Track initiation using sparse radar data for low earth orbit objects

International audienceThis paper deals with the track-initiation problem of low Earth orbit objects observed by a space surveillance radar system of wide cross-elevation, narrow elevation sized field of view. This sensor configuration involves short arcs from which no orbital state can be computed, making regular tracking techniques not applicable. However, a set of short arcs may contain enough information to deduce such a state, the main problem being to associate them due to the high number of objects and false alarms. Recently, a method to limit the association possibilities of short arcs at one revolution of interval has been proposed. In this paper, an approach to estimate the state (six orbital elements) starting from two short arcs at one revolution of interval is presented, in order to enable track initiation in a multi-target tracking algorithm such as Track- Oriented Multi-Hypothesis Tracking. The method is based on the geometrical determination of four orbital elements, enabling the association of a third short arc to find the two remaining orbital elements. The following hypotheses on the ground radar are made to stick to current specifications of space surveillance systems being designed: south-oriented, monostatic, wide cross-elevation (160 ), narrow elevation (2 ) field of view, provides range, azimuth and elevation measurements. To simulate detections from the ground radar, we use real data from the Space-Track Two-Lines Elements, a space objects catalog provided by USSTRATCOM, combined with an SGP4 propagator. The principle of the presented approach follows three steps: First, the semi-major axis, the inclination, the right ascension of ascending node and the mean anomaly are retrieved from geometrical considerations. Then, the covariance matrix of the obtained state-vector is computed using a Monte-Carlo method, added to a suited process noise covariance matrix. The resulting distribution is propagated at the times of new observations using an unscented transform to assess their correlation. Finally, an iterative Newton-Gauss least square algorithm is used on the set of three correlated short arcs to find the values of the eccentricity and argument of perigee. The resulting state may be used in regular tracking techniques. The principle and functioning of the method on realistic simulation are presented, as well as its performance and limiting cases

Track Initiation of Low-Earth-Orbit Objects using Statistical Modeling of Sparse Observations

International audienceIn this paper, we investigate a new track initiation technique enabling the use of a low-cost radar system for Low-Earth-Orbit surveillance. This technique is based on a first association of observations with little ambiguity followed by a fast Initial Orbit Determination. This study supports the feasibility of the system as this technique shows a coverage of 84,4% within 6 days, with a combinatorial complexity kept under control when assessed in a realistic multitarget tracking context

Integer and Floating-Point Constant Multipliers for FPGAs

International audienceReconfigurable circuits now have a capacity that allows them to be used as floating-point accelerators. They offer massive parallelism, but also the opportunity to design optimised floating-point hardware operators not available in microprocessors. Multiplication by a constant is an important example of such an operator. This article presents an architecture generator for the correctly rounded multiplication of a floating-point number by a constant. This constant can be a floating-point value, but also an arbitrary irrational number. The multiplication of the significands is an instance of the well-studied problem of constant integer multiplication, for which improvement to existing algorithms are also proposed and evaluated

Entry of Microparticles into Giant Lipid Vesicles by Optical Tweezers

Entry of micro- or nano-sized objects into cells or vesicles made of lipid membranes occur in many processes such as entry of viruses in host cells, microplastics pollution, drug delivery or biomedical imaging. Here, we investigated the microparticle crossing of lipid membranes in giant unilamellar vesicles in the absence of strong binding interactions (e.g. streptavidin-biotin binding). In these conditions, we observed that organic and inorganic particles can always penetrate inside the vesicles provided that an external picoNewton force is applied and for relatively low membrane tensions. In the limit of a vanishing adhesion, we pointed out the role of the membrane area reservoir and show that a force minimum exists when the particle size is comparable to the bendocapillary length

On Ziv's rounding test

International audienceA very simple test, introduced by Ziv, allows one to determine if an approximation to the value f (x) of an elementary function at a given point x suffices to return the floating-point number nearest f(x). The same test may be used when implementing floating-point operations with input and output operands of different formats, using arithmetic operators tailored for manipulating operands of the same format. That test depends on a "magic constant" e. We show how to choose that constant e to make the test reliable and efficient. Various cases are considered, depending on the availability of an fma instruction, and on the range of f (x)

Computing floating-point logarithms with fixed-point operations

International audienceElementary functions from the mathematical library input and output floating-point numbers. However it is possible to implement them purely using integer/fixed-point arithmetic. This option was not attractive between 1985 and 2005, because mainstream processor hardware supported 64-bit floating-point, but only 32-bit integers. Besides, conversions between floating-point and integer were costly. This has changed in recent years, in particular with the generalization of native 64-bit integer support. The purpose of this article is therefore to reevaluate the relevance of computing floating-point functions in fixed-point. For this, several variants of the double-precision logarithm function are implemented and evaluated. Formulating the problem as a fixed-point one is easy after the range has been (classically) reduced. Then, 64-bit integers provide slightly more accuracy than 53-bit mantissa, which helps speed up the evaluation. Finally, multi-word arithmetic, critical for accurate implementations, is much faster in fixed-point, and natively supported by recent compilers. Novel techniques of argument reduction and rounding test are introduced in this context. Thanks to all this, a purely integer implementation of the correctly rounded double-precision logarithm outperforms the previous state of the art, with the worst-case execution time reduced by a factor 5. This work also introduces variants of the logarithm that input a floating-point number and output the result in fixed-point. These are shown to be both more accurate and more efficient than the traditional floating-point functions for some applications

Correctly Rounded Exponential Function in Double Precision Arithmetic

We present an algorithm for implementing correctly rounded exponentials in double-precision floating point arithmetic. This algorithm is based on floating-point operations in the widespread IEEE-754 standard, and is therefore more efficient than those using multiprecision arithmetic, while being fully portable. It requires a table of reasonable size and IEEE-754 double precision multiplications and additions. In a preliminary implementation, the overhead due to correct rounding is a 2.3 times slowdown when compared to the standard library function

Clustering and Filtering Tandem Mass Spectra Acquired in Data-Independent Mode

Data-independent mass spectrometry activates all ion species isolated within a given mass-to-charge window (m/z) regardless of their abundance. This acquisition strategy overcomes the traditional data-dependent ion selection boosting data reproducibility and sensitivity. However, several tandem mass (MS/MS) spectra of the same precursor ion are acquired during chromatographic elution resulting in large data redundancy. Also, the significant number of chimeric spectra and the absence of accurate precursor ion masses hamper peptide identification. Here, we describe an algorithm to preprocess data-independent MS/MS spectra by filtering out noise peaks and clustering the spectra according to both the chromatographic elution profiles and the spectral similarity. In addition, we developed an approach to estimate the m/z value of precursor ions from clustered MS/MS spectra in order to improve database search performance. Data acquired using a small 3 m/z units precursor mass window and multiple injections to cover a m/z range of 400-1400 was processed with our algorithm. It showed an improvement in the number of both peptide and protein identifications by 8% while reducing the number of submitted spectra by 18% and the number of peaks by 55%. We conclude that our clustering method is a valid approach for data analysis of these data-independent fragmentation spectra. The software including the source code is available for the scientific community. Figure