Cooperative Indoor Localization under Uncertainties

Localization of wireless nodes in GPS-denied spaces is being applied in a number of scenarios such as sport teams requiring positioning data for post-match analysis, robot teams carrying out a common task in an indoor environment, among other similar applications. These applications would usually involve a sizable number of participating nodes making scalability a fundamental requirement of the localization setup under the constraints of energy efficiency and position update time. Adopting techniques that are resilient to uncertainties in the deployment region of the nodes is important for the overall accuracy of the setup. In this work, we focus on a range-based cooperative localization technique where nodes are distinguished as either fixed (anchors) or mobile (tags), and are subject to uncertainties in the environment. Cooperation here implies that the positions of all nodes are computed simultaneously using a joint pairwise distance information while uncertainty refers to any known condition that degrades localization accuracy. These uncertainties are present in the form of a) missing distance measurements; b) obstacles in the deployment region; and c) stochasticity in measurements for cases where Radio Frequency (RF) signal strength is employed for range estimation. The missing distances may be due to either tags being passive or tags acting as transmitters. For this, we propose a specialized form of Multidimensional Scaling (MDS) that tackles the problem by neglecting tag-to-tag interactions while inferring tag positions directly from those of anchors. Furthermore, obstacles in the deployment region force signals to travel in nonline-of-sight (NLOS) paths often leading to a lengthening of range estimates. For this, we develop a novel approach that reuses an intrinsic property of anchored MDS to cooperatively estimate NLOS biases in the range estimates. The problem is formulated as a constrained-optimization problem whose solution provides positions with improved accuracy and can be solved by Sequential Quadratic Programming (SQP). The approach works entirely at the application layer and is neither concerned with the probability distribution of LOS/NLOS nor any other a priori knowledge about the environment. Experimental results show that position errors can be reduced by up to 28% for a set up to 4 fixed and 3 mobile nodes. In the final discourse relating to uncertainties, we examine lightweight filtering techniques for smoothening Received Signal Strength (RSS) measurements to render them more suitable for range estimation. We formulate the expected values of range (in terms of the Cramér-Rao bound) when estimated directly from raw measurements using an unbiased estimator and compare with range estimates from the filtered measurements. Results show that applying a suitable filtering technique can significantly improve the accuracy of range estimation from raw RSSI measurements. In the last part of this work, we present an open discussion on design considerations for scalable indoor localization deployments.