Raj Thilak Rajan

Joint Clock Synchronization and Ranging: Asymmetrical Time-Stamping and Passive Listening

A fully asynchronous network with one sensor and M anchors (nodes with known locations) is considered in this letter. We propose a novel asymmetrical time-stamping and passive listening (ATPL) protocol for joint clock synchronization and ranging. The ATPL protocol exploits broadcast to not only reduce the number of active transmissions between the nodes, but also to obtain more information. This is used in a simple estimator based on least-squares (LS) to jointly estimate all the unknown clock-skews, clock-offsets, and pairwise distances of the sensor to each anchor. The Cramér-Rao lower bound (CRLB) is derived for the considered problem. The proposed estimator is shown to be asymptotically efficient, meets the CRLB, and also performs better than the available clock synchronization algorithms.

Joint ranging and clock synchronization for a wireless network

Synchronization and localization are two key aspects for the coherent functioning of a wireless network. Recently, various estimators have been proposed for pairwise synchronization between two nodes based on time stamp exchanges via two way communication. In this paper, we propose a closed form centralized Global Least Squares (GLS) estimator, which exploits the two way communication information between all the nodes in a wireless network. The fusion center based GLS uses a single clock reference and estimates all the unknown clock offsets, skews and pairwise distances in the network. The GLS estimate for clock offsets and skews is shown to outperform prevalent estimators. Furthermore, a new Cramer Rao Lower Bound (CRLB) is derived for the entire network and the proposed GLS solution is shown to approach the theoretical limits.

Orbiting Low Frequency Array for radio astronomy

Recently new and interesting science drivers have emerged for very low frequency radio astronomy from 0.3 MHz to 30 MHz. However Earth bound radio observations at these wavelengths are severely hampered by ionospheric distortions, man made interference, solar flares and even complete reflection below 10 MHz. OLFAR is Orbiting Low Frequency ARray, a project whose aim is to develop a detailed system concept for space based very low frequency large aperture radio interferometric array observing at these very long wavelengths. The OLFAR cluster could either orbit the moon, whilst sampling during the Earth-radio eclipse phase, or orbit the Earth-moon L2 point, sampling almost continuously or Earth-trailing and leading orbit. The aim of this paper is to present the technical requirements for OLFAR and first order estimates of data rates for space based radio astronomy based on the proposed scalable distributed correlator model. The OLFAR cluster will comprise of autonomous flight units, each of which is individually capable of inter satellite communication and down-link. The down-link data rate is heavily dependent on distance of the cluster from Earth and thus the deployment location of OLFAR, which are discussed.

Joint Ranging and Synchronization for an Anchorless Network of Mobile Nodes

Synchronization and localization are critical challenges for the coherent functioning of a wireless network, which are conventionally solved independently. Recently, various estimators have been proposed for pairwise synchronization between immobile nodes, based on time stamp exchanges via two-way communication. In this paper, we consider a network of mobile nodes for which a novel joint time-range model is presented, treating both unsynchronized clocks and the pairwise distances as a polynomial functions of true time. For a pair of nodes, a least squares solution is proposed for estimating the pairwise range parameters between the nodes, in addition to estimating the clock offsets and clock skews. Extending these pairwise solutions to network-wide ranging and clock synchronization, we present a central data fusion based global least squares algorithm. A unique solution is nonexistent without a constraint on the cost function e.g., a clock reference node. Ergo, a constrained framework is proposed and a new Constrained Cramér-Rao Bound (CCRB) is derived for the joint time-range model. In addition, to alleviate the need for a single clock reference, various clock constraints are presented and their benefits are investigated using the proposed solutions. Simulations are conducted and the algorithms are shown to approach the theoretical limits.

Space-based aperture array for ultra-long wavelength radio astronomy

The past decade has seen the advent of various radio astronomy arrays, particularly for low-frequency observations below 100 MHz. These developments have been primarily driven by interesting and fundamental scientific questions, such as studying the dark ages and epoch of re-ionization, by detecting the highly red-shifted 21 cm line emission. However, Earth-based radio astronomy observations at frequencies below 30 MHz are severely restricted due to man-made interference, ionospheric distortion and almost complete non-transparency of the ionosphere below 10 MHz. Therefore, this narrow spectral band remains possibly the last unexplored frequency range in radio astronomy. A straightforward solution to study the universe at these frequencies is to deploy a space-based antenna array far away from Earths’ ionosphere. In the past, such space-based radio astronomy studies were principally limited by technology and computing resources, however current processing and communication trends indicate otherwise. Furthermore, successful space-based missions which mapped the sky in this frequency regime, such as the lunar orbiter RAE-2, were restricted by very poor spatial resolution. Recently concluded studies, such as DARIS (Disturbuted Aperture Array for Radio Astronomy In Space) have shown the ready feasibility of a 9 satellite constellation using off the shelf components. The aim of this article is to discuss the current trends and technologies towards the feasibility of a space-based aperture array for astronomical observations in the Ultra-Long Wavelength (ULW) regime of greater than 10 m i.e., below 30 MHz. We briefly present the achievable science cases, and discuss the system design for selected scenarios such as extra-galactic surveys. An extensive discussion is presented on various sub-systems of the potential satellite array, such as radio astronomical antenna design, the on-board signal processing, communication architectures and joint space-time estimation of the satellite network. In light of a scalable array and to avert single point of failure, we propose both centralized and distributed solutions for the ULW space-based array. We highlight the benefits of various deployment locations and summarize the technological challenges for future space-based radio arrays.

Distributed correlators for interferometry in space

New and interesting science drivers have triggered a renewed interest in radio astronomy at ultra long wavelengths. However, at longer wavelengths (beyond 10 meters) ground-based radio astronomy is severely limited by earths ionosphere, in addition to man-made interferences and solar flares. An unequivocal solution to the problem is to establish a space based observatory for ultra low frequency (0.3MHz-30MHz) observations. In ground-based radio astronomy, interferometers comprising of widely spaced antennas are employed to enhance the sensitivity and angular resolution of the observations. The signals received from the antennas are pre-processed, phase corrected independently and then cross correlated with one another using a centralized correlator to estimate the coherence function. However, a space based array, in addition to several other obstacles, presents new challenges for both communication and processing. In this paper, we discuss various conventional correlator architectures, such as XF, FX and HFX. In addition, the importance of a distributed correlator is emphasized for a space based array, in particular Frequency distributed correlator. We compute transmission, reception and processing requirements for both centralized and distributed architecture. Finally, as a demonstration, we present 2 projects were these signal processing estimates are applied.

Joint motion estimation and clock synchronization for a wireless network of mobile nodes

Localization and synchronization are critical challenges for a wireless network, which are conventionally solved independently. Recently, various estimators have been proposed to jointly synchronize and localize a node in a static network based on two way communication. In this paper, we present a novel and generic model based on two way communication between nodes, which are in relative motion with respect to each other. Furthermore, for the entire network we propose a closed form Extended Global Least Squares (EGLS) solution to solve for all the unknown clock skews, clock offsets, initial pairwise distances and relative radial velocities using a single clock reference within the network. A new Cramer Rao Bound (CRB) is derived and the proposed fusion center based Extended Global Least Squares (EGLS) solution is shown to be asymptotically optimal.

Joint relative position and velocity estimation for an anchorless network of mobile nodes

Localization is a fundamental challenge for any network of nodes, in particular when the nodes are in motion and no reference nodes are available. Traditionally, the Multidimensional scaling (MDS) algorithm is employed at discrete time instances using pairwise distance measurements to find the relative node positions (with arbitrary rotation). In this paper, we present a novel framework to localize an anchorless network of mobile nodes given only time-varying inter-nodal distances. The time derivatives of the pairwise distances are used to jointly estimate the initial relative position and relative velocity of the nodes. Under linear velocity assumption for a small time duration, we show that the combination of the initial relative positions and relative velocity beget the relative motion of the nodes at discrete time instances. The proposed approach can be seen as an extension of the classical MDS, wherein Doppler measurements, if available, can be readily incorporated. We derive Cramer Rao bounds and perform simulations to evaluate the performance of the proposed estimators. Furthermore, the computational complexity and the benefits of the proposed algorithms are also presented.

Relative velocity estimation using multidimensional scaling

Localization is a fundamental challenge for any wireless network of nodes, in particular when the nodes are mobile. For an anchorless network of mobile nodes, we present a relative velocity estimation algorithm based on multidimensional scaling. We propose a generalized two-way ranging model, where the time-varying pairwise distances between the nodes are expressed as a Taylor series for a small observation period. The Taylor coefficients which are obtained by solving a Vandermonde system are in turn used to jointly estimate the initial relative position and the relative velocity of the nodes. Simulations are conducted to evaluate the performance of the proposed solutions and the results are presented.

Cramér rao lower bound for underwater range estimation with noisy sound speed profile

In this paper, the Cramér Rao bound (CRB) for range estimation between two underwater nodes is calculated under a Gaussian noise assumption on the measurements. The nodes can measure their depths, their mutual time of flight, and they have access to noisy sound speed samples at different depths. The effect of each measurement on the CRB will be analyzed, and it will be shown that for long distances, the effect of the sound speed measurement noise is dominant, and its impact depends on the positions of the nodes, actual sound speed profile, the number of sound speed samples, and the depths at which the sound speed samples are gathered.