Trilateration is the most adopted external reference-based localization technique for mobile robots, given the correspondence of external references. The nonlinear least-squares trilateration formulation provides an optimal position estimate from a general number (greater than or equal to the dimension of the environment) of reference points and corresponding distance measurements. This paper presents a novel closed-form solution to the nonlinear least-squares trilateration problem. The performance of the proposed algorithm in dealing with erroneous inputs of reference points and distance measurements has been analyzed through representative examples. The proposed trilateration algorithm has low computational complexity, high operational robustness, and reduced systematic error and uncertainty in position estimation. The effectiveness of the proposed algorithm has been further verified through an experimental test.

In the work package ‘Integrated Positioning’ of the Ubiquitous Cartography for Pedestrian Navigation project (UCPNAVI) alternative location methods using active Radio Frequency Identification (RFID) are investigated for positioning of pedestrians in areas where no GNSS position determination is possible due to obstruction of the satellite signals. In most common RFID applications, positioning is performed using cell-based positioning. RFID tags can be installed at active landmarks (i.e., known locations) in the surroundings and a user equipped with an RFID reader can be positioned using Cell of Origin (CoO). The positioning accuracy, however, depends on the size of the cell defined by the maximum range of the signal. Using long range RFID for positioning the cell size can be quite large, i.e., around 20 m. Therefore, the paper proposes two new methods for positioning, i.e., trilateration and location fingerprinting based on received signal strength indication (RSSI) if more than one RFID tag is visible. The trilateration approach is based on the deduction of ranges to the RFID tags from RSSI. An iterative approach to model the signal propagation will be introduced, i.e., the International Telecommunication Union (ITU) indoor location model that can be simplified to a logarithmic model, and a simple polynomial model is employed for the signal strength to range conversion. In a second attempt, location fingerprinting based on RSSI is investigated. In this case, RSSI is measured in a training phase at known locations inside the building and stored in a database. In the positioning phase these measurements are used together with the current measurements to obtain the current location of the user. For the estimation of the current location different approaches are employed and tested, i.e., a direction-based approach, a tag-based approach, a direction-tag-based approach and a heading-based approach. Using trilateration or fingerprinting positioning accuracies on the one to a few metres level can usually be achieved. The concept and the iterative approach of the different methods and test results are discussed in this paper.