Thesis - Leigh Moody.pdf - Bad Request - Cranfield University

Chapter 6 / Missile Guidance
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Whilst reviewing the literature it was surprising how readily the practical
application of PN is sacrificed to allow mathematical tractability. Several
authors were moved to note that reported improvement in capture regions
depends on underlying assumptions that often conflict with the requirements
of the weapon system. Unrealistic target assumptions are frequently
assumed, PPN targets with constant turn rates and TPN targets accelerating
normal to the target LOS. As noted in §2 intelligent targets manoeuvre to
counteract the oncoming missile leading to the application of 2-player game
theory, Ghose [G.2] .
Literature tends to deal only with idealised guidance laws. State observer
performance is often ignored as realistic sensor errors often leading to noisy
boundary conditions, indifferent target tracking performance during
manoeuvres, and manoeuvre detection, Looze [L.2] . The real value of this
work is to increase capture regions in limited regions using constrained
optimal solutions for specific applications. The most significance
enhancements are those supported by the provision of observer data,
particularly for target LOS to missile body scaling to ensure that the missile
delivers the required lateral acceleration.
6.5.1.1 2D True PN
The first closed form 2D analytical solution of the PN equation was
attributed to Guelman [G.3] (1976). The equation was linearised with
acceleration normal to the target LOS for constant velocity engagements.
Shukla [S.2] (1988) expanded the range of the engagement geometries for
practical applications by relaxing the linearisation conditions applied by
Guelman. Yang [Y.1] (1987) and Ghose [G.2&4] (1994) showed that the capture
region of Generalised TPN (GTPN) reduced when applying acceleration at
constant bias angles with respect to the target LOS, angles between the
missile acceleration vector and the target LOS for constant closing speeds.
In a review of TPN, GTPN and PPN, Shukla [S.1] (1990) cast doubt on the
larger capture regions being quoted for GTPN as they were obtained at the
expense of high LOS rates, control effort and unacceptable trajectories. In
the early 90’s Cochran [C.1&2] , Yuan [Y.2-4] and Dhar [D.1] varied the closing
speed whilst applying acceleration normal to the target LOS in Realistic
TPN (RTPN) laws against non-manoeuvring targets. In most cases the
capture region expanded and intercept times were reduced. The acceleration
direction constraint was removed by Rao [R.5] (1993) with similar results.
Chakravarthy [C.3] (1996) provided a generalised solution of the PN equations
without linearisation in which closing speed and applied acceleration angle
were varied in what is referred to as Realistic GTPN (RGTPN).
6.5.1.2 3D True PN
3D PN development mirrors that of 2D GTPN laws. Constrained planar
solutions to 3D PN motion appeared as early as 1956, Adler [A.2] . Guelman,
Cochran (1990) and Yang [Y.5] (1996) provide systematic solutions to
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