Abstract
In Kalman filter design, the filter algorithm and prediction model design are the most discussed topics in research. Another fundamental but less investigated issue is the careful selection of measurands and their contribution to the estimation problem. This is often done purely on the basis of empirical values or by experiments. This paper presents a novel holistic method to design and assess Kalman filters in an automated way and to perform their analysis based on quantifiable parameters. The optimal filter parameters are computed with the help of a nonlinear optimization algorithm. To determine and analyze an optimal filter design, two novel quantitative nonlinear observability measures are presented along with a method to quantify the dominance contribution of a measurand to an estimate. As a result, different filter configurations can be specifically investigated and compared with respect to the selection of measurands and their influence on the estimation. An unscented Kalman filter algorithm is used to demonstrate the method’s capabilities to design and analyze the estimation problem parameters. For this purpose, an example of a vehicle state estimation with a focus on the tire-road friction coefficient is used, which represents a challenging problem for classical analysis and filter parameterization.
Highlights
The degree of automation and technical support for humans has increased rapidly in recent years
In [10], a two-step method is presented in which particle swarm optimization (PSO) is used to tune both the filter parameterization and prediction model parameters
This paper considers its application to a vehicle state estimation problem using an unscented Kalman filter (UKF)
Summary
The degree of automation and technical support for humans has increased rapidly in recent years. The basic requirement for any control system is the existence of measurable control variables If they cannot be measured directly due to technical or economic reasons, state estimators are needed. The disturbances in the underlying mathematical model of the system and measurement equations are assumed to be white noise [1] This established and widely used method has been known and applied for more than 60 years now. There is still no simple procedure for an optimal design or parametrization of a Kalman filter. In order to parametrize a filter, the covariance matrices need to be determined (when dealing with other filter types such as, e.g., an unscented Kalman filter, there might be even more parameters) This leads to the crucial question for the filter design as to which measurands should be used and how they influence the estimation problem. How would other measurands affect the observability, and might they be even more dominant? Issues like these are addressed in this paper in a quantifiable way with the help of the novel design and analysis method presented below
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