Kalman-based filters are the most commonly used algorithms of processing noisy signals from real sensors in different application areas. However, they have no intrinsic means of fighting off outliers, which can deteriorate filter accuracy drastically. Existing outlier rejection and accommodation techniques are computationally expensive for embedded systems. Our goal is to develop a multiple-step gating procedure suitable for implementation in firmware. Primarily the work is based upon statistical and probabilistic methods. For deduction, representation and corroboration of principal ideas it utilizes also linear algebra and analytic geometry. Verification of the developed algorithm has been performed using simulation techniques including the Monte-Carlo method. Scientific novelty. A new gating algorithm has been developed, verified and presented in detail. In contrast to the wellknown combination of the rectangular and elliptic gates, the proposed algorithm assumes an additional step which allows rejection of points not lying between the tangents of tilted confidence ellipses parallel to their major axes. The step helps avoid computing inverse covariance matrices required by the Mahalanobis distance due to the fact that it recognizes most outliers that are able to pass the rectangular gate, which makes invocation of the elliptic gate redundant. The proposed algorithm has been implemented and verified both theoretically and practically upon a variety of the multivariate linear Kalman filters and normally distributed random numbers for simulating outliers. Implementation has been done using the stm32f407vg microcontroller by STMicroelectronics. Simulation results have corroborated that the proposed interim step between application of the rectangular and elliptic gates reduces computational complexity of the whole gating procedure without any losses in accuracy. Results: the developed algorithm is integrated into a complex hardware-software tool intended for verification, estimation and investigation into micro-electromechanical inertial sensors.

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