AORKF_t {RobKF}

A t-distribution based additive outlier robust Kalman filter

Description

An additive outlier robust Kalman filter, based on the work by Agamennoni et al. (2018). This function assumes that the additions are potentially polluted by a heavy tailed process, which is approximated by a t-distribution. Variational inference is used to approximate the posterior.

Usage

AORKF_t(
  Y,
  mu_0,
  Sigma_0 = NULL,
  A,
  C,
  Sigma_Add,
  Sigma_Inn,
  s = 2,
  epsilon = 1e-06
)

Arguments

Y

A list of matrices containing the observations to be filtered.

mu_0

A matrix indicating the mean of the prior for the hidden states.

Sigma_0

A matrix indicating the Variance of the prior for the hidden states. It defaults to the limit of the variance of the Kalman filter.

A

A matrix giving the updates for the hidden states.

C

A matrix mapping the hidden states to the observed states.

Sigma_Add

A positive definite matrix giving the additive noise covariance.

Sigma_Inn

A positive definite matrix giving the innovative noise covariance.

s

A numeric giving the shape of the t-distribution to be considered. It defaults to 2.

epsilon

A positive numeric giving the precision to which the limit of the covariance, and the variational inferences is to be computed. It defaults to 0.000001.

Value

An rkf S3 class.

References

Agamennoni G, Nieto JI, Nebot EM (2011). “An outlier-robust Kalman filter.” In 2011 IEEE International Conference on Robotics and Automation, 1551–1558. IEEE.

Examples

library(RobKF)

set.seed(2019)

A = matrix(c(1), nrow = 1, ncol = 1)
C = matrix(c(1), nrow = 1, ncol = 1)

Sigma_Inn = diag(1,1)*0.01
Sigma_Add = diag(1,1)

mu_0 = matrix(0,nrow=1,ncol=1)

Y_list = Generate_Data(1000,A,C,Sigma_Add,Sigma_Inn,mu_0,anomaly_loc = c(100,400,700),
                       anomaly_type = c("Add","Add","Add"),anomaly_comp = c(1,1,1),
                       anomaly_strength = c(10,10,10))

Output = AORKF_t(Y_list,mu_0,Sigma_0=NULL,A,C,Sigma_Add,Sigma_Inn)

plot(Output,conf_level = 0.9999)