Projectile launch point estimation from radar measurements

Abstract

Nonlinear regression with an intercept is investigated and a new nonlinear regression algorithm is developed. The application area considered is ballistic trajectory determination from battlefield radar measurements. Specifically, the geo-location of an enemy artillery piece is pursued. Careful modelling of the nonlinear measurement situation at hand and the inclusion of an intercept parameter in the nonlinear regression shows a considerable improvement over conventional iterative least squares estimation when nonlinearity is dominant. Moreover, the estimation performance does not degrade from standard iterative least squares (ILS) in cases where the nonlinearity is weak compared to the measurement noise in the equation error, provided that the data record is sufficiently long.

Adaptive and reconfigurable flight control using feed-forward action

“…We now apply our work on regression with an intercept [ [1], [2]] to flight control and expand on the reconfigurable flight control concept from [ [3], [4], [5], [6]]. We choose to use static system identification because it affords the use of linear regression for parameter estimation, which is rigorous.…”

A batch processing algorithm for moving surface target tracking

“…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.…”

“…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. Since the model analysed by the authors was characterised by strong non‐linearities for specific target‐to‐radar geometries, the standard ILS formulation was augmented with a so‐called intercept parameter to improve the algorithm convergence.…”