Comparison of recursive and batch processing for impact point prediction of ballistic targets

A batch processing algorithm for moving surface target tracking

“…through the target motion model given in (9) - (12). We will assume that the parameter vector q has the following known Gaussian a priori distribution…”

“…Unfortunately, such a solution doesn't exist and this derivative must be computed using numerical integration as follows. The dynamics given in (12) can be written as…”

“…Therefore at each update of ILS, the target's NED equations of motion and the sensitivity matrix equations are numerically integrated to give the target's position and the required Jacobian at each measurement time. See references [10][11][12][13][14][15] for more applications of this approach to parameter estimation. Section 8 gives a derivation of the tracking position estimation error covariance matrix and Section 9 summarizes the tracking algorithm.…”

Measurement fusion using maximum‐likelihood estimation of ballistic trajectories

“…In this case, the non‐linear model that fits the set of measurements is approximated with a finite precision. Such non‐linear batch estimator involves usually either the non‐linear regression [13, 14] or the maximum‐likelihood (ML) approach [15, 16]. The iterative least‐squares (ILSs) method, a variant of the non‐linear regression, was applied by Nelson et al [14] to firing point (FP) estimation of a mortar projectile based on radar measurements of its positions in flight.…”

“…Mathematical foundation of the MLE procedure for ballistic target trajectories is described in details in Section 3. Then the MLE measurement fusion is evaluated using simulations and compared with two other estimation methods: single‐sensor MLE [15, 16] and track fusion based on MLE [21], which is summarised in Section 4. Sensitivity and immunity of the algorithms are also examined in Section 5 with regard to glint noise, limited observation time, and uncertainty of ballistic coefficient characteristics.…”