# Distributed Information Compression for Target Tracking in Cluster-Based Wireless Sensor Networks
## 3 Data Processing Schemes
### Target Positioning  
The major difference between TCAT and CTCI is the bounding area formed by the different numbers of active sensors. In TCAT, the bounding area is determined by the active sensors in the same cluster. In CTCI, the bounding area is determined by not only the active sensors in a single cluster, but also the active sensors in other clusters. It is worth mentioning that including the active sensors in different clusters can effectively decrease the scope of the bounding area for sampling. The bigger the distance between the active sensor and the others, the smaller the intersection area of the transmission range of the active sensor will be, which suggests that we can provide a better sample area for particle filtering and even use fewer sampling points for the tracking task as the sample area decreases. Observe that in Figure 6, we can see that an active sensor node is added to form the bounding area A in CTCI, which is smaller than the bounding area B in TCAT (as shown in Figure 7). Accordingly, we may use a smaller number of samples (Figure 8) to achieve a comparable estimation accuracy with particle filtering. Figure 6: The bounding area A of CTCI. Figure 7: The bounding area B of TCAT. which roughly corresponds to the estimation distribution. The proposed algorithm uses the bitmap process and statistical properties to execute data processing, which consists of the following five steps:  
1. _Preliminary settings_\(\sim\) Each tasking sensor performs target positioning with Bayesian filtering of \(N\) samples, which leads to a target position estimate at time step \(k\), \(P_{k}=(X_{k},Y_{k})\), where \(X_{k}=(x_{k}(1),x_{k}(2),\ldots,x_{k}(N))\), \(Y_{k}=(y_{k}(1),y_{k}(2),\ldots,y_{k}(N))\). 2. _Configuring the bitmap of \(P_{k}\sim\)_ Each tasking sensor computes the average \(\bar{\mu}_{k}=(\bar{X}_{k},\bar{Y}_{k})\), \(\sigma_{X_{k}}\), \(\sigma_{Y_{k}}\), and generates the value of compressing bound, \(\varepsilon_{X_{k}}=\sigma_{X_{k}}\cdot\eta\) and \(\varepsilon_{Y_{k}}=\sigma_{Y_{k}}\cdot\eta\), where \(\eta\) is an adjustable factor to trade off the compression ratio and positioning accuracy. 3. _Compression of \((X_{k},Y_{k})\sim\)_ As shown in Figure 10b,c, scan and compress \(X_{k}\) and \(Y_{k}\) (using \(x_{k}(j)\) and \(y_{k}(j)\) as examples). Hence, if \((|x_{k}(j)-\bar{X}_{k}|>\varepsilon_{X_{k}})\), then bit\((x_{k}(j))\) = 1 and \(\triangle_{x_{k}(j)}=x_{k}(j)-\bar{X}_{k}\). Similarly, if \((|y_{k}(j)-\bar{Y}_{k}|>\varepsilon_{Y_{k}})\), then bit\((y_{k}(j))\) = 1 and \(\triangle_{y_{k}(j)}=y_{k}(j)-\bar{Y}_{k}\). Afterwards, the tasking sensor (_i.e._, a sub-cluster member) transmits the compressed data (\(\bar{\mu}_{k}\), \(\triangle(X_{k})\), \(\triangle(Y_{k})\), \(\sigma_{X_{k}},\sigma_{Y_{k}}\)). 4. _Data decompression_\(\sim\) As shown in Figure 10a, decompress the received data by scanning \(\bar{\mu}_{k}\), \(\triangle(X_{k})\) and \(\triangle(Y_{k})\). If bit\((x_{k}(j))\) = 1, then \(x_{k}(j)=\bar{X}_{k}+\triangle_{x_{k}(j)}\); otherwise, \(x_{k}(j)=\bar{X}_{k}\). 5. _Estimation fusion_\(\sim\) Figure 11 shows the external contour of the sample region and the distribution of the decompressed data. The leader node scans the information of each sample sub-region. Let \(p_{m}\) be the target appearance probability of sample region \(m\), which yields \(p_{m}=N_{m}/N_{L}\) (\(m=1,2,\ldots,9\)), where \(N_{m}\) is the number of sample points in region \(m\) and \(N_{L}\) is the total number of sample points. Let \(\bar{\mu}_{k}(m)\) be the average estimate of sample region \(m\). Accordingly, we obtain the location estimate \(P_{L}=\sum_{m=1}^{9}p_{m}\cdot\bar{\mu}_{k}(m)\). Therefore, the information processing of the CTCI scheme is completed. Figure 9: The conceptual processes of the CTCI scheme. Figure 10: The sampling points after the bitmap process (**a**) and the impact of the compressing bound on distortion: \(x\)-axis (**b**) and \(y\)-axis (**c**).