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Highlights • Although the second-order approximation closely matches the true distribution, it will not lead to a closed-form expression for the likelihood function, while the first-order approximation results in a simple closed-form expression at the expense of some accuracy loss. • Although the likelihood function deviates from its first-order approximation, the position of their maxima are close to each other, so the first-order approximation still results in an appropriate position estimate. • In the presence of orientation uncertainty, the proposed estimator outperforms the state-of-the-art estimators. Abstract As the positioning accuracy of a visible light positioning (VLP) system is highly susceptible to changes in the orientation of the receiver, accurate knowledge of the receiver orientation is required. In practice, the orientation of the receiver is estimated with an external orientation estimation device. However, these devices generally suffer from drift and misalignment, causing an uncertainty in the measured orientation that will degrade the performance of standard positioning algorithms. In this paper, we derive a novel positioning algorithm that takes into account the effect of the orientation uncertainty. To this end, we need to cope with the non-linear relationship between the received signal strength (RSS) and the orientation uncertainty, which makes the likelihood function of the RSS, required to derive the maximum likelihood (ML) estimator, hard to obtain. To solve this issue, we consider the first and second-order Taylor series expansion of the RSS. Although the accuracy of the second-order approximation is better than the first-order approximation, the first-order approximation results in a closed-form expression for the likelihood function, while this is not possible with the second-order approximation. Because of this, we derive the ML estimator using the first-order approximation, and employ the multivariate gradient descent algorithm to obtain the position estimate. Computer simulations show that the proposed algorithm outperforms state-of-the-art VLP algorithms subject to orientation uncertainty. [ABSTRACT FROM AUTHOR]

• A discrete kernel estimator is developed to estimate unknown, time-varying target birth cardinality distribution. • Exponential weighted moving average is employed to address the time-varying characteristics of birth cardinality distribution. • An improved Gaussian Mixture CPHD filter with birth cardinality distribution and birth intensity estimated online is designed for multi-target tracking. Cardinalized probability hypothesis density (CPHD) filter is a promising algorithm for multi-target tracking. However, the performance of standard CPHD is degraded when the target birth process is unknown and dynamically changing. To remove this limitation, a discrete kernel estimator in conjunction with exponential weighted moving average scheme is introduced in this study to estimate the time-varying target birth cardinality distribution (i.e. , probability distribution on number of newborn targets appearing during one sampling time) at each processing step. The target birth intensity is then updated according to the resulting estimated birth cardinality distribution. The estimated birth intensity and cardinality distribution can be employed by a tracker based on Gaussian mixture CPHD (GMCPHD) to modulate its filtering strength for target tracking. The performance of the proposed framework is demonstrated by both numerical simulations and experiment on a video surveillance dataset. Results show that the proposed algorithm can reduce the delay of standard GMCPHD filter's response to the changes in the number of targets, and thus improve the accuracy of cardinality estimates. Satisfactory estimation of cardinality can be obtained even when there is a fast change in the rate of birth. [ABSTRACT FROM AUTHOR]

• We propose an improved ℓ 0 -LMS (ℓ 0 -ILMS) algorithm for sparse system identification. • The convergence condition of the proposed ℓ 0 -ILMS algorithm on step size is derived. • The parameter selection criterion for optimal steady-state mean-square deviation (MSD) is discussed. • Compared to ℓ 0 -LMS algorithm, the steady-state MSD of the proposed ℓ 0 -ILMS algorithm is lower and less sensitive to tuning parameters and measurement noise power. The ℓ 0 -norm-constraint LMS (ℓ 0 -LMS) algorithm is one of the widely used sparse LMS algorithms for the identification of sparse system, and its performance is quite attractive compared to other precursors. However, ℓ 0 -LMS is still confronted with some limitations on the optimal parameter selection and the estimated coefficient accuracy of sparse system identification. In this paper, we proposed an improved ℓ 0 -LMS (ℓ 0 -ILMS) algorithm to address these limitations. The convergence condition and the parameter selection rules for optimal steady-state mean-square deviation (MSD) of ℓ 0 -ILMS are discussed. Compared with ℓ 0 -LMS, the steady-state MSD of ℓ 0 -ILMS is lower and less sensitive to the tuning parameters and measurement noise power. Numerical simulations comparing the performance of standard LMS, ℓ 0 -LMS and ℓ 0 -ILMS demonstrate the effectiveness of ℓ 0 -ILMS. [ABSTRACT FROM AUTHOR]