Kalmanfiltervarianter

Kalman filter variants refer to the various adaptations and extensions of the original Kalman filter, a mathematical algorithm primarily used for estimating the state of a linear dynamic system from a series of incomplete and noisy measurements. These variants are designed to address specific challenges or constraints not handled by the basic Kalman filter, such as non-linearities, high-dimensional systems, or non-Gaussian noise.

One notable variant is the Extended Kalman Filter (EKF), which linearizes the system dynamics and measurement models using a first-order Taylor expansion. This allows the EKF to handle mildly non-linear systems. For more pronounced non-linearities, the Unscented Kalman Filter (UKF) employs a deterministic sampling technique known as the unscented transform to capture the true mean and covariance of the state distribution.

The Ensemble Kalman Filter (EnKF) is another variant, particularly useful for high-dimensional systems. It uses a ensemble of state estimates to approximate the error covariance matrix, making it computationally efficient for large-scale applications. The Information Filter, or Inverse Kalman Filter, operates in the information space, using the inverse of the covariance matrix, which can be advantageous in certain scenarios.

For systems with non-Gaussian noise, the Particle Filter, also known as the Sequential Monte Carlo method, uses a set of random samples (particles) to represent the probability distribution of the state. This approach can handle complex, non-linear, and non-Gaussian problems but is generally more computationally intensive.

Other variants include the Square-Root Kalman Filter, which improves numerical stability, and the Fixed-Lag Smoother, which refines state estimates by incorporating future measurements. Each variant has its strengths and is chosen based on the specific requirements and constraints of the application.