding to each new sensor data point R S,new (t) as shown below.
 
 R   S,baseline ( t )= C   1   R   H,new ( t )+ C   0  
 
     In other words, any equation that is used in determining a set correlation coefficients such as in step  412  may be used in conjunction with the set of correlation coefficients and new reference data points to determine a set of instantaneous baseline values in step  612 . 
     Following step  612 , the step  622  includes subtracting instantaneous baseline values R S,baseline (t) from corresponding new sensor data points R S,new (t) to obtain corrected sensor data points R S,corrected (t). Continuing with the previous example, an equation describing step  622  might be as given below.
 
 R   S,corrected ( t )= R   S,new ( t )− R   S,baseline ( t )= R   S,new ( t )−[ C   1   R   H,new ( t )+ C   0 ]
 
     At this point corrected sensor data points R S,corrected (t) have been determined using correlation coefficients. Steps  612  and  622  may be part of a step  222  of adjusting sensor data points to correct for baseline variation which may be as previously described. 
     Following the correction for baseline variation, the corrected sensor data points may optionally be normalized in step  632  and represented as a relative percentage in step  642 . Steps  632  and  642  may be part of a step  232  of normalizing sensor data points which may be as previously described. 
     Step  632  includes dividing the corrected sensor data points R S,corrected (t) by corresponding new sensor data points R S,new (t) and results in normalized corrected sensor data points. Additionally, step  642  includes multiplying each normalized corrected sensor data point by 100 to obtain a set of normalized corrected sensor data points represented as a relative percentage R S,normalized (t). The set of normalized corrected sensor data points may be referred to as a normalized corrected response. An equation using the scenario of the above example is given below. 
     
       
         
           
             
               
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     In other embodiments step  642  may be omitted and the normalized corrected sensor data points may be represented as a relative ratio. In still other embodiments, steps  632  and  642  may be omitted and the corrected sensor data points may be post processed. 
     It should be noted that in the method embodiments described herein, like reference numbers between embodiments may represent interchangeability and/or like features. For example, method  600  as described in reference to  FIG.  6    includes steps  222  and  232  which are also described in reference to  FIGS.  2  and  3   . Therefore, steps  222  and  232  as described in method  600  may be incorporated into methods  200  and  300  and so on. 
       FIGS.  7 - 18    illustrate various sensor devices which may be included in implementations of sensing systems that are configured to perform the methods described in reference to  FIGS.  1 - 6   . All similarly numbered elements in  FIGS.  7 - 18    refer to like elements between the various embodiments. 
       FIG.  7    illustrates an example sensor device including a substrate, a heating element, and a sensor in accordance with an embodiment of the invention. 
     Referring to  FIG.  7   , a sensor device  700  includes a sensor  30  disposed on a substrate  10 . The sensor  30  may be any suitable type of sensor such as a chemical sensor configured to detect a target analyte or group of target analytes. In various embodiments, the sensor  30  is a gas sensor. In some embodiments, the gas sensor is a resistive gas sensor, and in one embodiment, sensor  30  is a graphene-based resistive gas sensor. The graphene-based resistive gas sensor may generate sensing events by monitoring the change in resistance of one or more sheets of graphene, which is modulated by gas molecules being adsorbed and desorbed from the surface of the graphene. The sensor resistance may decrease when adsorbed gas species provide donor electrons to the graphene surface. Alternatively, the resistance may decrease when adsorbed gas species draw electrons away from the path of conduction. 
     The transduction method for the graphene-based gas sensor may also be different in various embodiments. For example, rather than a resistive gas sensor, sensor  30  may be a capacitive gas sensor and is a graphene-based capacitive gas sensor in one embodiment. Other possible transduction methods include work function monitoring, inversion n-type to p-type and may be apparent to those of ordinary skill in the art. 
     Sensor  30  may be configured to have selectivity towards a target analyte. For example, sensor  30  may selectively sense concentrations of volatile organic compounds (VOCs) in the ambient atmosphere. In various embodiments, sensor  30  may be configured to sense volatile gases such as hydrocarbons, methylene chloride, formaldehyde, and the like. 
     The sensor  30  may be sensitive to one or more environmental factors that affect the baseline of the sensor  30 . For example, environmental factors may include fluctuations in temperature, humidity, pressure, electric field, magnetic field, composition of the ambient atmosphere, concentration of species in the ambient atmosphere, and the like. In the specific example of a graphene-based resistive gas sensor, fluctuations in temperature may affect the performance of the sensor  30 . 
     The sensor  30  may be suspended between two or more electrodes  34 . The electrodes  34  may include a conductive material and may be a patterned metal in various embodiments. For example, the electrodes  34  may include copper (Cu), silver (Ag), gold (Au), aluminum (Al), tungsten (W), and the like. 
     In some embodiments, the sensor  30  may also include surface modifications  32 . The surface modifications  32  may be chemical groups attached to the surface of sensor  30  to increase the sensitivity of sensor  30  to target analytes and/or reduce the sensitivity of sensor  30  to environmental factors or species other than target analytes. In other embodiments, the surface modifications  32  may be a protective coating and may cover all or most of the sensor  30 . 
     The substrate  10  may be any suitable substrate. In various embodiments, substrate  10  is a laminate substrate and is a printed circuit board in one embodiment. In other embodiments, substrate  10  is a semiconductor substrate and is part of a monolithic integrated circuit chip including sensor  30 . In one embodiment, substrate  10  is a silicon substrate and sensor  30  is included in an integrated circuit. In another embodiment, substrate  10  is a ceramic substrate. Substrate  10  may also be a metallic substrate or include a metallic substrate. In some embodiments, substrate  10  may be packaged to form a sensor package including sensor  30 . 
     A heating element  20  may be included on or within substrate  20 . The heating element  20  may heat the sensor  30  and sensor device  700  in order to maintain an optimal operating temperature or range of operating temperatures. For example, the heating element  20  may heat the sensor  30  to 200° C. in one embodiment. In another embodiment, the heating element  20  may heat the sensor  30  to 400° C. In the specific case of a resistive gas sensor, the temperature may need to be elevated to facilitate desorption of gas molecules for continued sensing. In some cases, refresh cycles may be used to heat the sensor  30  to a temperature well above the normal operating temperature in order to remove all species from the surface of sensor  30  before beginning a new data acquisition period. 
     The heating element  20  may also be used as a reference for baseline variation of sensor  30 . For example, the resistance of heating element  20  may be recorded periodically during data acquisition periods and used as reference data points when correcting for baseline variation of sensor  30 . 
     The heating element  20  may be a metal conductor in one embodiment. In other embodiments, the heating element  20  may be a microelectromechanical systems (MEMS) heater integrated into a semiconductor substrate. The heating element  20  and/or sensor  3   o  may also be suspended over an opening in substrate  10 . This may facilitate increased interaction with the ambient atmosphere as well as reduce heat loss in the heating element  20 . 
       FIG.  8    illustrates an example sensor device including a substrate, a heating element, a sensor, and an environmental sensor in accordance with an embodiment of the invention. 
     Referring to  FIG.  8   , a sensor device  800  includes a sensor  30  and a heating element  20  attached to a substrate  10  as previously described. In contrast to sensor device  700 , sensor device  800  also includes an environmental sensor  40 . The environmental sensor  40  may be a temperature sensor, humidity sensor, pressure sensor, and the like. The environmental sensor  40  may be configured to measure reference data points to for use in correcting the baseline variation of sensor  30  as described in previous methods. 
       FIG.  9    illustrates an example sensor device including a substrate, a heating element, a sensor, and a structural reference sensor in accordance with an embodiment of the invention. 
     Referring to  FIG.  9   , a sensor device  900  includes a sensor  30  and a heating element  20  attached to a substrate  10  as previously described. Instead of the environmental sensor  40  included in sensor device  800 , sensor device  900  includes a structural reference sensor  50 . The structural reference sensor  50  may be sufficiently similar in structure or function to sensor  30  so as to provide reference data points for use in correcting the baseline variation of sensor  30 . 
     For example, sensor  30  and structural reference sensor  50  may both be graphene-based resistive gas sensors, but structural reference sensor  50  may not include surface modifications  32 . Alternatively, the surface of sensor  30  is bare graphene and the surface of structural reference sensor  50  is coated or otherwise modified to be unresponsive to the target analyte of sensor  30 . In this way, the contribution of the sensing target may be removed from the signal of the structural reference sensor  50  and only the effects of environmental factors remain. Significant correlation between the sensor  30  and the structural reference sensor  50  may then be primarily caused by environmental factors and reflect baseline variation in both sensors. 
       FIG.  10    illustrates an example sensor device including a substrate, a heating element, a sensor, an environmental sensor, and a reference sensor where the environmental sensor is located on the substrate in accordance with an embodiment of the invention. 
     Referring to  FIG.  10   , a sensor device no includes a sensor  30 , an environmental sensor  40 , a reference sensor  50 , and a heating element  20  attached to a substrate  10 . Any combination of the heating element  20 , environmental sensor  4   o , and structural reference sensor  50  may be used to obtain reference data points to correct for baseline variation of sensor  30 . 
       FIG.  11    illustrates another example sensor device including a substrate, a heating element, a sensor, an environmental sensor, and a structural reference sensor where the environmental sensor is located on a second substrate in accordance with an embodiment of the invention. 
     Referring to  FIG.  11   , a sensor device  111  includes a sensor  30 , a structural reference sensor  50 , and a heating element attached to a substrate  10  as previously described. However sensor device  111  differs from sensor device no in that an included environmental sensor  40  is attached to a second substrate  12  rather than substrate  10 . The substrate  10  is operatively coupled to the second substrate  12  and both are contained in a package  60 . 
     The second substrate  12  may include a processor such as an application-specific integrated circuit (ASIC) or a field-programmable gate array (FPGA). The processor may be configured to perform any of the method steps as described in previous embodiments such as obtaining sensing data, preprocessing the sensing data, post processing the sensing data, and outputting sensed values. The substrate  10  and the second substrate  12  may be rigidly attached to the package  60 . However, in some embodiments, the substrate  10  and the second substrate  12  may be elastically attached to the package  60 . 
     The package  60  includes an opening  70  which facilitates interactions of sensor  30 , environmental sensor  40 , and reference sensor  50  with the ambient environment. It should be noted that although package  60  and opening  70  are only illustrated in  FIG.  11   , package  60  and opening  70  may be included in all embodiment sensor device described herein and apparent to those of ordinary skill in the art. 
       FIG.  12    illustrates a top view of an example sensor device including multiple sensors and a reference sensor in accordance with an embodiment of the invention. 
     Referring to  FIG.  12   , a sensor device  112  includes multiple sensors  30  and a centrally located structural reference sensor  50  attached to a substrate  10 . A heating element  20  is also included on or within substrate  10  which provides heat to the sensors  30  and structural reference sensor  50 . In this embodiment, eight sensors  30  form and array of sensors  30  and a single structural reference sensor  50  is included in the center of a box arrangement of sensors  30 . 
     However, any arrangement of multiple sensors  30  and a structural reference sensor  50  is possible. For example, a 5×5 array of sensors  30  may be located on the left side of substrate  10  while a structural reference sensor  50  is located on the right side. The number and arrangement of sensors  30  and structural reference sensor  50  may depend on specific application and is not limited to exactly the patterns illustrated in this or other embodiments. 
       FIG.  13    illustrates a top view of an example sensor device including multiple sensors and multiple reference sensors in accordance with an embodiment of the invention. 
     Referring to  FIG.  13   , a sensor device  113  includes multiple sensors  30  arranged in an array in a central region of a substrate  10  and four structural reference sensors  50  located in respective corner regions of the substrate  10 . The four structural reference sensors  50  may be averaged for use in determining correlation coefficients or a multiple regression may be used with four dependent variables as previously described. In all embodiments, the heating element may also be used as a reference. 
       FIG.  14    illustrates a top view of an example sensor device including multiple pairs of a sensor and a reference sensor in accordance with an embodiment of the invention. 
     Referring to  FIG.  14   , a sensor device  114  includes multiple pairs of a sensor  30  and a structural reference sensor  50  arranged in an array on a substrate  10 . The substrate  10  also includes a heating element  20  as previously described. In this arrangement a structural reference sensor  50  may be used to correct the baseline variation for each corresponding sensor  3   o . This may be useful if there is variation between sensors  30  over the substrate  10  or if there are multiple types of sensor  30  on the same substrate  10 . Additionally, the corrected sensor data from each sensor  30  may be treated individually or averaged before post processing depending on specific application. 
       FIG.  15    illustrates a top view of an example sensor device including multiple pairs of a sensor and a reference sensor and further including an environmental sensor in accordance with an embodiment of the invention. 
     Referring to  FIG.  15   , a sensor device  115  includes multiple pairs of sensor  30  and a structural reference sensor  50  arranged in an array on a substrate  10  and a heating element in or within substrate  10  as previously described. In contrast to sensor device  114 , sensor device  115  also includes an environmental sensor  40  centrally located on substrate  10 . The environmental sensor  40  may be used as a reference for correcting the baseline variation of sensors  30  in addition to the structural reference sensors  50 . 
       FIGS.  16 ,  17 , and  18    illustrate top views of example sensor devices including multiple sensors, and an environmental sensor where the environmental sensor is located on a second substrate in accordance with embodiments of the invention.  FIG.  16    illustrates an example sensor device that includes a single reference sensor,  FIG.  17    illustrates an example sensor device that includes multiple reference sensors, and  FIG.  18    illustrates an example sensor device that includes multiple pairs of a sensor and a reference sensor. 
     Referring to  FIG.  16   , a sensor device  116  includes a sensor device  112  as previously described in reference to  FIG.  12    operatively coupled to a second substrate  12 . An environmental sensor  40  is attached to the second substrate  12 . 
     Referring now to  FIG.  17   , a sensor device  117  includes a sensor device  113  as previously described in reference to  FIG.  13    operatively coupled to a second substrate  12 . An environmental sensor  40  is attached to the second substrate  12 . 
     Referring now to  FIG.  18   , a sensor device  118  includes a sensor device  114  as previously described in reference to  FIG.  14    operatively coupled to a second substrate  12 . An environmental sensor  40  is attached to the second substrate  12 . 
     In any of the previous embodiments, additional environmental sensors may also be included. Additional types of environmental sensors may also be included as described in an example in reference to  FIG.  4   . Multiple types of sensors may also be included on the same substrate or in the same sensor device, sensor package, or sensing system. The invention is also not limited to the correcting the baseline variation of sensors, but may also be applied to any device that is significantly affected by environmental factors. 
       FIGS.  19 A and  19 B  illustrate qualitative graphs of sensor resistance versus time and heating element resistance versus time with baseline variation due to sensor drift where  FIG.  19 A  illustrates resistance responses of a sensor and a heating element before correcting the baseline variation and  FIG.  19 B  illustrates resistance responses of the sensor and the heating element after correcting the baseline variation. 
     Referring to  FIG.  19 A , graph  190  shows a heating element resistance curve  85   a  and a sensor resistance curve  86   a  as a function of time. Heating element resistance  85   a  may be considered an indication of a variable baseline, as can be seen by the gradual increase in heater resistance over time. Sensor resistance curve  86   a  is also shown to follow this trend of increasing resistance which may indicate a correlation between the response of the heating element and the response of the sensor. 
     Now referring to  FIG.  19 B , the correlation between the response of the heating element and the response of the sensor have been used to correct for baseline variation and generate corrected heating element resistance curve  85   b  and corrected sensor resistance curve  86   b  as shown in graph  191 . Notably, corrected heating element resistance curve  85   b  is constant in time. 
     Sensor resistance curve  86   a  and corrected sensor resistance curve  86   b  are shown to have a feature in each of five time intervals: first time interval  80 , second time interval  81 , third time interval  82 , fourth time interval  83 , and fifth time interval  84 . In this specific example, a small concentration of a target analyte is detected in first time interval  80  and fifth time interval  85 , a medium concentration of a target analyte is detected in second time interval  81  and fourth time interval  83 , and a large concentration of a target analyte is detected in third time interval  82 . For corrected sensor response  86   b , the respective features of the five time intervals are now advantageously measured from a constant baseline. 
       FIGS.  20 A and  20 B  illustrate qualitative graphs of sensor resistance versus time with baseline variation due to sensor drift over multiple correction intervals where  FIG.  20 A  illustrates resistance responses of a sensor before correcting the baseline variation and  FIG.  20 B  illustrates resistance responses of the sensor after correcting the baseline variation. 
     Referring to  FIGS.  20 A and  20 B , graph  120  shows a sensor resistance curve  87   a  subject to baseline variation with a first correction interval  88  and a second correction interval  89 . Graph  121  shows a corrected sensor resistance curve  87   b  where the baseline is now constant. In this embodiment, a correlation is determined between the sensor and a reference prior to first correction interval  88  and then used to correct the sensor resistance during first correction interval  88 . After first correction time interval  88 , a correlation is again determined between the sensor and the reference and used to correct the sensor resistance during the second correction interval  89 . This may continue to be repeated as has been described in further detail in previous embodiments. 
     Example embodiments of the present invention are summarized here. Other embodiments can also be understood from the entirety of the specification as well as the claims filed herein. 
     Example 1. A method of sensing, the method including: obtaining, by a sensor, first sensor data points; obtaining first reference data points; determining a correlation between the first sensor data points and the first reference data points; measuring, by the sensor, second sensor data points; obtaining second reference data points; adjusting the second sensor data points using the correlation and the second reference data points to obtain corrected sensor data points; determining sensed values from the corrected sensor data points; and storing the sensed values. 
     Example 2. The method of example 1, where the sensor is a resistive gas sensor. 
     Example 3. The method of one of examples 1 and 2, where the sensor includes graphene. 
     Example 4. The method of one of examples 1 to 3, where determining the correlation includes determining a plurality of correlation coefficients using regression analysis. 
     Example 5. The method of one of examples 1 to 4, where adjusting the second sensor data points includes using the correlation to determine instantaneous baseline values for each of the second sensor data points, and subtracting the instantaneous baseline values from the corresponding second sensor data points. 
     Example 6. The method of one of examples 1 to 5, further including: normalizing the corrected sensor data points before determining the sensed values. 
     Example 7. The method of one of examples 1 to 6, where obtaining the first reference points and obtaining the second reference points includes obtaining resistance values of a heating element. 
     Example 8. The method of one of examples 1 to 6, where obtaining the first reference points and obtaining the second reference points includes obtaining ambient temperature measurements from a temperature sensor. 
     Example 9. A method of sensing, the method including: obtaining, by a sensor, first sensor data points during a first time interval; obtaining first reference data points during the first time interval; and during a second time interval and after the first time interval, measuring, by the sensor, second sensor data points, generating corrected second sensor data points by correcting for baseline variation in the second sensor data points using a relationship between the first sensor data points and the first reference data points, and determining sensed values from the corrected second sensor data points. 
     Example 10. The method of example 9, where the sensor is a resistive gas sensor. 
     Example 11. The method of one of examples 9 and 10, where the sensor includes graphene. 
     Example 12. The method of one of examples 9 to 11, further including: after an expiration of the second time interval and during a third time interval, obtaining, by a sensor, third sensor data points; obtaining third reference data points during the third time interval; and during a fourth time interval and after the third time interval, repeating the steps of measuring, by the sensor, fourth sensor data points, generating corrected fourth sensor data points be correcting for baseline variation in the fourth sensor data points using a relationship between the third sensor data points and the third reference data points, and determining second sensed values from the corrected fourth sensor data points. 
     Example 13. The method of one of examples 9 to 11, further including: during the second time interval, obtaining second reference data points; and during a third time interval and after the third time interval, obtaining, by the sensor, third sensor data points, generating corrected third sensor data points by correcting for baseline variation in the third sensor data points using a relationship between the second sensor data points and the second reference data points, and determining sensed values from the corrected third sensor data points. 
     Example 14. The method of one of examples 9 to 13, where obtaining the first reference points includes obtaining resistance values of a heating element. 
     Example 15. A sensor device including: a gas sensor disposed on a first substrate, the gas sensor being configured to measure first sensor data points and second sensor data points; a heating element disposed within the first substrate, where the gas sensor overlaps the heating element; a processor operatively coupled to the gas sensor and the heating element; and a memory storing a program to be executed by the processor, the program including instructions for recording first resistance values and second resistance values of the heating element, adjusting the second sensor data points using the first sensor data points, the first resistance values, and the second resistance values to obtain corrected sensor data points, and determining sensed values from the corrected sensor data points. 
     Example 16. The sensor device of example 15, where the gas sensor includes graphene. 
     Example 17. The sensor device of one of examples 15 and 16, where the gas sensor is a resistive gas sensor. 
     Example 18. The sensor device of one of examples 15 and 16, where the gas sensor is a capacitive gas sensor. 
     Example 19. The sensor device of one of examples 15 to 18, further including: a reference sensor disposed on the substrate and adjacent to the gas sensor, the reference sensor being configured to measure first reference sensor data points and second reference sensor data points, where the program includes further instructions for using the first reference sensor data points and the second reference sensor data points when adjusting the second sensor data points. 
     Example 20. The sensor device of one of examples 15 to 19, further including: an environmental sensor disposed on a second substrate operatively coupled to the first substrate, the environmental sensor configured to measure first environmental data points and second environmental data points, where the program includes further instructions for using the first environmental data points and the second environmental data points when adjusting the second sensor data points. 
     Example 21. The sensor device of example 20, where the environmental sensor is a humidity sensor. 
     Example 22. The sensor device of one of examples 20 and 21, where the processor is an application-specific integrated circuit (ASIC) and is disposed on the second substrate. 
     While this invention has been described with reference to illustrative embodiments, this description is not intended to be construed in a limiting sense. Various modifications and combinations of the illustrative embodiments, as well as other embodiments of the invention, will be apparent to persons skilled in the art upon reference to the description. It is therefore intended that the appended claims encompass any such modifications or embodiments.