Optimization of biased proportional navigation (guided projectiles)

An analytical treatment of the biased proportional navigation (BPN) is carried out with the aim of optimizing the bias parameter. It is shown that optimum biasing can lead to significantly more control-effort-efficient PN guidance in a wide variety of engagement situations, especially those involving higher target maneuvers. The performance of the BPN is compared with the standard (unbiased) PN system for the general case of a maneuvering target, and performance of the BPN is maximised to obtain the optimum bias value. The optimum bias is expressed through a simple algebraic equation, which can be readily solved. For the special (and very useful) case of the effective navigation constant being equal to three, the equation reduces to a quadratic, leading to an explicit expression for the optimum bias. Specific examples are provided to show the benefits of the BPN law. The higher control efficiency of the law is especially useful in extra-atmospheric interception, where the savings in control effort directly translates to a saving of propellent which forms part of the payload.<>