The problem of determining the state of a system from noisy measurements is called estimation or filtering. The use of the system naturally tries to minimize the inaccuracies caused by the presence of this noise by filtering. In order to have any sort of filtering problem in the first place, there must be a system of which measurements are available. But optimal filters require exact knowledge of the process noise and the measurement noise, and exact descriptions of system dynamics. Thus optimal filters are generally demanding on computational burden, and optimality is unachievable if the required computational capabilities are not available. Because an unlimited computer capability is not usually available, the designer of a filter or smoother purposely ignores or simplifies certain effects when he represents them in his design equations; this results in a suboptimal data processor[6]. We suggest suboptimal discrete filters for stochastic systems with different types of observations. Linear Kalman filter and extended Kalman filter are replaced by unconnected each other local filters which allow parallel processing of observations and reduce off-line and on-line computational requirements. This has been achieved via the use of a decomposition of multidimensional observation vector into a set of subvectors of lower dimension. The obtained filtering equations have a parallel structure and are very suitable for parallel programming. The numerical example demonstrates the efficiency and high-accuracy of the proposed suboptimal filters. And the practical application of approximate methods of optimal filtering is restricted by the high order of filters, especially in problems of high dimension. Even the application of the simplest method of normal approximation or other methods necessitates the integration of the set of high order equations in such problems. Therefore, the only way of designing practically realizable filters in high dimension problems is the decrease of order of filters. In order to understand how this may be attained Pugachev analyzed the structure of the equation for a suboptimal estimate in the several methods[20]. This leads to the theory of conditionally optimal filtering which has been the focus of attention on this thesis. The idea of conditionally optimal filtering theory is to find an optimal filter in some class of admissible filters which is defined by the condition that the behavior of a filter be described by the differential or difference equation of a given order and of a given form. On the basis of conditionally optimal filtering theory, we suggest iterated conditionally optimal filters for random processes determined random processes determined by nonlinear difference equations. As well as in the conditionally optimal filtering theory all calculations connected with determining the gains of the iterated conditionally optimal filters are based on a priori information about the structure of difference equations determining a random processes and a class of admissible filters. It does not use the results of current observations and therefore, it can be done in advance in the process of filters design. So the process of filtering may be realized in real time. These filters enable us to increase the accuracy of estimation in many nonlinear problems of data processing in real time. The example is given.
잡음이 있는 관측치(noisy measurement)로부터 시스템의 상태(state)를 결정하는 문제를 추정(estimation) 또는 필터링(filtering)이라고 부른다. 당연히 필터링에 의해 이 잡음(noise)으로부터 야기되는 부정확성을 최소화하는 것이 당면목적이 된다. 그러나, 최적인 필터들(optimal filters)은 잡음과정 (noise process)과 관측잡음(measurement noise)에 대한 정확한 지식과 시스템역학 (system dynamics)에 대한 정확한 묘사가 요구된다. 그러므로 일반적으로 최적인 필터는 계산부담을 요하게 되는데, 요구되어진 계산능력이 유효하지 않다면 이 최적인 필터는 달성될 수 없다. 그런데, 무한정한 계산능력이 항상 가능한것은 아니므로 필터고안자는 필터방정식을 만들 때, 어떤 효과를 무시하거나 또는 간단화시켜야 하는데 이로부터 준최적인 필터링 (suboptimal filtering)이 유도된다. 이 논문에서는 서로 다른 종류의 관측치를 갖는 확률적 시스템(stochastic system) 에 대한 준최적인 필터링을 소개한다. 이것은, 선형 Kalman 필터(linear Kalman filter)와 확장된 Kalman 필터(extended Kalman filter)가 각각의 다른 지역적 필터(local filter)에 사용되어 관측치의 병렬과정(parallel processing)을 가능하게 하여 계산적인 요구성을 감소시킨다. 한편 최적인 필터링의 실제적인 근사방법은 차수가 높은 문제에 있어서는 한계점이 있다. 그러므로 높은 차수의 문제에 있어서 실제적으로 실현가능한 필터를 구현하는 유일한 방법은 필터의 차수를 낮추는 것이다. 여기서 준최적인 필터링에 대한 구조를 분석하여 나온 이론이 조건적으로 최적인 필터링(conditionally optimal filtering)이다. 이 조건적으로 최적인 필터링 이론에 근거해서, 반복된 조건적으로 최적인 필터링(iterated conditionally optimal filtering) 방법을 소개한다. 이 방법에 대한 구체적인 방법과 효율성을 나타내 주는 예가 제시된다. 이 필터는 여러가지 데이타 처리과정의 많은 비선형 문제들에 있어서 추정의 정확성을 높여 줄 수 있다.
