估计与决策联合性能评估以及性能排序方法研究

Estimation and decision are two important parts in the field of information fusion. In many applications, estimation and decision are applied jointly, such as tracking and identification. For performance evaluation of such problems, a popular method is evaluating estimation performance and decision performance separately. It has the following drawbacks. First, it cannot describe the joint performance of estimation and decision well, thus it is a mismatch for the joint problem. Second, it often cannot compare the overall performance of two algorithms (e.g., algorithm 1 is better than algorithm 2 for estimation performance but algorithm 2 is better than algorithm 1 in terms of decision performance). To overcome the above drawbacks, this project will propose new performance evaluation methods to evaluate the joint performance of estimation and decision for computer simulations and actual scenarios. For computer simulations, this project will evaluate the joint performance in probability space by using a conditionally joint cumulative distribution function. For actual scenarios, this project will evaluate the joint performance by translating estimation results and decision results to the data space by a translation model with high fidelity. Besides, given multiple performance measures, how to rank the overall performance of the algorithms is a worthwhile problem. This project will dig order information and quantity information by pairwise partial order and pairwise data normalization, respectively, and then propose new performance ranking approaches. This project will analyze and prove the properties of the proposed performance evaluation and performance ranking methods, and verify the effectiveness of the proposed methods by software and semi-hardware simulation. The proposed methods have practical application values as well as the potential to further develop and enrich the theory of performance evaluation and performance ranking.

估计和决策是信息融合领域两大重要组成部分，很多应用中都涉及到估计与决策的联合（如跟踪与识别）。针对联合问题，常用性能评估方法是以估计和决策的真实值为参考分别评价估计性能和决策性能。这种割裂式的方法难以刻画估计与决策的联合性能且往往难以比较两套算法的整体优劣。本项目针对仿真中真实值已知的情况，在概率空间中建立条件联合累积分布函数来刻画估计与决策的联合性能，克服割裂式方法的缺陷；针对实际中真实值未知的情况，通过高保真度的转化模型将估计与决策输出转化到数据空间进而提出联合性能评估方法，突破对估计和决策真实值的依赖；在给定若干性能指标的情况下，通过两两偏序和两两数据标准化提取指标的序信息和量信息，建立针对联合问题的算法综合性能排序方法。然后分析和证明本项目所提出方法的性质并通过软件仿真和半实物仿真验证所提出方法的有效性。这些方法不仅具有实际应用价值，还将进一步丰富和发展性能评估和性能排序的理论。

估计和决策是信息融合领域两大重要组成部分，在很多应用中都涉及到估计与决策的联合 （比如联合跟踪与识别）。针对联合问题，常用性能评估方法是分开评价估计性能和决策性能。这种割裂式的评估方法不能很好地刻画估计与决策的联合性能，因此对于联合问题而言是失配的。针对真实值已知情况下的估计与决策联合性能评估，本项目以阶跃函数为桥梁来评价估计器和决策器的性能，从而实现将二者统一到共同的框架中，在数值上实现了两者的量纲、量级的统一。以此为基础，设计合理的条件联合累积分布函数与阶跃函数进行比较，从而联合评价估计与决策的性能。针对真实值未知情况下的估计与决策联合性能评估，本项目提出利用量测方程将估计器和决策器的输出转化到量测空间中，生成大量的转化数据，通过最小配对距离比较转化数据与真实量测数据之间的距离来评价估计决策性能的好坏。针对给定性能评估指标数量较少时的估计决策器综合性能排序，本项目提出两两数据标准化方法，也就是针对一个性能评估指标每次将两个待比较对象数据进行标准化处理，找到某个共同的完美值当作参考。通过两两数据标准化，在两两偏序基础上加入了数据的量信息。而后利用排序向量法得到估计决策器的排序向量，从而对性能进行综合排序。此外，本项目定义了一种在欧氏空间中取值范围在0到1之间的距离——相对欧氏距离，以用来拓展Lp空间中的距离度量，也是第一个取值在0到1之间的非概率距离。证明了定义的相对欧氏距离满足距离三公理——正定性、对称性以及三角不等式，而且证明了在Lp空间中具有所给定形式下的唯一性。基于相对欧氏距离，定义了一对相对接近度度量——乐观距离和悲观距离，对TOPSIS方法的相对接近度进行有效改进。