# On Solving Ambiguity Resolution With Robust Chinese Remainder Theorem for Multiple Numbers

@article{Xiao2019OnSA, title={On Solving Ambiguity Resolution With Robust Chinese Remainder Theorem for Multiple Numbers}, author={Hanshen Xiao and Guoqiang Xiao}, journal={IEEE Transactions on Vehicular Technology}, year={2019}, volume={68}, pages={5179-5184} }

Chinese remainder theorem (CRT) is a powerful approach to solve ambiguity resolution related problems such as undersampling frequency estimation and phase unwrapping. Recently, the deterministic robust CRT for multiple numbers (RCRTMN) was proposed, which can reconstruct multiple integers with the unknown relationship of residue correspondence via generalized CRT and achieve robustness to bounded errors simultaneously. Naturally, RCRTMN sheds light on CRT-based estimation for multiple… Expand

#### 7 Citations

Wrapped ambiguity Gaussian mixed model with applications in sparse sampling based multiple parameter estimation

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This paper is the first rigorous analysis on the underlying statistical model of CRT-based multiple parameter estimation and shows that the statistical schemes achieve much stronger robustness compared to state-of-the-art deterministic schemes, especially in heavy-noise scenarios. Expand

Statistical Robust Chinese Remainder Theorem for Multiple Numbers: Wrapped Gaussian Mixture Model

- Mathematics, Computer Science
- ArXiv
- 2018

This paper presents the first rigorous analysis on the underlying statistical model of CRT-based multiple parameter estimation, where a generalized Gaussian mixture with background knowledge on samplings is proposed and achieves much stronger robustness compared to state-of-the-art deterministic schemes. Expand

Multi-Tone Frequency Estimation Based on the All-Phase Discrete Fourier Transform and Chinese Remainder Theorem

- Medicine, Computer Science
- Sensors
- 2020

This work deals with the intractable issue of mapping relationship between an individual tone and its corresponding remainders by decomposing the desired multi-tone estimator into several single- tone estimators and shows that the proposed method possesses high accuracy. Expand

On the Foundation of Sparse Sensing (Part II): Diophantine Sampling and Array Configuration

- Computer Science, Mathematics
- ArXiv
- 2021

It is proved that given arbitrarily large down-sampling rates, there exist sampling schemes where the number of samples needed is only proportional to the sum of DoF and the numberof snapshots required, which implies a linear sampling time. Expand

On the Foundation of Sparse Sensing (Part I): Necessary and Sufficient Sampling Theory and Robust Remaindering Problem

- Computer Science, Mathematics
- ArXiv
- 2021

It is proved that, for N -frequency estimation in either complex or real waveforms, once the least common multiple of the sampling rates selected is sufficiently large, one may approach an error tolerance bound independent of N, as well as advancing the understanding of the robust multiple remainder problem. Expand

UAV-Relaying Cooperation for Internet of Everything with CRT-Based NOMA

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- Wirel. Commun. Mob. Comput.
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The potential and effective applications of UAVs are studied by introducing the Chinese remainder theorem (CRT) and nonorthogonal multiple access (NOMA) technologies into UAV relay networks and a low complexity and efficient two-stage power allocation scheme is established for the perspective of users and UAV relays. Expand

Exact and Robust Reconstructions of Integer Vectors Based on Multidimensional Chinese Remainder Theorem (MD-CRT)

- Computer Science, Mathematics
- IEEE Transactions on Signal Processing
- 2020

This article derives the robust MD-CRT for integer vectors when the remaining integer matrices of all the moduli left divided by their greatest common left divisor are pairwise commutative, and coprime. Expand

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