Jaganath Chandrasekar

What is the ensemble Kalman filter and how well does it work

In this paper we described the ensemble Kalman filter algorithm. This approach to nonlinear Kalman filtering is a Monte Carlo procedure, which has been widely used in weather forecasting applications. Our goal was to apply the ensemble Kalman filter to representative examples to quantify the tradeoff between estimation accuracy and ensemble size. For all of the linear and nonlinear examples that we considered, the ensemble Kalman filter worked successfully once a threshold ensemble size was reached. In future work we will investigate the factors that determine this threshold value

Higher-Harmonic-Control Algorithm for Helicopter Vibration Reduction Revisited

The higher-harmonic-control (HHC) algorithm is examined from a control theory perspective. A brief review of the history and variants of HHC is given, followed by a careful development of the algorithm. An analytic convergence and robustness analysis is then performed. Online identification with the adaptive variant of the algorithm is also addressed. A new version of the algorithm, relaxed HHC, is introduced and shown to have beneficial robustness properties. Some numerical results comparing these variants of the HHC algorithm applied to helicopter vibration reduction are also presented. The results presented unify and extend previous work on the higher-harmonic-control algorithm.

State estimation for linear and non-linear equality-constrained systems

This article addresses the state-estimation problem for linear and non-linear systems for the case in which prior knowledge is available in the form of an equality constraint. The equality-constrained Kalman filter (KF) is derived as the maximum-a-posteriori solution to the equality-constrained state-estimation problem for linear and Gaussian systems and is compared to alternative algorithms. Then, four novel algorithms for non-linear equality-constrained state estimation based on the unscented KF are presented, namely, the equality-constrained unscented KF, the projected unscented KF, the measurement-augmentation unscented KF, and the constrained unscented KF. Finally, these methods are compared on linear and non-linear examples.

Gain-Constrained Kalman Filtering for Linear and Nonlinear Systems

This paper considers the state-estimation problem with a constraint on the data-injection gain. Special cases of this problem include the enforcing of a linear equality constraint in the state vector, the enforcing of unbiased estimation for systems with unknown inputs, and simplification of the estimator structure for large-scale systems. Both the one-step gain-constrained Kalman predictor and the two-step gain-constrained Kalman filter are presented. The latter is extended to the nonlinear case, yielding the gain-constrained unscented Kalman filter. Two illustrative examples are presented.

State estimation for equality-constrained linear systems

We address the state-estimation problem for linear systems in a context where prior knowledge, in addition to the model and the measurements, is available in the form of an equality constraint. First, we investigate from where an equality constraint arises in a dynamic system. Then, the equality-constrained Kalman filter (ECKF) is derived as the solution to the equality-constrained state-estimation problem and compared to alternative algorithms. These methods are investigated in an example. In addition to exactly satisfying an equality constraint on the system, ECKF produce more accurate and more informative estimates than the unconstrained estimates.

Adaptive Harmonic Steady-State Control for Disturbance Rejection

We consider harmonic steady-state (HSS) control for active noise and vibration rejection when the system dynamics are unknown. After a brief review and analysis of the HSS control theory, we develop an adaptive control algorithm based on a recursive least squares algorithm that estimates the system dynamics. Active noise cancellation in an acoustic drum is demonstrated using the adaptive control algorithm. The results presented here unify and extend previous results on HSS control

Unscented filtering for equality-constrained nonlinear systems

This paper addresses the state-estimation problem for nonlinear systems in a context where prior knowledge, in addition to the model and the measurement data, is available in the form of an equality constraint. Three novel suboptimal algorithms based on the unscented Kalman filter are developed, namely, the equality-constrained unscented Kalman filter, the projected unscented Kalman filter, and the measurement-augmented unscented Kalman filter. These methods are compared on two examples: a quaternion-based attitude estimation problem and an idealized flow model involving conserved quantities.

State Estimation for Large-Scale Systems Based on Reduced-Order Error-Covariance Propagation

We compare several reduced-order Kalman filters for discrete-time LTI systems based on reduced-order error-covariance propagation. These filters use combinations of balanced model truncation and complementary steady-state covariance compensation. After describing each method, we compare their performance through numerical studies using a compartmental model example. These methods are aimed at large-scale data-assimilation problems where reducing computational complexity is critical.

A Comparison of the Extended and Unscented Kalman Filters for Discrete-Time Systems with Nondifferentiable Dynamics

We compare the performance of the extended Kalman filter, the unscented Kalman filter, and two extensions of the Hinfin filter when applied to discrete-time nonlinear state estimation problems with nondifferentiable dynamics. We compare the performance of all the estimation techniques on simple nonlinear examples and finally consider state estimation of one-dimensional hydrodynamic flow based on a finite volume model that contains nondifferentiable nonlinearities.

On the Zeros, Initial Undershoot, and Relative Degree of Collinear Lumped-Parameter Structures

This paper considers collinear lumped-parameter structures where each mass in the structure has a single degree of freedom. Specifically, we analyze the zeros and relative degree of the single-input, single-output (SISO) transfer function from the force applied to an arbitrary mass to the position, velocity, or acceleration of another mass. In particular, we show that every SISO force-to-motion transfer function of a collinear lumped-parameter structure has no positive (real open-right-half-plane) zeros. In addition, every SISO force-to-position transfer function of a spring-connected collinear lumped-parameter structure has no non-negative (real closed-right-half-plane) zeros. As a consequence, the step response does not exhibit initial undershoot. In addition, we derive an expression for the relative degree of SISO force-to-position transfer functions. The formula depends on the placement of springs and dashpots, but is independent of the values of the spring constants and damping coefficients. Next, we consider the special case of serially connected collinear lumped-parameter structures. In this case, we show that every SISO force-to-position transfer function of a serially connected collinear lumped-parameter structure is minimum phase, that is, has no closed-right-half-plane zeros. The proofs of these results rely heavily on graph-theoretic techniques.