18 Facts About Kalman filter

The filter is named after Rudolf E Kalman, who was one of the primary developers of its theory.

Kalman filter realized that the filter could be divided into two distinct parts, with one part for time periods between sensor outputs and another part for incorporating measurements.

The Kalman filter produces an estimate of the state of the system as an average of the system's predicted state and of the new measurement using a weighted average.

The Kalman filter-gain is the weight given to the measurements and current-state estimate, and can be "tuned" to achieve a particular performance.

Kalman filter is an efficient recursive filter estimating the internal state of a linear dynamic system from a series of noisy measurements.

Together with the linear-quadratic regulator, the Kalman filter solves the linear–quadratic–Gaussian control problem .

Kalman filter model assumes the true state at time k is evolved from the state at according to.

The Kalman filter can be written as a single equation; however, it is most often conceptualized as two distinct phases: "Predict" and "Update".

Practical implementation of a Kalman Filter is often difficult due to the difficulty of getting a good estimate of the noise covariance matrices Qk and Rk.

Kalman filter can be derived as a generalized least squares method operating on previous data.

In most real-time applications, the covariance matrices that are used in designing the Kalman filter are different from the actual noise covariances matrices.

The l·d·l square-root Kalman filter requires orthogonalization of the observation vector.

Kalman filter is efficient for sequential data processing on central processing units, but in its original form it is inefficient on parallel architectures such as graphics processing units .

Kalman filter can be presented as one of the simplest dynamic Bayesian networks.

The Kalman filter calculates estimates of the true values of states recursively over time using incoming measurements and a mathematical process model.

However, when a Kalman filter is used to estimate the state x, the probability distribution of interest is that associated with the current states conditioned on the measurements up to the current timestep.

The resulting Kalman filter depends on how the transformed statistics of the UT are calculated and which set of sigma points are used.

Traditional Kalman filter has been employed for the recovery of sparse, possibly dynamic, signals from noisy observations.