# A Task-Centric Cooperative Sensing Scheme for Mobile Crowdsourcing Systems
## 3 Problem Statements
### Sensing Range and Spatial Correlation Estimation  
For applications such as target detection, an active participant may be assigned a disk-shaped _sensing range_, centered at its location, as shown in Figure 1. If a target presents within an active participant's sensing range, the participant will detect the target with a pre-specified probability of detection. An active participant becomes _redundant_ if its sensing range is fully _covered_ by its neighboring active participants. Referring to Figure 1, the sensing range of active participant #5 is completely covered by the union of the sensing ranges of active participant #3, #4, #6, and #7. As such, active participant #5 becomes redundant and can be removed from operation without significantly affecting the overall probability of target detection of the MCS.  
For applications such as network monitoring [1], smartphone-based crowdsourcing plays an important role. By subcontracting a monitoring-task to the interested participants, the network-monitoring application can be fulfilled in a participatory manner, using as many participants' devices as possible distributed in the geographic area of the whole system. Nevertheless, through qualitative analysis, we can draw some interesting considerations. The received signal strength index (RSSI) in the same place may change dramatically with the different wireless communication operators. At this time, how can we select the operator that provides the best quality in those places?To address such a deficiency, we argue that one must use empirical sensing data measurements to directly and explicitly estimate the spatial correlations among neighboring active participants, and to exploit them for the purpose of participants' idle scheduling. We further assert that the spatial correlation may not even necessarily be decreasing as the distance between a pair of active participants increases. To illustrate this point, we use a publicly available Intel Berkeley Lab sensing dataset [32] which consists of sensing data and location information of all sensor nodes. In Figure 2, we compute the cross-correlation coefficients of the sensor data of each pair of active participants, and plot them against corresponding distance between the active participants. We fit this scatter plot using linear regression and plot the regression line in Figure 2. The line equation is:  
\[\rho\,=\,-0.00015\times d\,+\,1.0\,+\,\delta \tag{1}\]  
where \(\rho\) is the spatial correlation coefficient, \(d\) is the distance (in meter) between active participant pairs, and \(\delta\) is the fitting error which has a normal distribution with zero mean and variance \(\sigma^{2}=1.7250\times 10^{-5}\).  
It is clear that although a general trend of reduced spatial correlation with increasing distance exists, the variance is rather significant and there are plenty of outliers. Based on the above observations, we propose a _task-centric_ model to represent and exploit spatial correlations for applications where original sensing data are desired. We assume that before normal operation, the MCS will go through a _training_ period. During this period, all participants will be active so that the data correlation among spatially separate active participant can be empirically estimated. We further assume that such an estimated spatial correlation will remain unchanged during normal operations in the _testing_ period. If deemed necessary, re-training may be performed to update the spatial correlation estimations.  
Figure 1: Active participants in a clustered MCS.  
Figure 2: Data correlation _vs._ distance.