Multilateration, positioning a receiver using pseudodistances to known senders, is a problem with 5G and GNSS positioning applications. In contrast, trilateration uses direct distances and was reformulated as an eigenvalue problem in a recent work, resulting in a very competitive positioning method. This paper extends that reformulation to a more general class of problems subsuming multilateration and trilateration. The resulting multilateration method is fast, accurate, and numerically stable, outsourcing complex implementation details to existing mature eigensolvers. By allowing for reweightings of the terms, an iteratively reweighted least squares approach is feasible and can be used to improve the proposed algorithm further. Additionally, we demonstrate how partially known receiver positions are handled with experiments using real-world 5G data. The proposed method is evaluated against the state of the art and shown to be among the most accurate while remaining fast.

We present a synchronized multisensory dataset for accurate and robust indoor localization: the Lund University Vision, Radio, and Audio (LuViRA) Dataset. The dataset includes color images, corresponding depth maps, inertial measurement unit (IMU) readings, channel response between a 5G massive multiple-input and multiple-output (MIMO) testbed and user equipment, audio recorded by 12 microphones, and accurate six degrees of freedom (6DOF) pose ground truth of 0.5 mm. We synchronize these sensors to ensure that all data is recorded simultaneously. A camera, speaker, and transmit antenna are placed on top of a slowly moving service robot, and 89 trajectories are recorded. Each trajectory includes 20 to 50 seconds of recorded sensor data and ground truth labels. Data from different sensors can be used separately or jointly to perform localization tasks, and data from the motion capture (mocap) system is used to verify the results obtained by the localization algorithms. The main aim of this dataset is to enable research on sensor fusion with the most commonly used sensors for localization tasks. Moreover, the full dataset or some parts of it can also be used for other research areas such as channel estimation, image classification, etc. Our dataset is available at: https://github.com/ilaydayaman/LuViRA_Dataset

In this paper we study the problem of estimating receiver and sender positions using time-difference-of-arrival measurements. For this, we use a stratified, two-tiered approach. In the first step the problem is converted to a low-rank matrix estimation problem. We present new, efficient solvers for the minimal problems of this low-rank problem. These solvers are used in a hypothesis and test manner to efficiently remove outliers and find an initial estimate which is used for the subsequent step. Once a promising solution is obtained for a sufficiently large subset of the receivers and senders, the solution can be extended to the remaining receivers and senders. These steps are then combined with robust local optimization using the initial inlier set and the initial estimate as a starting point. The proposed system is verified on both real and synthetic data.

To improve the accuracy of indoor positioning systems it can be useful to combine different types of sensor data. This paper describes deep learning methods both for estimating absolute positions and for performing pedestrian dead reckoning, and then how to combine the resulting estimates using weighted least squares optimization. The positioning model is based on a custom neural network which uses measurements of received signal strength indication from one instant of time as input. The model for estimating relative positions is on the other hand based on inertial sensors, the accelerometer, magnetometer and gyroscope. The position estimates are then combined using a least squares approach with weights based on the standard deviations of errors in predictions from the used models.

Estimating receiver and sender positions is often solved using a stratified, two-tiered approach. In the first step the problem is converted to a low-rank matrix estimation problem. The second step can be seen as an affine upgrade. This affine upgrade is the focus of this paper. In the paper new efficient algorithms for solving for the upgrade parameters using minimal data are presented. It is also shown how to combine such solvers as initial estimates, either directly or after a hypothesis and test step, in optimization of likelihood. The system is verified on both real and synthetic data.

The problem of estimating receiver or sender node positions from measured receiver-sender distances is a key issue in different applications such as microphone array calibration, radio antenna array calibration, mapping and positioning using UWB or using round-trip-time measurements between mobile phones and WiFi-units. In this paper we address the problem of optimally estimating a receiver position given a number of distance measurements to known sender positions, so called trilateration. We show that this problem can be rephrased as an eigenvalue problem. We also address different error models and the multilateration setting where an additional offset is also unknown, and show that these problems can be modeled using the same framework.

In this paper we address the problem of registering and merging two maps in two dimensions, given covariance estimates of the two maps. We show that if two maps are given in the same coordinate system, then the problem of merging them in a statistically optimal way can be formulated as a linear least squares problem, but if they are given in different coordinate systems as well the problem becomes highly non-linear and nonconvex. We show how we can relax the problem slightly in order to optimize over the registration (i.e. putting the two maps in the same coordinate system) and at the same time optimize over the merged map. The approach is based on finding all stationary points of the optimization problem and evaluating these to choose the global optimum. We show on synthetic data that in many cases the proposed approach gives better results than naively registering and merging the maps. We also show results on real data, where we merge maps given by time-of-arrival measurements, and in these cases simpler linear methods perform just a good as the proposed method.