Informatics and Applications

2025, Volume 19, Issue 4, pp 12-25

A PRACTICAL STUDY OF THE EXTENDED KALMAN FILTER INSTABILITY

A. V. Bosov
I. V. Uryupin

Abstract

The paper examines the variants of unstable operation of the extended Kalman filter (EKF). The set of experiments was performed with a typical model of a stochastic observation system. The motion of an autonomous object with a constant average velocity was modeled under conditions of uncontrolled velocity perturbations forming a chaotic trajectory with a regular target direction. Observations of two independent complexes consist of measurements of bearing angles (azimuth and elevation angle) and range. The estimation of the object's position is performed by the basic EKF and its modification using the method of linear pseudoobservations. The basic EKF turns out to be unstable in the initial model. The EKF uses the method of pseudomeasurements to provide a stable assessment of the position with high accuracy. The purpose of the experiments is to show which changes in the monitoring system model led to unstable operation of this EKF modification. For this purpose, 4 scenarios have been proposed, calculated, and analyzed: (i) inaccurate detection of the initial position; (ii) inability to identify the speed parameters in advance; (iii) movement with an abrupt change in speed parameters while maintaining the direction of the target; and (iv) inaccurate setting of statistical characteristics (covariance) of measurement errors. In each of the scenarios, the EKF turns out to be unstable, forming an estimate of the object's position with unacceptable accuracy. At the same time, the nature of instability and the behavior of the EKF estimates are different as demonstrated by numerical and graphical calculation results.

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