Bias-correction of Kalman filter estimators associated to a linear state space model with estimated parameters

TLDR: In this article, the impact of the bias in the invariant state space models with estimated parameters is discussed and an adaptive correction procedure based on any parameters estimation method (for instance, maximum likelihood or distribution-free estimators).

About: This article is published in Journal of Statistical Planning and Inference.The article was published on 2016-09-01 and is currently open access. It has received 15 citations till now. The article focuses on the topics: Invariant extended Kalman filter & Estimator.

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Table 4: Parameters estimation.

Table 5: Mean square errors of both one-step-ahead estimates and update estimates of the anomalies considering the Gaussian ML estimators and with the bias correction.

Table 1: Parameters estimates in the iterative procedure.

Table 2: Estimate of the mean bias and the convergence criterion in the iterative procedure.

Table 3: Mean square errors of radar calibrate estimates using both forecast and filtered calibration factors.

Figure 1: Accumulated precipitation during the storm (AP – based on rain gauge data; AP ML – estimated with the Gaussian ML; AP corr– estimated with the corrected parameters).

Frequently asked questions

Q1. What are the contributions in this paper?

8 This paper aims to discuss some practical problems on linear state space 9 models with estimated parameters. While the existing research focuses on 10 the prediction mean square error of the Kalman filter estimators, this work 11 presents some results on bias propagation into both one-step ahead and up12 date estimators, namely, non recursive analytical expressions for them. The theoretical results presented in this work provide an adaptive 15 correction procedure based on any parameters estimation method ( for in16 stance, maximum likelihood or distribution-free estimators ).