A recursive model for partially correlated χ2 targets

This work considers the problem of χ
²
target detection in normal (Gaussian) noise. The single pulse power, and target RCS, are χ
²
distributed with an arbitrary form factor k. The correlation between pulses is determined by target dynamics, according to a simple rule of thumb. The sequence of target pulses is constructed using a recursive model of Markov chain, and the value of the correlation coefficient is derived. An approximation of 'strict sense χ
²
' is assumed for the probability density function (p.d.f) of the sum of the integrated pulses. The form factor K of this density is calculated in terms of the correlation coefficient, number of integrated pulses and the form factor for the single pulse p.d.f - k. By determination of the normalized threshold for the given P
_fa
(probability of false alarm), the probability of detection - P
_d
can be obtained. One way to do these calculations is using the "universal detection equation" suggested by D.K Barton (7.2005). The model can be used in radar system performance analysis and in simulations. The advantage of these methods is the elimination of the use of tables and graphs, and enabling direct computations such as in multiple situation simulations. It can be done using commercially available advanced mathematical software.