The zero-velocity-update (ZUPT)-aided foot-mounted pedestrian inertial navigation system (PINS) is a powerful, high-precision and autonomous positioning system for the IOT applications, such as ...pedestrian indoor and outdoor seamless positioning. The ZUPT-aided PINS always suffers from the heading error, which leads to a high-order divergence rate of the positioning result. This study uses a magnetometer, and proposes a Coriolis-based Heading Estimation (CHE) method to address this challenge. While the magnetometer is capable of directly correcting heading information, it is susceptible to environmental magnetic interference (MI). Based on the Coriolis theory, the CHE method ingeniously leverages angular rate and magnetic measurement to realize the decoupling between the effective magnetic information and MI. Furthermore, the pedestrians need high-precision height estimation, when walking between multiple floors. This study proposes a height polynomial model based on linear transformation based on the barometer. The proposed method suppresses the long-term drift of air-pressure measurement, and improves the height-estimation precision. The above models are integrated into the ZUPT-aided PINS. A linear Kalman filter is designed to fuse the information, and suppress the errors of heading and height. At a complex-walking scenes, the experimental result shows that the proposed algorithm achieves higher three-dimensional average positioning precision. It is 2.897 meters (0.145% mileage) under thirty-minute two-kilometer walking.
The objective of this paper is to study the representation of neutrosophic matrices defined over a neutrosophic field by neutrosophic linear transformations between neutrosophic vector spaces, where ...it proves that every neutrosophic matrix can be represented uniquely by a neutrosophic linear transformation. Also, this work proves that every neutrosophic linear transformation must be an AH-linear transformation; i.e., it can be represented by classical linear transformations.
As cardiovascular diseases are one of the most prominent illnesses, a continuous, non-invasive, and comfortable monitoring of blood pressure (BP) is indispensable. This paper investigates the best ...method for obtaining highly accurate BP values in non-invasive measurements through the extraction of hemodynamic variables from the arteries of young subjects. After literature review, five state-of-the-art BP models were analysed and qualitatively compared in a novel in-silico study. Relevant arterial parameters such as luminal area, flow velocity, and pulse wave velocity, of 1458 subjects were extracted from a computer-simulated database and served as input parameters in the BP models' simulation. The five models were calibrated to each arterial-site. Contrarily to the expected, the linear model (linear transformation of the distending diameter into BP) revealed more accuracy than the commonly used exponential transformation. In an ex-vivo experimental setup, the linear model was used for the extraction of BP by using an ultrasound (US) sensor and validated with a commercial pressure sensor. The results showed an in-silico pulse pressure correlation of 0.978 and mean difference of (-2.845 ± 2.565) mmHg at the radial artery and ex-vivo pulse pressure correlation of 0.986 and mean difference of (1.724 ± 3.291) mmHg. Thus, with the linear model, the US measurement complies with the Association for the Advancement of Medical Instrumentation standard with smaller deviations than ±5 mmHg.
The reliability-based design optimization (RBDO) using performance measure approach for problems with correlated input variables requires a transformation from the correlated input random variables ...into independent standard normal variables. For the transformation with correlated input variables, the two most representative transformations, the Rosenblatt and Nataf transformations, are investigated. The Rosenblatt transformation requires a joint cumulative distribution function (CDF). Thus, the Rosenblatt transformation can be used only if the joint CDF is given or input variables are independent. In the Nataf transformation, the joint CDF is approximated using the Gaussian copula, marginal CDFs, and covariance of the input correlated variables. Using the generated CDF, the correlated input variables are transformed into correlated normal variables and then the correlated normal variables are transformed into independent standard normal variables through a linear transformation. Thus, the Nataf transformation can accurately estimates joint normal and some lognormal CDFs of the input variable that cover broad engineering applications. This paper develops a PMA-based RBDO method for problems with correlated random input variables using the Gaussian copula. Several numerical examples show that the correlated random input variables significantly affect RBDO results.
We investigate the finitary functions from a finite field
F
q
to the finite field
F
p
, where
p
and
q
are powers of different primes. An
(
F
p
,
F
q
)
-linearly closed clonoid is a subset of these ...functions which is closed under composition from the right and from the left with linear mappings. We give a characterization of these subsets of functions through the invariant subspaces of the vector space
F
p
F
q
\
{
0
}
with respect to a certain linear transformation with minimal polynomial
x
q
-
1
-
1
. Furthermore we prove that each of these subsets of functions is generated by one unary function.
This paper presents a convex-analytic framework to learn sparse graphs from data. While our problem formulation is inspired by an extension of the graphical lasso using the so-called combinatorial ...graph Laplacian framework, a key difference is the use of a nonconvex alternative to the ℓ1 norm to attain graphs with better interpretability. Specifically, we use the weakly-convex minimax concave penalty (the difference between the ℓ1 norm and the Huber function) which is known to yield sparse solutions with lower estimation bias than ℓ1 for regression problems. In our framework, the graph Laplacian is replaced in the optimization by a linear transform of the vector corresponding to its upper triangular part. Via a reformulation relying on Moreau's decomposition, we show that overall convexity is guaranteed by introducing a quadratic function to our cost function. The problem can be solved efficiently by the primal-dual splitting method, of which the admissible conditions for provable convergence are presented. Numerical examples show that the proposed method significantly outperforms the existing graph learning methods with reasonable computation time.
Orthogonal space-time block codes (OSTBC) from orthogonal designs have both advantages of complex symbol-wise maximum-likelihood (ML) decoding and full diversity. However, their symbol rates are ...upper bounded by 3/4 for more than two antennas for complex symbols. To increase the symbol rates, they have been generalized to quasi-orthogonal space-time block codes (QOSTBC) in the literature but the diversity order is reduced by half and the complex symbol-wise ML decoding is significantly increased to complex symbol pair-wise (pair of complex symbols) ML decoding. The QOSTBC has been modified by rotating half of the complex symbols for achieving the full diversity while maintaining the complex symbol pair-wise ML decoding. The optimal rotation angles for any signal constellation of any finite symbols located on both square lattices and equal-literal triangular lattices have been found by Su-Xia, where the optimality means the optimal diversity product (or product distance). QOSTBC has also been modified by Yuen-Guan-Tjhung by rotating information symbols in another way such that it has full diversity and in the meantime it has real symbol pair-wise ML decoding (the same complexity as complex symbol-wise decoding) and the optimal rotation angle for square and rectangular QAM constellations has been found. In this paper, we systematically study general linear transformations of information symbols for QOSTBC to have both full diversity and real symbol pair-wise ML decoding. We present the optimal transformation matrices (among all possible linear transformations not necessarily symbol rotations) of information symbols for QOSTBC with real symbol pair-wise ML decoding such that the optimal diversity product is achieved for both general square QAM and general rectangular QAM signal constellations. Furthermore, our newly proposed optimal linear transformations for QOSTBC also work for general QAM constellations in the sense that QOSTBC have full diversity with good diversity product property and real symbol pair-wise ML decoding. Interestingly, the optimal diversity products for square QAM constellations from the optimal linear transformations of information symbols found in this paper coincide with the ones presented by Yuen-Guan-Tjhung by using their optimal rotations. However, the optimal diversity products for (nonsquare) rectangular QAM constellations from the optimal linear transformations of information symbols found in this paper are better than the ones presented by Yuen-Guan-Tjhung by using their optimal rotations. In this paper, we also present the optimal transformations for the co-ordinate interleaved orthogonal designs (CIOD) proposed by Khan-Rajan for rectangular QAM constellations.
This study deals with the problem of gain‐scheduled robust control for multi‐agent linear parameter varying (LPV) systems with or without communication delays. The system matrices are assumed to ...depend on the scheduling parameters, which are supposed to be time‐varying within a priori known bounds. First, a linear transformation matrix is constructed from the directed spanning tree of the communication topology of the agents, which equivalently transforms the robust consensus control problem of multi‐agent LPV systems into the robust stability problem of a set of parameter‐dependent systems. What's more, the effect of the time‐varying communication delays is considered, and consensus condition in terms of linear matrix inequalities (LMIs) is derived by using the parameter‐dependent Lyapunov–Krasovskii approach. Then, the control gain matrices are obtained through solving a convex optimization problem. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.
The P-property of the linear transformation in second-order cone linear complementarity problems (SOCLCP) plays an important role in checking the globally uniquely solvable (GUS) property due to the ...work of Gowda et al. However, it is not easy to verify the P-property of the linear transformation, in general. In this paper, we provide matrix characterizations for checking the P-property, which is a new approach different from those in the literature. This is a do-able manipulation, which helps verifications of the P-property and globally uniquely solvable (GUS) property in second-order cone linear complementarity problems. Moreover, using an equivalence relation to the second-order cone linear complementarity problem, we study some sufficient and necessary conditions for the unique solution of the absolute value equations associated with second-order cone (SOCAVE).
We consider goodness‐of‐fit tests for the multivariate Student's t‐distribution with i.i.d. data and for the innovation distribution in a generalized autoregressive conditional heteroskedasticity ...model. The methods are based on the empirical characteristic function and are relatively easy to implement, invariant under linear transformations, and globally consistent. Asymptotic properties of the proposed procedures are investigated, while the finite‐sample properties are illustrated by means of a Monte Carlo study. The procedures are also applied to real data from the financial markets.
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