Prior knowledge processing for initial state of Kalman filter

Abstract

The paper deals with a specification of the prior distribution of the initial state for Kalman filter. The subjective prior knowledge, used in state estimation, can be highly uncertain. In practice, incorporation of prior knowledge contributes to a good start of the filter. The present paper proposes a methodology for selection of the initial state distribution, which enables eliciting of prior knowledge from the available expert information. The proposed methodology is based on the use of the conjugate prior distribution for models belonging to the exponential family. The normal state-space model is used for demonstrating the methodology. The paper covers processing of the prior knowledge for state estimation, available in the form of simulated data. Practical experiments demonstrate the processing of prior knowledge from the urban traffic control area, which is the main application of the research.

A unified framework for estimating parameters of kinetic biological models

“…This informed prior is provided to the CSUKF which utilizes it to uniquely estimate the parameters even in the case of non-identifiability. The CSUKF belongs to the Gaussian family, thus the conjugate prior distribution can be used to define the prior for the parameters and state variables, while maintaining the same probability density function (pdf) after transformation [ 53 ]. Lindley & El-Sayyad [ 54 ] applied a similar treatment for non-identifiable parameters, using Bayesian inference to estimate parameters with respect to linear constraints.…”

Gaussianity and the Kalman Filter: A Simple Yet Complicated Relationship

“…• "Since the Kalman framework requires Gaussian distributions, the model can only be constructed if ... " [2] • "The Kalman filter which is used for integrated navigation requires Gaussian variables ... a multimodal un-symmetric distribution has to be approximated with a Gaussian distribution before being used in the Kalman filter." [3] • "...can be best reconciled with the KF (which requires Gaussian probability distributions) by making the assumption that ... " [4] • " [The] Kalman filter requires Gaussian prior f (x 0 ) ... " [5] • "Notice that each of the distributions can be effectively approximated by a Gaussian. This is a very important result for the operation for many systems, especially the ones based on a Kalman filter since the filter explicitly requires Gaussian distributed noise on measurements for proper operation."…”