Accommodating the multi-state constraint Kalman filter for visual-inertial navigation in a moving and stationary flight

For more than a decade, the multi-state constraint Kalman filter is used for visual-inertial navigation. Its advantages are the light-weight calculations, consistency, and similarity to the current mature GPS/INS Kalman filters. For using it in an airborne platform, an important deficiency exists. It diverges while the object stops moving. In this work, this deficiency is accounted for, by changing the state augmentation and measurement update policy from a time-based to horizontal travel-based scheme, and by reusing the oldest tracked point over and over. Besides the computational savings, it works infinitely with no extra errors in full-stops and with minor error build up in very low speeds.

Lyapunov Perron Transformation for Quasi-Periodic Systems and its Applications

This paper depicts the application of symbolically computed Lyapunov Perron (L-P) Transformation to solve linear and nonlinear quasi-periodic systems. The L-P transformation converts a linear quasi-periodic system into a time-invariant one. State augmentation and the method of Normal Forms are used to compute the L-P transformation analytically. The state augmentation approach converts a linear quasi-periodic system into a nonlinear time invariant system as the quasi-periodic parametric excitation terms are replaced by ‘fictitious’ states. This nonlinear system can be reduced to a linear system via Normal Forms in the absence of resonances. In this process, one obtains near identity transformation that contains fictitious states. Once the quasi-periodic terms replace the fictitious states they represent, the near identity transformation is converted to the L-P transformation. The L-P transformation can be used to solve linear quasi-periodic systems with external excitation and nonlinear quasi-periodic systems. Two examples are included in this work, a commutative quasi-periodic system and a non-commutative Mathieu-Hill type quasi-periodic system. The results obtained via the L-P transformation approach match very well with the numerical integration and analytical results.

Computation of Lyapunov–Perron transformation for linear quasi-periodic systems

The transformation of a linear time periodic system to a time-invariant system is achieved using the Floquet theory. In this work, the authors attempt to extend the same toward the quasi-periodic systems, using a Lyapunov–Perron transformation. Though a technique to obtain the closed-form expression for the Lyapunov–Perron transformation matrix is missing in the literature, the application of unification of multiple theories would aid in identifying such a transformation. In this work, the authors demonstrate a methodology to obtain the closed-form expression for the Lyapunov–Perron transformation analytically for the case of a commutative quasi-periodic system. In addition, for the case of a noncommutative quasi-periodic system, an intuitive state augmentation and normal form techniques are used to reduce the system to a time-invariant form and obtain Lyapunov–Perron transformation. The results are compared with the numerical techniques for validation.

Optimal input filters for iterative learning control systems with additive noises, random delays and data dropouts in both channels

In wireless networked iterative learning control systems, the controller is separated from the plant, and additive noises, random delays and data dropouts arise in both sensor-to-controller and controller-to-actuator channels. In order to guarantee the convergence performance of such systems with the effect of these uncertainties, an input filter is designed based on a proportional iterative learning controller, so that updated inputs can be filtered at the actuator side. Specifically, two data transmission processes are first developed to describe the mix of those uncertainties in both channels by Bernoulli and Gaussian distributed variables with known distributions. Based on state augmentation, the two data transmission processes are further combined with the iterative learning process of controllers to build a unified filtering model. According to this unified model, an optimal filter is designed via the projection theory and implemented at the actuator side to filter the updated inputs in iteration domain. Moreover, the convergence performance of the filtering error covariance matrix is proved theoretically. Finally, some numerical results are given to illustrate the effectiveness of the proposed method.

Lyapunov Perron Transformation for Linear Quasi-Periodic Systems

It is known that a Lyapunov Perron (L-P) transformation converts a quasi-periodic system into a reduced system with a time-invariant coefficient. Though a closed form expression for L-P transformation matrix is missing in the literature, the application of combination of multiple theories would aid in such transformation. In this work, the authors have worked on extending the Floquet theory to find L-P transformation. As an example, a commutative system with linear quasi-periodic coefficients is transformed into a system with time-invariant coefficient analytically. Furthermore, for non-commutative systems, similar results are obtained in this work, with the help of an intuitive state augmentation and Normal Forms technique. The results of the reduced system are compared with the numerical integration technique for validation.

Reducibility and Analysis of Linear Quasi-Periodic Systems Via Normal Forms

This article introduces a technique to accomplish reducibility of linear quasi-periodic systems into constant-coefficient linear systems. This is consistent with congruous proofs common in literature. Our methodology is based on Lyapunov–Floquet transformation, normal forms, and enabled by an intuitive state augmentation technique that annihilates the periodicity in a system. Unlike common approaches, the presented approach does not employ perturbation or averaging techniques and does not require a periodic system to be approximated from the quasi-periodic system. By considering the undamped and damped linear quasi-periodic Hill-Mathieu equation, we validate the accuracy of our approach by comparing the time-history behavior of the reduced linear constant-coefficient system with the numerically integrated results of the initial quasi-periodic system. The two outcomes are shown to be in exact agreement. Consequently, the approach presented here is demonstrated to be accurate and reliable. Moreover, we employ Floquet theory as part of our analysis to scrutinize the stability and bifurcation properties of the undamped and damped linear quasi-periodic system.

Reinforcement-Learning Based Portfolio Management with Augmented Asset Movement Prediction States

Portfolio management (PM) is a fundamental financial planning task that aims to achieve investment goals such as maximal profits or minimal risks. Its decision process involves continuous derivation of valuable information from various data sources and sequential decision optimization, which is a prospective research direction for reinforcement learning (RL). In this paper, we propose SARL, a novel State-Augmented RL framework for PM. Our framework aims to address two unique challenges in financial PM: (1) data heterogeneity – the collected information for each asset is usually diverse, noisy and imbalanced (e.g., news articles); and (2) environment uncertainty – the financial market is versatile and non-stationary. To incorporate heterogeneous data and enhance robustness against environment uncertainty, our SARL augments the asset information with their price movement prediction as additional states, where the prediction can be solely based on financial data (e.g., asset prices) or derived from alternative sources such as news. Experiments on two real-world datasets, (i) Bitcoin market and (ii) HighTech stock market with 7-year Reuters news articles, validate the effectiveness of SARL over existing PM approaches, both in terms of accumulated profits and risk-adjusted profits. Moreover, extensive simulations are conducted to demonstrate the importance of our proposed state augmentation, providing new insights and boosting performance significantly over standard RL-based PM method and other baselines.