__Keywords:__the passive multistatic radar system multitarget neighbourhood multitarget tracking radiosignals’ parametres pseudorandom hopping identification of signals discrete-continuous Markov filtering in quantized time Gaussian approximating a stationary correlation matrix erroneous identification probability

V. B. Grebennikov, V. I. Merkulov, A. G. Teterukov

The main advantage of passive multistatic radar systems (PMRS) is the hiding of their operation. However, the prior uncertainty of parametres of received signals leads to complicating of algorithms of their operation. In the conditions of multitarget environment when electronic systems tracking by PMRS use pulse radiosignals with a pseudorandom hopping of parametres, one of the major stages of signal processing is the identification of the received radiosignals which is setting up a correspondence between the receiving radiosignals and transmitting objects. This problem is complicated because any signal parametres are unsufficient for signal identification in the conditions of multitarget environment and pseudorandom hopping of parametres. The purpose of the present article is: working up an algorithm of multitarget tracking objects radiating the pulse radiosignals with a pseudorandom hopping parametres and design the computation procedure for random errors estimation.
All processes happening in PMRS are observed in a discrete time. Presence of a central information processing point (CIPP) linked to all positions by reception/trans-mission information channels is provided. Presence of the cross fixation system ensuring measuring of co-ordinates and a velocity of peripheral points in real scale of a common time is supposed also. The point targets are characterised by radius vectors and the velocity vectors, derivating targets state vectors. Any object (target) on each time slice can radiate one of pulsing radiosignals of 1st, …, m th, …, Nω th type where Nω
is the number of used types of signals. The selection of type of a radiated signal happens by the random way. The values of parametres characterising used types of signals are considered as a priori known (reconnoitered). For working up required algorithm Markov approximating of the targets’ state vectors and process of a pseudorandom hopping of parametres of signals is used. An optimum filter and quasioptimal structure are synthesised on the basis of the theory of nonlinear Markov filtering.
In a general view the structure of the optimum Markov filter follows from Stratonovich equation. This equation defines a current joint a posteriori probability distribution of the unknown quantities sought for. However, in most cases this equation cannot be decided analytically because of mathematical difficulties. Therefore for obtaining of technical implemented algorithm the simplified quasioptimal filter structure has been synthesised. For this purpose the dimensions of a jointly estimating vectors has been reduced, filtering process has been fragmentated and Gaussian approximation has been used. Further the decision rule for identification of received signals has been designed. The targets’ state vectors estimation is realized according to the Kalman filtering equations.
The algorithm of multitarget tracking gained on the basis of synthesised quasioptimal filter consists of three stages:
(a) radiosignals’ reception and processing on peripheral points,
(b) identification of received signals,
(c) a posteriori estimation of target’s state vectors.
An algorithm feature is its linearity in relation to the partial estimates gained on different positions and also adaptability to the signal interruption from one or more jammed positions or non-simultaneous data receipt on CIPP.
For example the analysis of signals identification error in dual-target situation is given.
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