The environment is being affected more and more by the release of odorant pollutants in the atmosphere. These odors may discomfort the olfaction system and can even be harmful to human health. Electronic noses (e-noses) have been widely investigated [1,2], and are used for real-time environmental monitoring to prevent poison gas attacks by terrorists and gas leaks in chemical plants [3-5]. A single e-nose can only measures the odor strength at one location, and cannot evaluate the overall odor plume map around the monitored environment. The proposed wireless e-nose network system is able to collect remote odor data in real time and conduct further analysis for effective odor management.

In environment monitoring using a wireless e-nose network [3,5,6], accurate odor measurement is essential for many applications such as development of odor dispersion models and estimation of odor source location based on the odor data [7]. A wireless e-nose network system is composed of many e-nose nodes that are deployed in a monitoring region. These e-nose nodes are composed of an array of Metal-Oxide Semiconductor (MOS) gas sensors. The output signals from the MOS gas sensors contain not only gas signals, but also noise. The noise results in inaccuracies in analyzing data and estimating the odor strength. In a previous study, an e-nose consisted of a sensor array and an intelligent analysis system was developed, but the noise reduction of gas sensors was not well investigated [8,9].

The Kalman filtering algorithm is a recursive algorithm to solve the state estimation problems of known systems based on certain mathematical models and the observation of noisy measurements. Many modified filtering schemes have been developed to tackle the problems in various applications [10], e.g., a decentralized Kalman filtering algorithm to estimate collaborative information in wireless sensor networks [11], an adaptive Kalman filtering algorithm to reduce the noise for GPS and INS systems [12].

In this paper, a wireless e-nose prototype is developed to acquire MOS gas sensor output signals and send them to a remote server. A modified Kalman filtering technique is developed for improving the sensor sensitivity and precision of odor strength measurement. It can adapt in real time to adjust the measurement noise variance of the filter parameters. In addition, the optimal parameter of system noise variance is obtained by using the experimental data. Application of Kalman filter theory to the acquired MOS gas sensors data is discussed.

The block diagram of the proposed e-nose prototype is presented in Figure 1. It is mainly composed of two parts: the odorant gas measurement chamber unit, and the signal processing and wireless communication unit.

Noise unavoidably appears at all times in an odor sensing system. The two most common forms of noise are the circuit factor noise and environmental factor noise (see Figure 5).

The Kalman filtering model is based on two sources of uncertainties: measurement noise introduced by the sensor and circuit noise, and the true strength variability; odor strength optimal estimation problem is modeled by a linear stochastic system. The system state vector x_k and the measurement vector y_k are described as: (2) x k + 1 = A x k + u k + ω k = x k + ω k , (3) y k = C x k + ν k ,where, x_k is the system state vector; y_k is the measurement vector; u_k is the input vector (there is no input, u_k =0); ω_k is the process noise vector; and v_k is the measurement noise vector. Pa rameter A is an identity matrix, which denotes the system matrix, and C is the measurement matrix, which transforms measurement voltage value to resistor value using Equation (1).

The noise covariance of ω_k and v_k are given as: (4) E [ ω k ω k T ] = Q , (5) E [ ν k ν k T ] = R k , (6) E [ ω k ν k T ] = 0 ,the a priori estimation error and estimation error variance are defined as: (7) e K − = x k − x ^ k − , (8) p k − = E [ e k − ( e k − ) T ] ,and, the a posteriori estimation error and estimation error variance are defined as: (9) e K + = x k − x ^ k + , (10) p k + = E [ e k + ( e k + ) T ] .

The system state prediction at step k+1 can be denoted by the a posteriori estimation at step k as: (11) x ^ k + 1 − = x ^ k + .

The a posteriori estimation can be denoted by a linear combination of the a priori estimate and a weighted difference between actual measurement and the a priori estimate as [10]: (12) x ^ k + 1 + = x ^ k + 1 − + k k + 1 ( y k + 1 − C x ^ k + 1 − ) .

In practice, x ^ k + is the strength estimation at step k; x ^ k + 1 − is the predicted strength estimation at step; k + 1 x ^ k + 1 + is the a posteriori strength estimation at step; k + 1; y_k+1 is the actual strength measurement value at step k+1; the difference ( y k + 1 − C x ^ k + 1 − ) is called the measurement innovation, which reflects the discrepancy between the system state prediction and the actual measurement quantity; and the weighted value k+1 is the Kalman gain at step k+1. The Kalman gain k_k is defined as: (13) k k = p k − ( p k − + R k ) − 1 = p k − p k − + R k ,where p k − and R_k are from Equations (8) and (5), respectively.

The Kalman gain reflects the relationship between measurement and estimation. It indicates which one would be more reliable and should be “accepted” by the final estimation. The sensor is more reliable and the samples have lower variability, then the measurement error variance R_k will be smaller, and the Kalman gain, which can be obtained from Equation (13), will be larger, because the Kalman gain is the weight factor of the measurement innovation in Equation (12); if the Kalman gain increases, then the weight factor of the measurement innovation will increase, and the a posteriori strength estimate quantity x ^ k + 1 + will have more from the actual measurement value and less from the predicted value.

The a posteriori estimate error variance p k + is defined as a function of the weight factor k_k and the a priori estimation error variance. Thus the a priori and posteriori estimates p k − and p k + are defined as: (14) p k − = E [ ( x k − x ^ k − ) ( x k − x ^ k − ) T ] = p k − 1 + + Q k − 1 , (15) p k + = E [ ( x k − x ^ k + ) ( x k − x ^ k + ) T ] = ( I − C k k ) p k − .

Tian et al. [8] analyzed the circuit and noise of MOS gas sensors in an e-nose; they concluded that the noise of these resistive type MOS gas sensors can be treated as Gaussian white noise plus some stronger low frequency direct current components. A standard Kalman filter solves the state estimation problems based on some certain assumptions in a system mathematical model, obtaining complete information about noise statistics as a Gaussian white noise; however, if there is uncertainty about the noise characteristics, the filter may not be robust enough. In this section, a modified filter algorithm based on the standard Kalman filter is proposed, which can adjust measurement noise covariance by using a slip windows average to reduce the noises, even if the sensor noise characteristics is unknown in advance.

The modified Kalman filter reduced the noise in the strength measurement process by using feedback control. The filter estimates the strength from the odor strength at a previous time step and the sensor measurement with the noise component. The equations for the modified Kalman filter fall into two groups: time updating equations and measurement updating equations. The time updating equations are responsible for projecting forward the time, obtaining an a priori estimation and error covariance estimation of the next time step. The measurement updating equations are responsible for the feedback, incorporating a new measurement into the a priori strength estimation, in order to obtain an improved a posteriori estimation.

The time updating equations from time step k−1 to step k, the previous state x ^ k − 1 + and previous error covariance estimates p k − are used to obtain the next time a priori estimations s x ^ k − and p k −, which are given as: (30) x ^ k − = x ^ k − 1 + , (31) p k − = p k − 1 + Q k − 1 .

The measurement updating equations incorporate a new observation y_k into an a priori estimation x ^ k − from the time updating equations to obtain an improved a posteriori estimation x ^ k +, which are given as: (32) d ^ k = 1 j ∑ n = k − j + 1 k ɛ n , (33) R ^ k = E ( v k v k T ) = 1 n ∑ i = 1 n ( z k − H k x ^ k ) ( z k − H k x ^ k ) T − H k p k − H k T , (34) k k = p k − ( p k − + R k ) − 1 = p k − p k − + R k , (35) p k + = ( I − C k k ) p k − , (36) x ^ k + = x ^ k − + k k ( z k − C x ^ k − ) , (37) Q k = R k λ .

The first step is to select an initial a priori value x ^ 0 + and the error variance. p₀ The selection of these values has no constraints, since the filter will converge to an appropriate value automatically; however, if they are chosen in the dynamic range of the expected odor strength then the errors will converge rapidly.

Subsequently, the sensor performs a strength measurement to obtain y_k, using the proposed slip window average method to estimate the direct current components d̂_k and. R̂_k The next step involves taking those estimations to compute the Kalman gain, k_k a posteriori error variance p k + and a posteriori estimation x ^ k +. The following step is to calculate the system error variance Q_k using the measurement variance and variance ratio factor. A loop cycle of the modified Kalman filter algorithm is thus finished. The filter will use the new a posteriori estimation and system variance in the time updating equations.

The developed e-nose prototype was used in a livestock research farm at the University of Guelph in Canada. In the experiments, the four MOS gas sensors in Table 1 were installed in every e-nose node. In addition, the continuous heat regime was used in the experiments. By running the e-nose prototype to collect odor data for approximately 500 minutes in this period, each sensor acquired 500 simultaneous odor measurements data. A laptop computer running Matlab 7.0 software was used to process the data and to determine the optimal error variance ratio factor. These optimal values were then used in the noise reduction for the e-nose gas sensors.

In this paper, a wireless e-nose prototype for a wireless sensor network that can accurately measure odorant gases and estimate odor strengths has been designed and implemented. The advantages of the e-nose prototype are its light weight, very small size, and flexibility in applications. Four commercial gas sensors are used. An interface circuit and a MicaZ are used for data acquisition, data analysis, and data transfer. Using the developed wireless e-nose network, remote and real-time odor measurements become possible.

Based on the output noise from gas sensor circuits, a real-time odor strength estimation model and a modified Kalman filter algorithm are proposed, which can improve the prediction capability and the accuracy of measurement. Using the proposed model and algorithm, the direct current component and Gaussian white noise are reduced considerably at the sensor outputs. In addition, even if the sensor noise characteristics is unknown in advance, the variance of measurement error can be changed adaptively. The experiments demonstrate that the modified Kalman algorithm is effective in the measurement of real-time odor strength of livestock farms odors.