戰術目標追蹤演算法之研究:即時輸入估計及雜訊鑑別

Abstract

現有目標追蹤演算法都有預設的系統參數，包括加速輸入值及雜訊參數值。然而，這些參數值通常會隨時間及環境而改變，因此需要即時地鑑別這些參數。就即時加速輸入值估計而言，它在戰術目標追蹤問題上有重要的應用：目前戰術目標追蹤演算法主要使用多重追蹤濾波器的方式，這類方式同時執行多個追蹤器來涵蓋目標物的可能運動狀態，而這些追蹤器是根據預設的加速輸入值來設計的；當追蹤如戰鬥機之類具高度機動性及大範圍之可能加速輸入值的目標物時，所需追蹤器數會隨著加速輸入值的範圍而增加，導致很高的複雜度，一種降低複雜度的可能方法是即時地估計加速輸入值，並根據估計結果來調整追蹤器的設定值，如此，便可使用較少的追蹤器，達成複雜度降低的目標。另一方面，就即時雜訊鑑別而言，它在雷達目標追蹤問題上有重要的應用：雷達追蹤環境中，由於目標物反射中心的隨機晃動所造成的量測雜訊呈現非高斯機率分佈，而且隨著目標物的移動，量測雜訊的統計特性也會呈現非穩態的改變，當追蹤器的雜訊參數預設值與實際值不符合時，會導致追蹤精確度的降低；藉由即時鑑別雜訊統計參數，調整追蹤器的設定值，可以改善在此環境下的追蹤效能。 在加速輸入值的估計問題上，我們提出適用於高斯量測雜訊的貝氏估計法及適用於非高斯量測雜訊的修正最小平方法。藉由假設加速輸入值的機率分佈是高斯混和分佈所推導出的貝氏估計法，是以加權平均各個高斯單元之期望值，來求出輸入估計值，而加權比重是以遞迴的方式動態調整。與利用最小平方法，從一段等速卡爾曼濾波器之預測誤差來估計輸入值的演算法比較起來，我們的方法能夠比較快速地估計出加速輸入值。為了減小量測雜訊對於估計精確度的影響，我們提出一個利用卡爾曼濾波的前處理法，能夠有效地消除量測雜訊。在非高斯量測雜訊下之輸入值估計問題上，我們是以二階多項式來近似目標物的位置量測值，並以修正最小平方法求出輸入估計值。在這個方法裡，我們去除了包含脈衝雜訊的量測值，使得估計精確度能夠優於傳統最小平方法。 在非高斯雜訊的即時鑑別問題上，我們提出了一個批次處理演算法及一個遞迴處理演算法。由於量測雜訊是隱藏於量測訊號中，無法直接獲取以進行鑑別，因此我們首先利用一階及二階差分濾波器，搭配中間值濾波器，從量測訊號中抽取出與量測雜訊相關的訊號。在第一個批次處理演算法中，利用抽取出的量測雜訊，我們用最大相似度法進行鑑別，結果顯示從量測訊號做即時鑑別所得到的模型參數值相當接近從量測雜訊做鑑別所得到的結果。由於最大相似度法需要很高的計算複雜度，而且其批次處理方式無法對雜訊統計參數的改變做出即時的反應，所以我們提出了另一個利用隨機梯度搜尋的遞迴處理演算法。我們分析了這個遞迴演算法的收斂特性，並推導出修正步階的有效上限。結果顯示遞迴演算法所得到的模型參數估計可以快速地收斂，並相當接近最大相似度法所得到的結果，對於雜訊統計值的改變，也能夠有快速的反應。根據即時鍵別的結果，我們可以動態地調整追蹤演算法中的設定值，使得因為量測雜訊統計值改變而造成追蹤精確度降低的問題得以獲得改善。

The existing target tracking algorithms mostly rely on prior selection of system parameters: the input exciting target maneuver and the parameters of the measurement noise distributions. However, these parameters are actually unknown and time-varying. To obtain more accurate tracking results, online identification is then necessary. In maneuvering target tracking, the existing algorithms mainly use the multiple-filter approach. This approach simultaneously run multiple tracking filters, designed based on pre-selected maneuver input values, to estimate the state of a maneuvering target. When applying this approach to track a highly maneuverable target, such as a tactical fighter, a large number of tracking filters will be required which results in high computational complexity. A possible method to reduce complexity is to online estimate the maneuver input, and adjust the setting of tracking filters. In this way, the tracking filters can be made adaptive with target maneuvers and hence less tracking filters will be required. On the other hand, due to the random wandering of the radar reflection center, the measurement noise presents non-Gaussian behavior. This type of noise is referred to as glint and its distribution is heavy-tailed. The statistics of glint noise change with target aspect and motion making it a non-stationary process. Although nonlinear tracking algorithms have been developed to solve the problem, knowledge of the noise distribution model has to be known. Thus, online noise identification is required. In this thesis, we propose algorithms for online maneuver input estimation and noise identification for tracking maneuvering targets. For the problem of online maneuver input estimation, we derive a Bayesian method for the Gaussian measurement noise and a trimmed least-squares method for the glint measurement noise. The Bayesian method is derived based on a Gaussian-mixture model for the maneuver input distribution. This method obtains the input estimate from a weighted combination of the means of the mixture components. By considering the transition among the mixture components as a Markov process, our method can respond more quickly to the abrupt change of maneuver values than the least-squares method. To reduce the effect of measurement noise, we propose a pre-filtering scheme using a reduced-gain Kalman filter. When the measurement noise is non-Gaussian, we propose to estimate the input by fitting a second-order polynomial to the position measurements. A trimmed least-squares method is used to find the solution. This method can reduce the effect of the glint spike achieving higher accuracy than the conventional least-squares method. As to the problem of online identifying the non-Gaussian measurement noise, we propose a batch-processing and a recursive-processing algorithm. Since measurement noise is usually unavailable, we first extract measurement noise from target position measurements. The proposed noise extraction method uses a first- or second-order differentiator and a order statistic filter. In the first algorithm, we perform identification using the maximum-likelihood (ML) method. The results show that the parameter estimates are close to those obtained from exact knowledge of the measurement noise. Since the ML method has high computational complexity and cannot react immediately with the change of the noise statistics, we thus propose a recursive algorithm, which uses the stochastic-gradient-descent (SGD) method. We analyze its convergence property and derive closed-form expressions for sufficient step size bounds. It is shown that the identified parameters using the simpler SGD method can converge fast and the accuracy is comparable to that of the ML method. Using the sufficient step size bounds, the change of the noise statistics can be well tracked. The online identified parameters can be directly fed into the tracking algorithm making it adapt to the change of the noise statistics.