Globally Optimal Distributed Kalman Filtering for Multisensor Systems with Unknown Inputs

In this paper, the state estimation for dynamic system with unknown inputs modeled as an autoregressive AR (1) process is considered. We propose an optimal algorithm in mean square error sense by using difference method to eliminate the unknown inputs. Moreover, we consider the state estimation for multisensor dynamic systems with unknown inputs. It is proved that the distributed fused state estimate is equivalent to the centralized Kalman filtering using all sensor measurement; therefore, it achieves the best performance. The computation complexity of the traditional augmented state algorithm increases with the augmented state dimension. While, the new algorithm shows good performance with much less computations compared to that of the traditional augmented state algorithms. Moreover, numerical examples show that the performances of the traditional algorithms greatly depend on the initial value of the unknown inputs, if the estimation of initial value of the unknown input is largely biased, the performances of the traditional algorithms become quite worse. However, the new algorithm still works well because it is independent of the initial value of the unknown input.

How do cumulative live birth rates and cumulative multiple live birth rates over complete courses of assisted reproductive technology treatment per woman compare among registries?

STUDY QUESTION

How do the national cumulative (multiple) live birth rates over complete assisted reproduction technology (ART) courses of treatment per woman in Belgium compare to those in other registries?

SUMMARY ANSWER

Cumulative live birth rates (CLBRs) remain high with a low cumulative multiple live birth rate when compared with other registries and publications.

WHAT IS KNOWN ALREADY

In ART, a reduction in the multiple live birth rate could be achieved by reducing the number of embryos transferred. It has been shown that by doing so, live birth rates per cycle were maintained, particularly when the augmentation effect of attached frozen-thawed cycles was considered.

STUDY DESIGN, SIZE, DURATION

A retrospective cohort study included all patients with a Belgian national insurance number who were registered in the national ART registry (Belrap) and who started a first fresh ART cycle between 1 July 2009 until 31 December 2011 with follow up until 31 December 2012. We analysed 12 869 patients and 38 008 cycles (both fresh and attached frozen cycles).

PARTICIPANTS, MATERIALS, SETTINGS, METHODS

CLBRs per patient who started a first ART cycle including fresh and consecutive frozen cycles leading to a live birth. Conservative estimates of cumulative live birth assumed that patients who did not return for treatment had no chance of achieving an ART-related live birth, whereas optimal estimates assumed that women discontinuing treatment would have the same chance of achieving a live birth as those continuing treatment. A maximum of six fresh ART cycles with corresponding frozen cycles was investigated and compared with other registries and publications.

MAIN RESULTS AND ROLE OF CHANCE

The CLBR was age dependent and declined from 62.9% for women <35 years, to 51.4% for women 35-37 years, to 34.1% for women 38-40 years and 17.7% for women 41-42 years in the conservative analysis after six cycles. In the optimal estimate, the CLBR declined from 85.9% for women <35 years, to 72.0% for women 35-37 years, to 50.4% for women 38-40 years and 36.4% for women 41-42 years. The cumulative multiple live birth rates for the whole population were 5.1 and 8.6% for the conservative and optimal estimate, respectively.

LIMITATIONS, REASONS FOR CAUTION

Conservative and optimal estimates use assumptions for the whole ART population and do not take the individual patient into account.

WIDER IMPLICATIONS OF THE FINDINGS

These data reinforce the validity of the Belgian model of coupling reimbursement of ART costs to a restriction in the number of embryos transferred. Our data can improve decision-making in medical ART practice both on the patient level and for society at large and could provide health care takers and insurance companies with a valid model.

STUDY FUNDING COMPETING INTERESTS

none.