In environments where GNSS is unavailable or not useful for positioning, the use of low cost MEMS-based inertial sensors has paved a way to a more cost effective solution. Of particular interest is a foot mounted pedestrian navigation system, where zero velocity updates (ZUPT) are used with the standard strapdown navigation algorithm in a Kalman filter to restrict the error growth of the low cost inertial sensors. However heading drift still remains despite using ZUPT measurements since the heading error is unobservable. External sensors such as magnetometers are normally used to mitigate this problem, but the reliability of such an approach is questionable because of the existence of magnetic disturbances that are often very difficult to predict. Hence there is a need to eliminate the heading drift problem for such a low cost system without relying on external sensors to give a possible stand-alone low cost inertial navigation system. In this paper, a novel and effective algorithm for generating heading measurements from basic knowledge of the orientation of the building in which the pedestrian is walking is proposed to overcome this problem. The effectiveness of this approach is demonstrated through three field trials using only a forward Kalman filter that can work in real-time without any external sensors. This resulted in position accuracy better than 5 m during a 40 minutes walk, about 0 . 1% in position error of the total distance. Due to its simplistic algorithm, this simple yet very effective solution is appealing for a promising future autonomous low cost inertial navigation system. K E Y W O R D S 1. MEMS. 2. INS. 3. Pedestrian Navigation.

Shoe mounted Inertial Measurement Units (IMU) are often used for indoor pedestrian navigation systems. The presence of a zero velocity condition during the stance phase enables Zero Velocity Updates (ZUPT) to be applied regularly every time the user takes a step. Most of the velocity and attitude errors can be estimated using ZUPTs. However, good heading estimation for such a system remains a challenge. This is due to the poor observability of heading error for a low cost Micro-Electro-Mechanical (MEMS) IMU, even with the use of ZUPTs in a Kalman filter. In this paper, the same approach is adopted where a MEMS IMU is mounted on a shoe, but with additional constraints applied. The three constraints proposed herein are used to generate measurement updates for a Kalman filter, known as ‘Heading Update’, ‘Zero Integrated Heading Rate Update’ and ‘Height Update’.The first constraint involves restricting heading drift in a typical building where the user is walking. Due to the fact that typical buildings are rectangular in shape, an assumption is made that most walking in this environment is constrained to only follow one of the four main headings of the building. A second constraint is further used to restrict heading drift during a non-walking situation. This is carried out because the first constraint cannot be applied when the user is stationary. Finally, the third constraint is applied to limit the error growth in height. An assumption is made that the height changes in indoor buildings are only caused when the user walks up and down a staircase. Several trials were shown to demonstrate the effectiveness of integrating these constraints for indoor pedestrian navigation. The results show that an average return position error of 4·62 meters is obtained for an average distance of 1557 meters using only a low cost MEMS IMU.

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This paper considers optimal control of a quadrotor unmanned aerial vehicles (UAV) using the discrete-time, finite-horizon, linear quadratic regulator (LQR). The state of a quadrotor UAV is represented as an element of the matrix Lie group of double direct isometries, SE2(3). The nonlinear system is linearized using a left-invariant error about a reference trajectory, leading to an optimal gain sequence that can be calculated offline. The reference trajectory is calculated using the differentially flat properties of the quadrotor. Monte-Carlo simulations demonstrate robustness of the proposed control scheme to parametric uncertainty, state-estimation error, and initial error. Additionally, when compared to an LQR controller that uses a conventional error definition, the proposed controller demonstrates better performance when initial errors are large.