This paper presents a low-complexity input-to-state stable ellipsoidal outer-bounding state estimation approach with unknown but bounded disturbances. The bounds on the noise are specified by ellipsoids. The feasible set is updated through computing the Minkowski sum and intersection of two ellipsoids. At the observation stage, the observation noise bounding ellipsoid is replaced by a parallelotope containing it. Then, each observation update is transformed into multiple consecutive iterations to intersect ellipsoid with strips, which significantly reduces its per-update computational complexity.Furthermore, an adaptive selection scheme of the parameters is derived to ensure the stability of the estimation error. As a result, the proposed approach entails stability and delivers a trade-off between performance and complexity.

The set-membership information fusion problem is studied for general multi-sensor dynamic systems. Based on set-membership theory, three centralized state fusion estimation algorithms in the presence of bounded disturbances are proposed, namely augmented algorithm, combined measurement filtering algorithm and pseudo-sequential filtering algorithm. Theoretical discussions on the convergence and boundedness of the proposed fusion algorithms are provided and their stability is proved. The estimate accuracy, computational complexity and flexibility of these three fusion algorithms are compared through theoretical analysis and simulation. And their exchanging property of measurement update order is discussed. Results show that these algorithms are functionally equivalent in terms of the estimation accuracy and the exchangeability of the measurement update order can be guaranteed as long as the parameters satisfy certain conditions. Meanwhile the simulation results prove the role of the proposed algorithms in improving state estimation accuracy. In addition, the combined measurement filtering algorithm has the highest calculation speed due to lower dimension. But it is less flexible because the sensor measurement matrices need to satisfy some additional conditions. These conclusions are valuable in applications.

The gyro array is a useful technique in improving the accuracy of a micro-electro-mechanical system (MEMS) gyroscope, but the traditional estimate algorithm that plays an important role in this technique has two problems restricting its performance: The limitation of the stochastic assumption and the influence of the dynamic condition. To resolve these problems, a multi-model combined filter with dual uncertainties is proposed to integrate the outputs from numerous gyroscopes. First, to avoid the limitations of the stochastic and set-membership approaches and to better utilize the potentials of both concepts, a dual-noise acceleration model was proposed to describe the angular rate. On this basis, a dual uncertainties model of gyro array was established. Then the multiple model theory was used to improve dynamic performance, and a multi-model combined filter with dual uncertainties was designed. This algorithm could simultaneously deal with stochastic uncertainties and set-membership uncertainties by calculating the Minkowski sum of multiple ellipsoidal sets. The experimental results proved the effectiveness of the proposed filter in improving gyroscope accuracy and adaptability to different kinds of uncertainties and different dynamic characteristics. Most of all, the method gave the boundary surrounding the true value, which is of great significance in attitude control and guidance applications.

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