Extended Kalman Filtering With Nonlinear Equality Constraints: A Geometric Approach

Kalman Filtering with State Equality Constraints

For linear dynamic systems with white process and measurement noise, the Kalman filter is known to be an optimal estimator. In the application of Kalman filters there is often known model or signal information that is either ignored or dealt with heuristically [1]. This work presents a way to generalize the Kalman filter in such a way that known relations among the state variables (i.e., state ...

Kalman Filtering with Equality and Inequality State Constraints

Both constrained and unconstrained optimization problems regularly appear in recursive tracking problems engineers currently address – however, constraints are rarely exploited for these applications. We define the Kalman Filter and discuss two different approaches to incorporating constraints. Each of these approaches are first applied to equality constraints and then extended to inequality co...

On-Line Nonlinear Dynamic Data Reconciliation Using Extended Kalman Filtering: Application to a Distillation Column and a CSTR

Extended Kalman Filtering (EKF) is a nonlinear dynamic data reconciliation (NDDR) method. One of its main advantages is its suitability for on-line applications. This paper presents an on-line NDDR method using EKF. It is implemented for two case studies, temperature measurements of a distillation column and concentration measurements of a CSTR. In each time step, random numbers with zero m...

Kalman Filtering with State Constraints

The Kalman filter is the optimal minimum-variance state estimator for linear dynamic systems with Gaussian noise. In addition, the Kalman filter is the optimal linear state estimator for linear dynamic systems with non-Gaussian noise. For nonlinear systems various modifications of the Kalman filter (e.g., the extended Kalman filter, the unscented Kalman filter, and the particle filter) have bee...

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