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Traditional algorithms require at least two complete vector observations to estimate orientation parameters. However, sensor faults and disturbances may cause some components of vector observations unavailable. This paper aims to propose algorithms to realize orientation estimation using vector observations with one or two components lost.

The fundamental of the proposed method is using norm equation and dot product equation to estimate the lost components, then, using an improved TRIAD to calculate attitude matrix. Specific algorithms for one and two lost components cases are constructed respectively, and the nonuniqueness of orientation estimation is analyzed from a geometric point of view. At last, experiments are performed to test the proposed algorithms.

The loss of components results in the loss of orientation information. The introduction of the norm equation and dot product equation can partially compensate for the loss of information. Experiment results and analysis show that the proposed algorithms can provide effective orientation estimation, and in vast majority of applications, the proposed algorithms can provide a unique solution in one lost component case and double solutions in two lost components case.

The proposed method addresses the problem of orientation estimation when one or two components of vector observations are unavailable. The introduction of the norm equation and dot product equation makes the calculation cost low, while the analyses from a geometric point of view makes the study of nonuniqueness more intuitive.

The purpose of this paper is to understand how market uncertainty affects sustainability management for long-term survival and growth.

Structural equation modeling is applied to evaluate the research model using data from a survey of 210 firms in China.

Empirical findings show that market uncertainty encourages entrepreneurship, which is an impetus for sustainability management. Economic and environmental responsibility positively affects balanced scorecard, but social responsibility does not.

The study results show that economic and environmental responsibility is essential for success, but social responsibility appears to lack effect. Therefore, future research might further explore why social responsibility fails to enhance corporate performance.

When firms consider sustainability management for long-term survival and growth, they should not only strive to grow regional economic benefits but also adhere to environmental regulations and protect the local ecosystem.

This study observes how market uncertainty, entrepreneurship and corporate sustainability (economic, environmental and social responsibility) affect the overall performance of firms in China.