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Abstract-Compressed sensing, viewed as a type of random undersampling, considers the acquisition and reconstruction of sparse or compressible signals at a rate significantly lower than that of Nyquist. Exact reconstruction from incompletely acquired random measurements is, under certain constraints, achievable with high probability. However, randomness may not always be desirable in certain applications. Taking a nonrandom approach using deterministic chaos and following closely a recently proposed novel efficient structure of chaos filters, we propose a chaos filter structure by exploring the use of chaotic deterministic processes in designing the filter taps. By numerical performance, we show that, chaos filters generated by the logistic map, while being possible to exactly reconstruct original timesparse signals from their incompletely acquired measurements, outperforms random filters.Index Terms-Compressed sensing, random undersampling, random filters, chaos filters, chaotic undersampling. I. NONRANDOMNESS IN COMPRESSED SENSING?Compressed sensing (CS), recently been introduced by Candes and Tao [1] and Donoho [2] as a type of random undersampling, allows for the acquisition and reconstruction of sparse/compressible signals at a rate lower than that of Nyquist. First, random linear projection is used to acquire efficient representations of the signals directly. Then, nonlinear techniques, such as l 1 optimization-based algorithms or sparse approximation algorithms, are used to faithfully reconstructed the acquired compressed data under certain constraints.CS framework has attracted an overwhelming research attention, due to several advantages. In data compression, significant reduction of data storage can be obtained thanks to the incomplete measurements. In data acquisition, much less power consumption is used at the sensing device since simple and less signal acquisition is performed while the computational load is pushed toward the reconstruction side. In addition, it can trade for fundamental limits of physical systems, such as the limited sampling clock frequency of ADCs used in sensing extremely high frequency spectrum holes in ultra-wideband cognitive radio communications [3].The use of randomness, which leads to the so-called incoherence property in CS, facilitates the faithful reconstruction with high probability. In practice, however, the use of purely random undersampling is expensive in hardware design. Concerned with the undesirable randomness in such situations, a question naturally arises: Can we use a nonrandom structure that still mimics or approximates the incoherence property for compressed sensing framework? Our approach to find an answer to this question is to explore the use of deterministic chaos. A chaos system is a nonlinear system that has a very unstable structure so that, under specific initial and control conditions, the output of the system behaves as random in just a few steps. Chaos have been studied in various scientific and engineering contexts [4], and recently found various...

While working on fire ground, firefighters risk their well-being in a state where any incident might cause not only injuries, but also fatality. They may be incapacitated by unpredicted falls due to floor cracks, holes, structure failure, gas explosion, exposure to toxic gases, or being stuck in narrow path, etc. Having acknowledged this need, in this study, we focus on developing an efficient portable system to detect firefighter’s falls, loss of physical performance, and alert high CO level by using a microcontroller carried by a firefighter with data fusion from a 3-DOF (degrees of freedom) accelerometer, 3-DOF gyroscope, 3-DOF magnetometer, barometer, and a MQ7 sensor using our proposed fall detection, loss of physical performance detection, and CO monitoring algorithms. By the combination of five sensors and highly efficient data fusion algorithms to observe the fall event, loss of physical performance, and detect high CO level, we can distinguish among falling, loss of physical performance, and the other on-duty activities (ODAs) such as standing, walking, running, jogging, crawling, climbing up/down stairs, and moving up/down in elevators. Signals from these sensors are sent to the microcontroller to detect fall, loss of physical performance, and alert high CO level. The proposed algorithms can achieve 100% of accuracy, specificity, and sensitivity in our experimental datasets and 97.96%, 100%, and 95.89% in public datasets in distinguishing between falls and ODAs activities, respectively. Furthermore, the proposed algorithm perfectly distinguishes between loss of physical performance and up/down movement in the elevator based on barometric data fusion. If a firefighter is unconscious following the fall or loss of physical performance, an alert message will be sent to their incident commander (IC) via the nRF224L01 module.

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