Corresponding Cramer-Rao Lower Bound Research Articles

Cooperative Received Signal Strength-Based Sensor Localization With Unknown Transmit Powers

Cooperative localization (also known as sensor network localization) using received signal strength (RSS) measurements when the source transmit powers are different and unknown is investigated. Previous studies were based on the assumption that the transmit powers of source nodes are the same and perfectly known which is not practical. In this paper, the source transmit powers are considered as nuisance parameters and estimated along with the source locations. The corresponding Cramer-Rao lower bound (CRLB) of the problem is derived. To find the maximum likelihood (ML) estimator, it is necessary to solve a nonlinear and nonconvex optimization problem, which is computationally complex. To avoid the difficulty in solving the ML estimator, we derive a novel semidefinite programming (SDP) relaxation technique by converting the ML minimization problem into a convex problem which can be solved efficiently. The algorithm requires only an estimate of the path loss exponent (PLE). We initially assume that perfect knowledge of the PLE is available, but we then examine the effect of imperfect knowledge of the PLE on the proposed SDP algorithm. The complexity analyses of the proposed algorithms are also studied in detail. Computer simulations showing the remarkable performance of the proposed SDP algorithm are presented.

The Large Sample Performance of a Maximum Likelihood Method for OFDM Carrier Frequency Offset Estimation

This paper is concerned with the performance analysis of a blind method for carrier frequency offset (CFO) estimation in OFDM systems. The method generates a maximum likelihood CFO estimate when message-carrying symbols and channel are assumed nonrandom. It has been observed in simulation that, when a large number of OFDM blocks are in use under noisy scenarios, the performance of the method does not achieve the corresponding Cramer-Rao lower bound (CRB) and is lower bounded by another (larger) CRB when symbols are assumed random. This phenomenon is caused by the inconsistency of nonrandom symbol estimates and is further verified by using first-order perturbation analysis and comparison with the two CRBs.

Target Localization and Tracking in Noncoherent Multiple-Input Multiple-Output Radar Systems

For a noncoherent multiple-input multiple-output (MIMO) radar system, the maximum likelihood estimator (MLE) of the target location and velocity, as well as the corresponding Cramer-Rao lower bound (CRLB) matrix, is derived. MIMO radar's potential in localization and tracking performance is demonstrated by adopting simple Gaussian pulse waveforms. Due to the short duration of the Gaussian pulses, a very high localization performance can be achieved, even when the matched filter ignores the Doppler effect by matching to zero Doppler shift. This leads to significantly reduced complexities for the matched filter and the MLE. Further, two interactive signal processing and tracking algorithms, based on the Kalman filter and the particle filter (PF), respectively, are proposed for noncoherent MIMO radar target tracking. For a system with a large number of transmit/receive elements and a high signal-to-noise ratio (SNR) value, the Kalman filter (KF) is a good choice; while for a system with a small number of elements and a low SNR value, the PF outperforms the KF significantly. In both methods, the tracker provides predictive information regarding the target location, so that the matched filter can match to the most probable target locations, reducing the complexity of the matched filter and improving the tracking performance. Since tracking is performed without detection, the presented approach can be deemed as a track-before-detect approach. It is demonstrated through simulations that the noncoherent MIMO radar provides significant tracking performance improvement over a monostatic phased array radar with high range and azimuth resolutions. Further, the effects of coherent integration of pulses are investigated for both the phased array radar and a hybrid MIMO radar, where only the pulses transmitted and received by colocated transceivers are coherently integrated and the other pulses are combined noncoherently. It is shown that the hybrid MIMO radar achieves significant tracking performance improvement when compared with the phased array radar, by using the extra Doppler information obtained through coherent pulse integration.

Received Signal Strength-Based Wireless Localization via Semidefinite Programming: Noncooperative and Cooperative Schemes

The received signal strength (RSS)-based approach to wireless localization offers the advantage of low cost and easy implementability. To circumvent the nonconvexity of the conventional maximum likelihood (ML) estimator, in this paper, we propose convex estimators specifically for the RSS-based localization problems. Both noncooperative and cooperative schemes are considered. We start with the noncooperative RSS-based localization problem and derive a nonconvex estimator that approximates the ML estimator but has no logarithm in the residual. Next, we apply the semidefinite relaxation technique to the derived nonconvex estimator and develop a convex estimator. To further improve the estimation performance, we append the ML estimator to the convex estimator with the result by the convex estimator as the initial point. We then extend these techniques to the cooperative localization problem. The corresponding Cramer-Rao lower bounds (CRLB) are derived as performance benchmarks. Our proposed convex estimators comply well with the RSS measurement model, and simulation results clearly demonstrate their superior performance for RSS-based wireless localization.

Semi-Definite Programming Algorithms for Sensor Network Node Localization With Uncertainties in Anchor Positions and/or Propagation Speed

Finding the positions of nodes in an ad hoc wireless sensor network (WSN) with the use of the incomplete and noisy distance measurements between nodes as well as anchor position information is currently an important and challenging research topic. However, most WSN localization studies have considered that the anchor positions and the signal propagation speed are perfectly known which is not a valid assumption in the underwater and underground scenarios. In this paper, semi-definite programming (SDP) algorithms are devised for node localization in the presence of these uncertainties. The corresponding Cramer-Rao lower bound (CRLB) is also produced. Computer simulations are included to contrast the performance of the proposed algorithms with the conventional SDP method and CRLB.

Multisensor target tracking performance with bias compensation

In this paper, multisensor-multitarget tracking performance with bias estimation and compensation is investigated when only moving targets of opportunity are available. First, we discuss the tracking performance improvement with bias estimation and compensation for synchronous biased sensors, and then a novel bias estimation method is proposed for asynchronous sensors with time-varying biases. The performance analysis and simulations show that asynchronous sensors have a slightly degraded performance compared with the "equivalent" synchronous ones. The bias estimates as well as the corresponding Cramer-Rao lower bound (CRLB) on the covariance of the bias estimates, i.e., the quantification of the available information on the sensor biases in any scenario are also given. Tracking performance evaluations with different sources of biases-offset biases, scale biases, and sensor location uncertainties, are also presented and we show that tracking performance is significantly improved with bias estimation and compensation compared with the target tracking using the original biased measurements. The performance is also close to the lower bound obtained in the absence of biases

Channel parameter estimation in mobile radio environments using the SAGE algorithm

This study investigates the application potential of the SAGE (space-alternating generalized expectation-maximization) algorithm to jointly estimate the relative delay, incidence azimuth, Doppler frequency, and complex amplitude of impinging waves in mobile radio environments. The performance, i.e., high-resolution ability, accuracy, and convergence rate of the scheme, is assessed in synthetic and real macro- and pico-cellular channels. The results indicate that the scheme overcomes the resolution limitation inherent to classical techniques like the Fourier or beam-forming methods. In particular, it is shown that waves which exhibit an arbitrarily small difference in azimuth can be easily separated as long as their delays or Doppler frequencies differ by a fraction of the intrinsic resolution of the measurement equipment. Two waves are claimed to be separated when the mean-squared estimation errors (MSEEs) of the estimates of their parameters are close to the corresponding Cramer-Rao lower bounds (CRLBs) derived in a scenario where only a single wave is impinging. The adverb easily means that the MSEEs rapidly approach the CLRBs, i.e., within less than 20 iteration cycles. Convergence of the log-likelihood sequence is achieved after approximately ten iteration cycles when the scheme is applied in real channels. In this use, the estimated dominant waves can be related to a scatterer/reflector in the propagation environment. The investigations demonstrate that the SAGE algorithm is a powerful high-resolution tool that can be successfully applied for parameter extraction from extensive channel measurement data, especially for the purpose of channel modeling.