Filtering method based on norm regularization discrete linear system, and discrete linear system

Abstract

The invention belongs to the technical field of discrete linear system filtering, discloses a filtering method based on a norm regularization discrete linear system, and the discrete linear system, and uses l1-norm regularization to explicitly model and estimate an outlier and obtain a sparse solution. Due to the fact that explicit modeling is carried out on the outlier, the negative effect of theoutlier propagating through noise correlation can be estimated and reduced, and a more accurate estimation result can be obtained. According to the invention, the method provided by the invention provides the flexibility of allocating different penalty weights to the state outlier and the measurement outlier respectively, which is difficult to realize in a common M estimation method. By selectingproper regularization parameters, the proposed filter can be simplified into a linear optimal Kalman filter, so a good balance can be provided between robustness and optimality, and the effectivenessand superiority of the proposed robust filtering method are proved by using examples of simulation and experimental data.

Description

technical field

[0001] The invention belongs to the technical field of discrete linear system filtering, and in particular relates to a filtering method and a discrete linear system based on norm regularization of the discrete linear system. Background technique

[0002] Modeling physical systems often results in a resulting state-space model with associated process noise and measurement noise. For example, in applications such as aircraft inertial navigation systems, vibrations from the aircraft introduce a common noise source for dynamic driving systems and airborne radar measurements, so that the process noise and measurement noise sequences are statistically correlated. Also note that due to sampling, even if the process noise and measurement noise of a continuous-time system are uncorrelated, the covariance of the process noise and measurement noise of the discrete-time system obtained after sampling may not be zero. Although the problem of robust estimation has always...

Images