Mobile Position Tracking in Three Dimensions using Kalman and Lainiotis Filters

Abstract

Abstract:In this paper we present two time invariant models mobile position tracking in three dimensions, which describe the movement in x-axis, y-axis and z-axis simultaneously or separately, provided that there exist measurements for the three axes. We present the time invariant filters as well as the steady state filters: the classical Kalman Filter and Lainiotis Filter and the Join Kalman Lainiotis Filter, which consists of the parallel usage of the two classical filters. Various implementations are proposed and compared with respect to their behavior and to their computational burden: all time invariant and steady state filters have the same behavior using both the proposed models but have different computational burden.

Speedup of Kalman and Lainiotis filters for partitionable models

“…Consider the systems described in [7] for mobile position tracking in three dimensions simultaneously (single model) or separately (partitioned models). In this example the single model with 6 n  and 3 m  is partitioned into 3 p  models with 2 N  and 1 M  .…”