## 7 RF-Based Localisation for Aerial and Ground Robots
Executing experiment in 2D, decimeter accuracy is delivered. A new particle-filter-based algorithm is introduced in [83] to improve the estimation with fewer particles. To this goal, the traditional sequential prediction and update steps are carried out in one stage through the maximum likelihood estimator. Experimental results with WiFi RSS indoors show improvement, reaching about 0.5 m\({}^{2}\) means squared error. For target localisation, a fingerprinting method is explored in [82]. The radio map is continuously updated while collecting RSS and performing the target localisation simultaneously. The database, the anchor positions, and propagation model parameters are stored and updated. Instead of using the log-distance model, a new model based on collected data is fitted. The model consists of three terms: path loss, measurement noise, and multi-path effect. Four simple functions are proposed and tested for the path loss model to select the best one: linear, nonlinear, and two log-distance models with different parameters. The result indicates that the log-distance model is not as accurate as the first two. The best model is of the form \(c_{1}d^{\lambda_{1}d}+c_{2}e^{\lambda_{2}d}\). Based on the model extracted, the fingerprints are modelled as the probability density function. In the sequel, a particle filter is employed for target tracking in online mode. Two complex ML algorithms are reported in [91; 92], where simulations are performed for evaluation. The work [91] uses RSS from multiple BS along with trajectory information (velocity) of the drone to localize an UAV with unknown transmission power. A Joint ML is formulated and solved based on the trajectory information and multiple BS. Fixing the positions in the ML function, first, transmission powers are estimated, which are assumed to be constant. The result is then used to optimise the ML functions based on positions, employing an exhaustive grid search. Two low-complexity alternative algorithms are also suggested, where the former ML problem is broken into several parts, which are solved separately. Then, the final result is calculated as the weighted combination of the separate estimations. Notably, constant velocity is assumed at each time step. A different scenario is considered in [92], where multi-UAVs are supposed to localize a fixed passive RF emitter based on the RSS. A group of UAVs is flying and tracking a predefined trajectory, with one at the centre. To optimise the aggregate likelihood function in a distributed manner, second-order Taylor expansion is exploited to introduce a surrogate function, based on which the Min-Max algorithm is applied. In a two-step procedure that is iterated over, a local update is performed on each UAV based on the centre UAV estimation. In the fusion step executed on the centre UAV, all UAVs share their local estimation with the centre UAV for fusion to generate a new estimation and distribute it among all other UAVs. To reduce the communication overload, an alternative approach is proposed requiring one round of communication, i.e., edge UAVs transmit their information to the centre UAV. In the centre UAV, all estimations are linearly fused with weights approximated based on the Fisher information matrix. On simulations, the authors show that this algorithm improves the result in terms of the root of mean square error (RMSE) in cost of complexity. Another MLE-based method is suggested in [93] based on UWB time-of-flight, in which non-convexity is handled by linearisation. Moreover, the geometry configuration of the anchors and how it impacts the localisation is investigated in terms of CRLB, while both simulations and experiments are conducted. Simultaneous Localisation and Mapping (SLAM) using multiple robots are explored in [94] leveraging Wi-Fi fingerprinting and odometry in 2D. A graph is constructed with nodes as robots pose and constraints including odometry, individual RSS fingerprints, and similarity of RSS fingerprints between robots.