[00580] Mathematical Challenges in Current and Future Location Estimation Systems
Session Time & Room : 3E (Aug.23, 17:40-19:20) @E502
Type : Proposal of Minisymposium
Abstract : Location-estimation systems, and in particular Global Navigation Satellite Systems (e.g. GPS), are mature and ubiquitous. Many aspects of modern life are today completely dependent on these systems. However, deriving additional benefits (higher accuracy, resilience to jamming and spoofing) from existing systems and building future systems to fill application gaps require addressing challenging mathematical and computational problems. These challenges revolve around difficult nonconvex optimization problems, some with integer parameters, and some in high dimensions. Effective solutions require a combination of state-of-the-art mathematical tools with application-specific insights. The minisymposium will present both challenges and recent progress towards their solution.
[01325] Local Strong Convexity of Source Localization and Error Bound for Target Tracking under Time-of-Arrival Measurements
Format : Talk at Waseda University
Author(s) :
Anthony Man-Cho So (The Chinese University of Hong Kong)
Yuen-Man Pun (The Australian National University)
Abstract : We consider a time-varying optimization approach to the problem of tracking a moving target using noisy time-of-arrival {TOA} measurements. To analyze the tracking performance of online gradient descent {OGD}, we first revisit the classic least-squares formulation of the {static} TOA-based source localization problem and elucidate its estimation and geometric properties. Then, we show that the loss function in the formulation, albeit non-convex in general, is locally strongly convex at its global minima. To the best of our knowledge, these results are new and can be of independent interest. By combining them with existing techniques from online strongly convex optimization, we then establish the first non-trivial bound on the cumulative target tracking error of OGD.
[01604] Machine learning techniques for resolving GNSS integer ambiguities
Format : Talk at Waseda University
Author(s) :
Xiao-Wen Chang (McGill University)
Qincheng Lu (McGill University)
Abstract : A key computational component in high precision GNSS positioning is to resolve carrier phase ambiguities as integers. The optimal method is to solve an integer least squares problem. Since the integer least squares problem is NP-hard, efficiency of traditional algorithms becomes problematic when the dimension of the integer ambiguity vector becomes large. To meet the challenge, we propose some machine learning based algorithms. Numerical results will demonstrate their effectiveness and efficiency.
[01656] Fast and almost unbiased position estimation for location service
Format : Talk at Waseda University
Author(s) :
Peiliang Xu (Kyoto University)
Abstract : We propose a bias-corrected weighted LS method for precise location service, which consists of two basic elements: one to automatically correct the bias due to model nonlinearity and the induced biases in squared ranges/pseudoranges and the other to sequentially estimate unknown location parameters by treating equality constraints as a condition adjustment. The method is applied to ranges, squared ranges and the differences of squared rangesand further to pseudoranges, squared pseudoranges and the differences of pseudoranges.
[01296] Robust Location Estimation in Wildlife Tracking Systems
Format : Talk at Waseda University
Author(s) :
Sivan Toledo (Tel Aviv University)
Eitam Arnon (Tel Aviv University)
Shlomo Cain (Tel Aviv University)
Assaf Uzan (Tel Aviv University)
Ran Nathan (Hebrew University of Jerusalem)
Orr Spiegel (Tel Aviv University)
Abstract : The talk will describe new location-estimation algorithms for time-of-arrival transmitter localization systems. The new algorithms use the consensus principle and they detect and discard outlier time-of-arrival observations, which can be caused by non-line-of-sight propagation, radio interference, clock glitches, or an overestimation of the signal-to-noise ratio. They also detect cases in which two locations are equally consistent with the measurements and can usually select the correct one based on unambiguous estimates shortly before or after.
