Tracking Multiple Air Targets in a Sparse Data Environment

The main issue with multiple target tracking is associating the observations of a target from one scan with subsequent scans of the target in order to determine which data from one scan are associated with data from previous scans. Once these data points are correlated over several scans, the next step is to determine the trajectory of the underlying targets. Multiple target tracking MTT is essential in military surveillance operations and air tracking control systems. Most MTT systems incorporate linear or piecewise linear algorithms for the filtering and prediction of target positions and finite state Markov Chain techniques. In many instances, data received from one instance to the next consists of a time delay. The greater the time span between data points the more important the ability to be able to estimate the targets position between time spans. Large separations in data points results in a sparse data file requiring the data to be linked together through data fusion in order to capture the complete picture of the targets flight path. In predicting the targets next location it is necessary for the estimate to be determined prior to receiving the targets next true location. We must be able to process the data in a timely fashion and therefore have an efficient algorithm. This problem is best modeled with time series with the process given in a state-space representation that can handle the multivariate case. The state space model allows the trend and seasonal component to evolve randomly as a stochastic process rather than deterministically. The state-space model consists of two equations. The observation or measurement equation, Yt, expresses the n-dimensional observations in vector form. The state equation determines the state at time Xt1i in terms of the previous condition and a noise term. The state space model is also referred to as a Markovian or canonical representation of a multivariate time series process.