Performance Analysis of Linear-Equality-Constrained Least-Squares Estimation

We analyze the performance of a linear-equality-constrained least-squares (CLS) algorithm and its relaxed version, called rCLS, that is obtained via the method of weighting. The rCLS algorithm solves an unconstrained least-squares problem that is augmented by incorporating a weighted form of the linear constraints. As a result, unlike the CLS algorithm, the rCLS algorithm is amenable to our approach to performance analysis presented here, which is akin to the energy-conservation-based methodology. Therefore, we initially inspect the convergence properties and evaluate the precision of estimation as well as satisfaction of the constraints for the rCLS algorithm in both mean and mean-square senses. Afterwards, we examine the performance of the CLS algorithm by evaluating the limiting performance of the rCLS algorithm as the relaxation parameter (weight) approaches infinity. Numerical examples verify the accuracy of the theoretical findings

Bandpass sampling of almost-cyclostationary signals

The problem of bandpass sampling a continuous-time almost-cyclostationary signal is addressed. Sufficient conditions are derived such that the cyclic spectra of the complex envelope of the continuous-time signal can be reconstructed by samples obtained by bandpass sampling the continuous-time bandpass real signal

A Hybrid Approach to Optimal TOA-Sensor Placement With Fixed Shared Sensors for Simultaneous Multi-Target Localization

This paper focuses on optimal time-of-arrival (TOA) sensor placement for multiple target localization simultaneously. In previous work, different solutions only using non-shared sensors to localize multiple targets have been developed. Those methods localize different targets one-by-one or use a large number of mobile sensors with many limitations, such as low effectiveness and high network complexity. In this paper, firstly, a novel optimization model for multi-target localization incorporating shared sensors is formulated. Secondly, the systematic theoretical results of the optimal sensor placement are derived and concluded using the A-optimality criterion, i.e., minimizing the trace of the inverse Fisher information matrix (FIM), based on rigorous geometrical derivations. The reachable optimal trace of Cramér-Rao lower bound (CRLB) is also derived. It can provide optimal conditions for many cases and even closed form solutions for some special cases. Thirdly, a novel numerical optimization algorithm to quickly find and calculate the (sub-)optimal placement and achievable lower bound is explored, when the model becomes complicated with more practical constraints. Then, a hybrid method for solving the most general situation, integrating both the analytical and numerical solutions, is proposed. Finally, the correctness and effectiveness of the proposed theoretical and mathematical methods are demonstrated by several simulation examples

Optimal Beacon Placement for Self-Localization Using Three Beacon Bearings

Autonomous vehicles need to localize themselves within the environment in order to effectively perform most tasks. In situations where a Global Navigation Satellite System such as the Global Positioning System cannot be used for localization, other methods are required. One self-localization method is to use signals transmitted by beacons at known locations to determine the relative distance and bearing of the vehicle from the beacons. Estimation performance is influenced by the beacon–vehicle geometry and the investigation into the optimal placement of beacons is of interest to maximize the estimation performance. In this article, a new solution to the optimal beacon placement problem for self-localization of a vehicle on a two-dimensional plane using angle-of-arrival measurements is proposed. The inclusion of heading angle in the estimation problem differentiates this work from angle-of-arrival target localization, making the optimization problem more difficult to solve. First, an expression of the determinant of the Fisher information matrix for an arbitrary number of beacons is provided. Then, a procedure for analytically determining the optimal angular separations for the case of three beacons is presented. The use of three beacons is motivated by practical considerations. Numerical simulations are used to demonstrate the optimality of the proposed method

An Image Focusing Method for Sparsity-Driven Radar Imaging of Rotating Targets

This paper presents a new image focusing algorithm for sparsity-driven radar imaging of rotating targets. In the general formulation of off-grid scatterers, the sparse reconstruction algorithms may result in blurred and low-contrast images due to dictionary mismatch. Motivated by the natural clustering of atoms in the sparsity-based reconstructed images, the proposed algorithm first partitions the atoms into separate clusters, and then the true off-grid scatterers associated with each cluster are estimated. Being a post-processing technique, the proposed algorithm is computationally simple, while at the same time being capable of producing a sharp and correct-contrast image, and attaining a scatterer parameter estimation performance close to the Cramér–Rao lower bound. Numerical simulations are presented to corroborate the effectiveness of the proposed algorithm