Nonlinear filter

A nonlinear filter is a signal-processing device whose output is not a linear function of its input. Examples of nonlinear filters include:

• phase-locked loops
• detectors
• mixers
• median filters

Nonlinear filters are sometimes used for removing very short wavelength, but high amplitude features from data. Such a filter can be thought of as a noise spike-rejection filter, but it can also be effective for removing short wavelength geological features, such as signals from surficial features.

Nonlinear filters locate and remove data that is recognised as noise. The algorithm is 'nonlinear' because it looks at each data point and decides if that data is noise or valid signal. If the point is noise, it is simply removes and replaced by an estimate based on surrounding data points, and parts of the data that are not considered noise are not modified at all. Linear filters, such as those used in bandpass, highpass, and lowpass, lack such a decision capability and therefore modify all data.

Nonlinear filter (estimation theory)

In estimation theory, control theory, and engineering, a nonlinear filter is an algorithm that estimates the state of a (stochastic) dynamical system from noisy measurements, where either the system dynamics model or measurement model is a nonlinear function of the state. The problem of optimal nonlinear filtering was solved by Ruslan L. Stratonovich (1959, 1960). Its linear case is known as the Kalman filter (or Kalman-Bucy filter).

• Extended Kalman Filter and Unscented Kalman Filter
• Particle filter

See also

• Nonlinearity
• Filtering problem (stochastic processes)