*2.2. Motivation and Objective*

Although the CL and DT problems have been extensively studied, their combination still draws limited attention, especially when considering practical multi-robot operation conditions such as nonlinear models or limited sensing and communication capabilities. One answer to the above challenge was provided in [9] by implementing the EKF scheme and asynchronized measurement update. However, this only covered the CL task, and the uncooperative target was not considered. On the other hand, it is also well known that the computation of Jacobian matrices is required by EKF-based algorithms. This may

cause difficulties during implementation. Moreover, the estimation performance may deteriorate if the assumption of local linearity is not valid (e.g., bearing sensors). An alternative approach to extending the algorithm while avoiding the aforementioned potential drawbacks is to use the UT.

Motivated by the above observations, in this paper, a UT-based CLAT scheme (UT-CLAT) is proposed that can realize self-localization and target tracking simultaneously in practical multi-robot operation scenarios. The correlations are properly addressed by implementing split covariance methods, similar to the method in [9], and the covariance intersection method. The UT approach was adopted to approximate the statistics of random variables in nonlinear models. In the end, the effectiveness of the proposed UT-CLAT algorithm is illustrated using not only simulations with synthetic data but also experiments with a networked quadrotor system and off-the-shelf sensors (cameras and UWB transmitters).

#### **3. UT-Based CLAT**

In this section, the proposed UT-CLAT is described. The states of local robots and targets are estimated using a recursive UT-based Kalman filter, with the aforementioned three types of measurements updated in an asynchronous fashion. For each robot *i*, the local states, covariance, and the correlation between it and other robots *j* ∈ V are tracked. Specifically, the correlation term is approximately tracked in a distributed fashion, similar to [9]. As a matter of fact, the target may be detected by different robots at different times. It is difficult to track the robot–target correlation in a local robot when there are inter-robot correlations. To realize consistent state estimation under unknown robot–target correlations, a conservative CI method is introduced to safely remove the robot–target correlation terms and the correlation between target estimates from different robots. The above algorithm consists of state propagation (Section 3.1) and three types of measurement update processes (Section 3.2). In particular, the communication link is supposed to be established only during the cooperative relative measurement update process and the data from different robots are fused.

Suppose that at time *k*, each robot *i* has a posterior estimated state and its error covariance at a previous time instance, denoted as **x**ˆ*i*,*k*−<sup>1</sup> and **P***i*,*k*−1, respectively. If a relative measurement between robots *i* and *j* is taken before time instance *k*, then the correlated term **P***ij*,*k*−<sup>1</sup> is arbitrarily decomposed as

$$\mathbf{P}\_{ij,k-1} = \sigma\_{ij,k-1} \sigma\_{ji,k-1}^\parallel \tag{6}$$

and respectively stored in robots *i* and *j*. Robot *i* also holds an estimation of the target *t* locally, denoted as **x**ˆ*ti*,*k*−<sup>1</sup> and **P***ti*,*k*−1.
