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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]