**2. Problem Formulation**

#### *2.1. Models*

Consider *N* homogeneous cooperative robots, denoted as *i* ∈ V, performing collaborative self-localization and distributed tracking of a target of interest, denoted as *t*. The dynamics of the cooperative robots and the target are expressed respectively with the following nonlinear process models:

$$\mathbf{x}\_{i,k+1} = f\_{\mathbb{P}}(\mathbf{x}\_{i,k}, \mathbf{u}\_{i,k}),\tag{1}$$

$$\mathbf{x}\_{t,k+1} = f\_t(\mathbf{x}\_{t,k}, \mathbf{w}\_{t,k}),\tag{2}$$

where **<sup>x</sup>***i*,*<sup>k</sup>* <sup>∈</sup> <sup>R</sup>*nv* and **<sup>x</sup>***t*,*<sup>k</sup>* <sup>∈</sup> <sup>R</sup>*nt* respectively denote the state of robot *<sup>i</sup>* and target *<sup>t</sup>* at time *<sup>k</sup>*. **<sup>u</sup>***i*,*<sup>k</sup>* <sup>∈</sup> <sup>R</sup>*nu* is the control input of robot *i*, which is assumed to be subject to a Gaussian distribution **u***i*,*<sup>k</sup>* ∼ N (**u**¯*i*,*k*, **Q***i*). **<sup>u</sup>**¯*<sup>i</sup>* denotes the control command, and **<sup>Q</sup>***<sup>i</sup>* is the control input covariance. **<sup>w</sup>***t*,*<sup>k</sup>* <sup>∈</sup> <sup>R</sup>*nw* is the process noise of the target and is assumed to be drawn from a zero-mean Gaussian distribution **w***t*,*<sup>k</sup>* ∼ N (**0**, **Q***t*). It is assumed that all robots *<sup>i</sup>* ∈ V share the same nonlinear transformation *fv* : <sup>R</sup>*nv* <sup>×</sup> <sup>R</sup>*nu* , and the moving target nonlinear transformation *ft* : <sup>R</sup>*nt* <sup>×</sup> <sup>R</sup>*nw* is known to all robots.

In the cooperative localization and target tracking scenario, each robot *i* is able to measure three pieces of information: its absolute state and the relative pairwise measurements to neighboring robots and to the target. The measurements at time instance *k* are denoted respectively as **z***<sup>a</sup> <sup>i</sup>*,*<sup>k</sup>* <sup>∈</sup> <sup>R</sup>*nza* , **<sup>z</sup>***<sup>c</sup> ij*,*<sup>k</sup>* <sup>∈</sup> <sup>R</sup>*nzc* , *<sup>j</sup>* ∈ V\{*i*}, and **z***<sup>t</sup> it*,*<sup>k</sup>* <sup>∈</sup> <sup>R</sup>*nzt* . The corresponding measurement functions are listed below:

$$\mathbf{z}\_{i,k}^{a} = h^{a}(\mathbf{x}\_{i,k'} \mathbf{v}\_{i,k}^{a}),\tag{3}$$

$$\mathbf{z}\_{ij,k}^{c} = h^{c}(\mathbf{x}\_{i,k}, \mathbf{x}\_{j,k}, \mathbf{v}\_{i,k}^{c})\_{\prime} \tag{4}$$

$$\mathbf{z}\_{\rm it,k}^{t} = h^{t}(\mathbf{x}\_{i,k'}, \mathbf{x}\_{t,k'}, \mathbf{v}\_{i,k}^{t}), \tag{5}$$

where **v***<sup>a</sup> <sup>i</sup>*,*k*, **<sup>v</sup>***<sup>c</sup> <sup>i</sup>*,*<sup>k</sup>* and **<sup>v</sup>***<sup>t</sup> <sup>i</sup>*,*<sup>k</sup>* are the measurement noise of the above three measurement processes and assumed to be drawn from zero-mean Gaussian distributions, i.e., **v***<sup>a</sup> <sup>i</sup>*,*<sup>k</sup>* ∼ N (**0**, **<sup>R</sup>***<sup>a</sup> <sup>i</sup>* ), **<sup>v</sup>***<sup>c</sup> <sup>i</sup>*,*<sup>k</sup>* ∼ N (**0**, **<sup>R</sup>***<sup>c</sup> <sup>i</sup>*), and **<sup>v</sup>***<sup>t</sup> i*,*k* ∼ <sup>N</sup> (**0**, **<sup>R</sup>***<sup>t</sup> i* ).

Defining the CLAT as a graph *G*(*V*, *E*), the node set *V* = V∪{*t*}∪{0}, and the special node 0 denotes the absolute position origin. The edge set is denoted as *E* ⊆V× *V*. For a robot *i* ∈ V, an edge (*i*, 0) denotes a robot that can access its own absolute position. In this paper, it is assumed that a subset of the robots <sup>V</sup> can obtain the absolute measurement **<sup>z</sup>***<sup>a</sup> <sup>k</sup>*. An edge (*i*, *t*) indicates that a robot *i* is able to detect a target *t*. Since the sensing range of an uncooperative sensor is limited, the availability of an uncooperative target measurement depends on the relative positions of the robot and the target. An edge (*i*, *j*), *j* ∈ V\*i* denotes that a pairwise measurement between robots *i* and *j* is obtained. Similarly, a cooperative relative measurement is available when two robots are within the cooperative sensing range. Moreover, in this paper, it is assumed that whenever a relative measurement **z***<sup>c</sup> ij*,*<sup>k</sup>* is taken, a communication link is established simultaneously between robots *i* and *j* so that they can share information.
