Application of adaptive filtering techniques to interceptors
Joe Hill · Guidance, Navigation and Control Conference · 1996
An interceptor may encounter highly maneuverable targets that may cause its on-board filter to lose tracking of the target, thereby causing the interceptor to miss the target. These tracking filters typically estimate either line-of-sight/line-of-sight rate or position/velocity (depending on the type of measurements available) for guidance purposes and are usually constant-parameter Kalman filters. There has been a significant amount of research performed recently in the area of adaptive filtering. In this effort, we will demonstrate the applicability of a particular adaptive filtering technique which monitors the innovations process to detect the presence of a maneuver and subsequently modifies the filter process noise term. This particular technique is less computationally intensive than other adaptive filtering techniques and seems to be well-suited for implementation on board an interceptor. We will then implement and test the algorithm in a 6 Degree of Freedom terminal homing simulation of both interceptor and target and will demonstrate improved tracking performance and miss distance using the adaptive filter for a limited set of accelerating targets. Introduction A typical interceptor kinetic kill vehicle (KKV) is equipped with attitude and divert pulse width modulated thrusters and associated control systems, as well as body fixed seekers (infrared and/or laser) which are used for homing guidance as well as for target identification and discrimination. Typically, the attitude control system (ACS) thrusters are sized to provide adequate control authority to overcome the effects of divert thrusters which do not produce forces exactly through the KKV center of gravity, and to account for uncertainties due to true airframe response. Traditionally, classical proportional or proportional plus integral (PI) control is employed in the autopilot attitude and rate control for stabilization and pointing accuracy performance. These interceptors are typically of the hit-to-kill variety, thus requiring small miss distances in order to assure destruction of the target. The interceptor is also equipped with an implementation of an on-line estimator, which provides for the ability to compute estimates of target line-ofsight/line-of-sight rates or position/velocity, depending on the type of measurement information available and the type of seeker being employed. These estimates are then used for guidance and navigation to allow the interceptor to guide to the target. These estimators are typically constant-parameter Kalman filters. While these type of filters perform quite well for nonmaneuvering targets, the encountering of highly maneuverable targets can cause instabilities in Kalman filter performance, which can cause the filter to lose tracking and thus cause the interceptor to miss the target. When designing the Kalman filter, the process noise term (Qk) is selected such that the 65 to 95% confidence region about zero contains the maximum acceleration level of the target. However, when targets maneuver, the acceleration changes in a deterministic manner. Thus, the white noise assumption is violated and the filter develops a bias in the state estimates. If a larger Qk is chosen, the bias in the state estimates is less during a maneuver, but then Qt poorly characterizes the target motion when the target is not maneuvering and the filter performance is far from optimal [20]. Thus, when attempting to track maneuvering targets with single usual constant-parameter filtering techniques, the gains are often either too high, which results from a high process noise covariance and gives poor noise reduction, or too low, which results from a low process noise covariance and yields poor tracking performance during target maneuvers [15]. There has been a significant amount of previous research done in the area of adaptive filtering, using several different techniques. Many of these techniques are described in [1] and will be briefly 1 American Institute of Aeronautics and Astronautics summarized here. There are three broad classes of adaptive filtering algorithms which have been used to improve the tracking of maneuvering targets. The first class involves modification of the filter process noise upon detection of the target maneuver [2-7]. This modification may be either continuous or discrete, where several levels of noise can be assumed for the filter, with a switching mechanism provided. The second class of adaptive filtering algorithms, input estimation, is implemented assuming the input (i.e., target acceleration) to be constant over a certain period of time. The state estimate can either be corrected [8] or augmented, where the input becomes an extra state component that is re-estimated sequentially within the augmented state. The latter approach leads to the variable state dimension technique [9]. The third class of adaptive estimation algorithms are based on the socalled approaches [10], which assume that the system behaves according to one of a finite number of models (that is, it is operating in one of several modes). The approaches with this type of algorithm involve both fixed (nonswitching) models as well as switching models. Two suboptimal approaches for model switching include the generalized pseudoBay seian approach [11,12] as well as the interacting multiple model approach [13,14,16,17]. Since the innovation-based process noise modification techniques seem to be less computationally intensive and seem to be well-suited for application on board an interceptor, an algorithm of this type was chosen for implementation. The particular algorithm that will be used is completely described in [2] and [3]. Algorithm Description Since the complete mathematical details of the algorithm are well described in [2] and [3], they will not be repeated here. The basic notion of an algorithm of this type is to monitor the Kalman filter innovations process and detect the presence of a target maneuver based on the sum of the innovations computed over a sliding window, whose length can be optimally determined based on the assumed false-alarm rate. The (discrete, extended) Kalman filter equations are described in [19]. Mathematically, for the Kalman filter, the innovation sequence z(k) is the difference between the measurement and its predicted value and is defined as where z(k) = z(k) H(k)x(kl k -1), k = 1,2,... and x(kl k-1) is the state estimate. For the purposes of this example, we assume that the state estimate consists of the target position, velocity, and acceleration implemented in a 9-state Kalman filter. Since we typically measure target angular position and range with a seeker, the innovation sequence is a deviation in target position. It can be shown that the mean value of the innovation sequence z(k) is nominally zero, but that this mean value is no longer equal to zero when the target begins to maneuver. The innovation sequence is summed over an interval of fixed length, L (containing a fixed number of points) to obtain the statistic DL(k), as follows: