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The conventional proportional navigation studied before involves a guidance law that the commanded acceleration is regulated proportionally to the product of line-of-sight rate and closing speed. It is wildly used on the simple scenario of missile interception with small heading error. But on the dogfight scenario with high heading error, its performance is not so good as that with small heading error. In this article, an extended proportional navigation is introduced and studied. In this proposed guidance scheme, the commanded acceleration is regulated proportionally to the product of relative speed and line-of-sight rate between interceptor and its target, and it can be generalized to be applied in a different direction with a bias angle to the normal direction of line-of-sight. The relative speed is always greater than the closing speed and finally approaches to the closing speed till intercept. The exact and complete closed-form solutions are derived for both maneuvering and non-maneuvering targets. Some related important characteristics, such as capture capability and energy cost, are investigated and discussed. From the result, it is found that some improvement can be achieved under this new guidance scheme, as compared with the previous ones. Also, a typical example of target maneuver is introduced to describe the effect of target maneuver easily. It shows that the target maneuver will usually decrease the capture area and increase the energy cost for effective intercept of target.
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