## 3 System Models
### GCI Fusion  
In our aquaculture sensor network, multiple sensors (including normal nodes and anchors) are sensing, exchanging, and processing location, state, and other tracking information from targets and their neighbors. Suitable information fusion strategies are taken into account in such an energy-limited system with limited sensing capabilities, limited processing capabilities, and limited computation capabilities. The centralized fusion methods cannot be adopted for such large-scale sensors and large monitoring areas. The pairwise fusion means cannot be adopted; although it can substantially decrease the computational burden, it brings about some problems. One is that it needs to establish location correlations before coupling these sensors, which consumes great energy for the uncertainty location of mobile sensors. The other is that one residual sensor cannot couple with any other sensor after coupling with its corresponding sensor, leading to missed detection. Thus, a distributed fusion method based on GCI, a multitarget fusion strategy, is proposed in this sensor network to iterate local fusion among neighboring nodes for scalability requirement. The GCI fusion process is briefly described below [31]. Given estimates \(\hat{x}_{k}\) of the state from multiple estimators with relative covariances \(P_{k}\) and unknown correlations, the GCI fusion can be presented as  
\[GCI(x)=\frac{\prod_{k}[p_{k}(x)]^{w_{k}}}{\int\prod_{k}[p_{k}(x)]^{w_{k}}dx}, \tag{25}\]  
where \(p_{k}(\mathrm{x})\sim N(x;\hat{x}_{k},P_{k})\) is the Gaussian PDF with mean \(\hat{x}_{k}\) and covariance \(P_{k}\), and \(w_{k}\) is the weight of \(x_{k}\). Of course, the fusion of PDF in Equation (25) can be used for an arbitrary PDF, not only for a Gaussian PDF. Given that the target RFS set follows an independent and identically distributed cluster process [30], the sensor multitarget densities to be fused to take the following form:  
\[GCI_{k}(X)=|X|!p_{k}(X)\prod_{x\in X}D_{k}(x), \tag{26}\]  
\[\overline{GCI}_{k}(X)=|X|!\overline{p}_{k}(X)\prod_{x\in X}\overline{D}_{k}(x). \tag{27}\]  
As related above, \(D_{k}(x)\) and \(N_{k}(x,n)\) are considered the state density and cardinality density of multiple targets, respectively. The GCI fusion of \(D_{k}(x)\) and \(N_{k}(x,n)\) of the multiple targets adopting Equations (25) and (26) can be obtained as follows:  
\[\overline{D}(\mathrm{x})=\frac{\prod_{i=1}^{N_{A}}\left[D_{k}(x)\right]^{w_{i }}}{\int\prod_{i=1}^{N_{A}}\left[D_{k}(x)\right]^{w_{i}}dx}, \tag{28}\]  
\[\overline{\mathrm{N}}(x,n)=\frac{\prod_{i=1}^{N_{A}}\left[N_{i}(n)\right]^{w_{ i}}\left\{\int\prod_{i=1}^{N_{A}}\left[D_{k}(x)\right]^{w_{i}}dx\right\}^{n}}{ \sum\limits_{j=1}^{\infty}\prod_{i=1}^{N_{A}}\left[N_{k}(j)\right]^{w_{i}} \left\{\int\prod_{i=1}^{N_{A}}\left[D_{k}(\mathrm{x})\right]^{w_{i}}dx\right\} ^{j}}. \tag{29}\]  
GCI fusion of \(\overline{D}(x)\) expressed in Equation (28) describes the target state density \(\overline{D}(x)\) at time \(k\) is the weighted geometric mean of target state densities \(D(x)\), and the fusion cardinality \(\overline{N}(x,n)\) expressed in Equation (29) is an interconnected mean not only with the target state density but also with the target cardinality density. For practical implementation, GCI fusions of \(\overline{D}(x)\) and \(\overline{N}(x,n)\) can be considered as finite dimensional parameters, such as the target number of \(n_{\mathrm{max}}=N_{k}\) in \(\overline{N}(x,n)\). Two finite parameterized methods are most commonly adopted to process the infinite dimensional problem of target state density, SMC and GM. For our computation-limited and process-limited sensor network, the GM approach is adopted, which promises to be more applicable. Generally, the order of magnitude of the involved number of Gaussian components is lower than the number of particles of the SMC, which is required for applicable tracking performance.