摘要
本文研究了在非线性观测和高密度杂波环境中的目标跟踪技术及其性能预测的方法。
论文首先简要介绍了目标跟踪领域的研究内容，评述了前人的研究成果，总结了研究现状和存在的问题，阐述了研究背景和主要工作。
针对非线性观测下的目标跟踪问题，首先将二维CMKF跟踪算法推广到三维情况，然后基于正规变换技术提出了解耦的CMKF算法，得到了正规变换矩阵的解析表达式，可以方便地对算法进行理论分析。为了提高初始跟踪精度，提出了一种对CMKF以及解耦CMKF算法的滤波初值进行估计的方法。同时将正规变换技术推广应用到机动目标“当前”统计模型下的解耦问题，推导了雷达二维观测下的正规变换矩阵。最后，基于一维“稳态”滤波器的已有研究成果，提出了非线性观测下滤波器的“暂稳态”概念和实现方法，并推导了状态估计“暂稳态”误差方差的解析表达式，为非线性观测下的目标跟踪性能分析提供了理论依据。
考虑多传感器非线性观测下的融合跟踪，论文将单传感器解耦CMKF、“暂稳态”滤波器以及“暂稳态”方差分析的结论推广应用到融合跟踪中，研究了其在基本的量测融合和航迹融合算法中的应用，推导了航迹融合中互协方差的递推公式和“暂稳态”公式，为多雷达融合跟踪的稳态性能估计提供了一种新途径。
针对高密度杂波环境中的目标跟踪问题，首先分析和修正了PDA算法中误差方差的计算公式，提出了修正的PDA算法(MPDA)，它不仅提高了跟踪性能，而且使得误差方差与算法的实际误差能够很好地匹配。然后应用两种方法对其进行性能估计和预测，一是基于Riccati方程的稳态性能估计，其结果与PDA算法近似条件下得出的结论相同；二是基于HYCA方法的瞬态性能预测，不仅给出了误差方差的离线递推关系，而且得到了航迹寿命等一系列性能指标的估计值。
基于MPDA算法及其稳态性能估计的结论，在适当选择检测模型和一定假设条件下，将自适应检测门限的选择归结为一个最优化问题，通过近似拟合性能估计结论中的衰减因子，得到了最佳检测门限自适应调整的解析表达式，为检测—跟踪系统的联合优化设计提供了一种新思路。
In this paper, the target tracking algorithms and their performance evaluation techniques are studied under non-linear measurement and high-density clutter circumstance.
Firstly, the paper introduces in brief the research subjects, reviews the predecessors' achievement, summaries the current situation and the existing problems in target tracking field. Afterwards, the main subjects and research background of this essay are expatiated.
Aimed at target tracking under non-linear measurement, this paper extends two-dimension CMKF algorithms to three-dimension, uses canonical transform to obtain decoupled CMKF algorithm which makes the theoretical analysis for the algorithm easily. In order to improve the tracking precision at the beginning, an approach for estimate initial value of CMKF and decoupled CMKF algorithm are proposed. In the meantime, the canonical transform technique is generalized and adopted to solve decoupling problem of maneuver target "current" statistic model, and the transformation matrix is derived for the 2D radar measurement. Lastly, the concept of "Transient Steady State " (TSS) and its realized approach is put forward, and TSS filter's error variance is obtained, which provides theoretical reference for the analysis of the tracking performance under the non-linear measurements.
Given the condition of the fusion tracking under multiple sensors non-linear measurements, this paper applies the conclusion of the analysis of single sensor decoupled CMKF, TSS filter and TSS variance to the fusion tracking system. It also studies their application in basic measurement fusion and track fusion algorithm, and covariance recursive formula of track fusion is deduced. Which offers a new way for steady-state performance evaluation of multi-radar fusion tracking.
Under the background of target tracking in high-density clutter, the calculation formula of the PDA algorithm's error variance is analyzed and revised firstly, and the modified PDA (MPDA) is derived, which not only improves the tracking performance, but also makes the error variance and the real error of the algorithm match well. Then, two methods are adopted to evaluate and to predict its performance. One is the steady-state performance evaluation based on the Riccati equation. The same conclusion as derived from the original PDA under approximate condition is concluded this way without any approximations. The second method is the instant-state performance prediction based on the HYCA method. This method not only gives the off-line recursive error variance relation, but also gets a series of performance measurement such as track life.
On the ground of MPDA algorithm and the conclusion of its steady-state performance
evaluation, the choice of the detection threshold becomes a matter of optimization under the condition of properly chosen detection model and hypothesis. And the analytic expression of auto-adjusted detection threshold can be deduced via approximate fitting attenuation factor derived from the conclusion of performance estimation. It presents a novel approach for the optimization of detection-tracking system.
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