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This paper studies the localization problem using noisy range-difference measurements, or equivalently time difference of arrival (TDOA) measurements. There is a reference sensor, and for each other sensor, the TDOA measurement is obtained with respect to the reference one. By minimizing the sum of squared errors, a nonconvex constrained least squares (CLS) problem is formulated. In this work, we focus on devising an algorithm to seek the global minimizer of the CLS problem, hoping that the numerical solution meets some precision requirement in terms of relative error. Based on the Lagrange multiplier method, we first branch the feasible Lagrange multiplier set into several subsets and develop a workflow in terms of if-then-else control structure to seek the global minimizer by searching for the optimal Lagrange multiplier. The execution order is carefully organized so that it is in line with the general principle of putting the flow that one normally understands to be executed first. We then dive into detailed searching methods in different cases and conduct computational error analysis, giving the error bound on the Lagrange multiplier, when we search for it, to meet the precision requirement on an approximate solution. Based on the above achievements, a programmable global minimizer seeking algorithm is proposed for the CLS problem. Simulations and experimental tests on a public dataset demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

We consider collision channel without feedback in which collided packets are considered unrecoverable. For each user, the transmission of packets foHows a specific periodical pattern, called the protocol sequence. Due to the lack of feedback, the beginning of the protocol sequences cannot be synchronized and nonzero relative offsets are inevitable. It results in variation of throughput. In this paper, we investigate optimal protocol sequence sets, in the sense that the throughput variance is zero. Such protocol sequences are said to be shift-invariant (SI). The characterizing properties of SI protocol sequences are presented. We also prove that SI sequences are identifiable, meaning that the receiver is able to determine the sender of each successfully received packet without any packet header. A general construction of SI sequences that meets the lower bound on sequence length is given. Besides, we study the least periods of SI sequences, and show that the least periods must be distinct in some cases. The throughput performance is compared numerically with other protocol sequences. Index Terms--Collision channel without feedback, protocol sequences.

In this article, we propose a learning approach to analyze dynamic systems with an asymmetric information structure. Instead of adopting a game-theoretic setting, we investigate an online quadratic optimization problem driven by system noises with unknown statistics. Due to information asymmetry, it is infeasible to use the classic Kalman filter nor optimal control strategies for such systems. It is necessary and beneficial to develop an admissible approach that learns the probability statistics as time goes forward. Motivated by the online convex optimization (OCO) theory, we introduce the notion of regret, which is defined as the cumulative performance loss difference between the optimal offline-known statistics cost and the optimal online-unknown statistics cost. By utilizing dynamic programming and linear minimum mean square biased estimate (LMMSUE), we propose a new type of online state-feedback control policy and characterize the behavior of regret in a finite-time regime. The regret is shown to be sublinear and bounded by $O(\ln T)$. Moreover, we address an online optimization problem with output-feedback control policy and propose a heuristic online control policy. [ABSTRACT FROM AUTHOR]

A class of periodic unipolar binary sequences is investigated for their potential applications in defining new protocols for distributed multiple accessing. Based on linear congruence sequences, one can show that, for any finite subset of these sequences, with the total proportional rate not exceeding a specific threshold, there cannot be enough collisions to completely block any particular sequence, no matter how they are shifted with respect to one another. This property can be exploited in certain applications, such as wireless sensor and ad hoc networks. A further investigation into how to enhance the allowable rate sum is conducted. New protocol sequences with interesting and useful properties are accordingly designed. Index Terms--Collision channel without feedback, multiple access, protocol sequence, shift invariant, user unsuppressibility.

With recent developments in ad hoc networks and sensor networks, random-access protocol without feedback is a technique that deserves a closer look. This paper is based on Massey's model on random-access channel without feedback. A central concept of this model is the idea of protocol sequences. For these sequences, it is desirable that their cross correlation should be as low as possible and that the length of their period should not be too long, even if there is a large number of active users. Another useful feature is to be able to support multirate communication. Based on these considerations, a new family of protocol sequences is proposed in this paper. These new protocol sequences are built on the concept of prime sequences. It is shown that these sequences possess properties that make them suitable candidates for designing random access protocols for certain ad hoc or sensor networks. Index Terms--Hamming cross-correlation function, linear congruence sequence, prime sequence, protocol sequence, random-access channel without feedback, wobbling sequence.

This paper proposes and analyzes a new distributed power-control algorithm based on the theory of stochastic approximation. The power-control problem is first converted into a stochastic approximation problem in which the zero point of a specific function is determined. A distributed power-control algorithm is then derived and its convergence properties are analyzed using standard techniques. In the distributed algorithm, each user iteratively updates its power level by using estimates of the inverse of the signal-to-interference ratio (SIR) of its channel. No knowledge of the channel gains or state information of other users is required. Moreover, the algorithm is robust in the sense that it can handle errors in the bit-error rate estimates, and hence, can be used in practical scenarios. Convergence of the algorithm is analyzed in the almost-sure sense. Index Terms--Decentralized control, power control, stochastic approximation, time-varying systems.

This paper deals with a class of power control problems where the system link gains are assumed to be time varying and the signal-to-interference ratio (SIR) estimates are allowed to be corrupted with bounded noises. A simple control algorithm is devised by applying a distributed, fixed step approach. It is a feedback algorithm that requires only local information. By modifying the distributed, fixed step power control algorithm proposed by Sung and Wong, we obtain here a more robust version that can handle time varying link gains and measurement noises. The convergence property of the new algorithm is established and simulation studies were carried out to show that it is effective. Index Terms--Cellular mobile system, distributed algorithm, power control, time-varying channels.

We consider the convergence issues of distributed power-control algorithms for mobile cellular systems. A convergence theorem for power-control algorithms of canonical type is proved. Our result generalizes Yates' framework and provides a new outlook on the problem. The general applicability of the theorem is demonstrated by showing that many well-known distributed algorithms are canonical. Furthermore, by devising some new discrete algorithms, we exemplifY how the theorem can be used to aid new design. Index Terms--Canonical algorithm, distributed algorithms, framework, power control.

This note is focused on control systems in which the observer is not co-located with the controller and the communication channel between them is of limited bandwidth. Due to the low data rate requirement, the control law must be of simple form. As a result, a tristate distributed controller is examined. The control algorithm is proven to be convergent if the system structure satisfies certain technical conditions. The convergence is robust in the sense that the system parameters and even the structure of the underlying system dynamics need not to be completely known. Index Terms--Communication constaints, distributed controllers, performance-target tracking, robust convergence.