α–β–γ tracking filters using acceleration measurements

BACKGROUND: Although real-time tracking of moving objects using a variety of sensor parameters is in great demand in monitoring systems, no studies have reported α–[Formula: see text] –[Formula: see text] tracking filters using simultaneous measurements including acceleration. In this report, we propose and analyze two α–[Formula: see text] –[Formula: see text] filters using acceleration measurements, namely, position–acceleration-measured (PAM) and position–velocity–acceleration-measured (PVAM) α–[Formula: see text] –[Formula: see text] filters. FINDINGS: Based on our previous work on position–velocity-measured (PVM) α–[Formula: see text] –[Formula: see text] filters, performance indices of the proposed filters are theoretically derived. Then, numerical analyses clarify the conditions under which the performance of the PAM filter surpasses that of the position-only-measured (POM) α–[Formula: see text] –[Formula: see text] filter. The results indicate that the PVAM filter achieves better accuracy than the other filters, even with a relatively large measurement noise. CONCLUSIONS: This report verifies the effectiveness of the [Formula: see text] –[Formula: see text] –[Formula: see text] filters using acceleration measurements based on numerical analyses using derived performance indices. These results are useful in the design of tracking systems including acceleration measurements (e.g., in deciding whether to use the measured acceleration to improve tracking filter performance). ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s40064-016-1960-8) contains supplementary material, which is available to authorized users.