Radar tracking performance was compared among two choices of statistical filtering algorithms for the noisy measurements of exo-atmospheric objects in ballistic motion. Such motion is characteristic of satellites and missiles. Object position and velocity were governed by the nonlinear dynamics of body motion in a central force field, and measurements were modeled as nonlinear observations of those object motions in Cartesian coordinates. The two choices of statistical filtering algorithms were distinguished by their method of handling a sequence of noisy measurements. The first processed measurements, one-at-a-time, in a sequential recursive estimation using the Extended Kalman Filter (EKF), and the second processed that same sequence of measurements, simultaneously, in a batch-least-squares (BLS) estimation algorithm. Both algorithms used first-variation approximations of the nonlinear observations and error dynamics of object motion. Taylor series expansions were centered about the current best estimates of the state vector. The EKF used those approximations to implement the often referenced linear-minimum-variance (Kalman) estimation formulas. The BLS processed those same measurements simultaneously in a least-squares search over object trajectories spanning the tracking interval, and initial state estimation was based on convergence to the best object path. Results were obtained for both algorithms performing in a desktop program with a reasonable degree of radar systems modeling, and in a comprehensive mission simulator where radar system errors were represented in greater detail. Those included radar-cross-section fluctuations, scan angle loss, antenna gain patterns, radar signal-to-noise sensitivity, monopulse measurement errors, and front-end noise. The BLS algorithm was seen to converge faster, and predict more accurate 1-sigma values, than the EKF in all comparisons.

A review of effective radar tracking filter methods and their associated digital filtering algorithms. It examines newly developed systems for eliminating the real-time execution of complete recursive Kalman filtering matrix equations that reduce tracking and update time. It also focuses on the role of tracking filters in operations of radar data processors for satellites, missiles, aircraft, ships, submarines and RPVs.

TRACKING, PREDICTION, AND SMOOTHING BASICS. g and g-h-k Filters. Kalman Filter. Practical Issues for Radar Tracking. LEAST-SQUARES FILTERING, VOLTAGE PROCESSING, ADAPTIVE ARRAY PROCESSING, AND EXTENDED KALMAN FILTER. Least-Squares and Minimum-Variance Estimates for Linear Time-Invariant Systems. Fixed-Memory Polynomial Filter. Expanding- Memory (Growing-Memory) Polynomial Filters. Fading-Memory (Discounted Least-Squares) Filter. General Form for Linear Time-Invariant System. General Recursive Minimum-Variance Growing-Memory Filter (Bayes and Kalman Filters without Target Process Noise). Voltage Least-Squares Algorithms Revisited. Givens Orthonormal Transformation. Householder Orthonormal Transformation. Gram--Schmidt Orthonormal Transformation. More on Voltage-Processing Techniques. Linear Time-Variant System. Nonlinear Observation Scheme and Dynamic Model (Extended Kalman Filter). Bayes Algorithm with Iterative Differential Correction for Nonlinear Systems. Kalman Filter Revisited. Appendix. Problems. Symbols and Acronyms. Solution to Selected Problems. References. Index.

Four different filtering options are considered for the problem of tracking an exoatmospheric ballistic target with no maneuvers. The four filters are an alpha-beta filter, an augmented alpha-beta filter, a decoupled Kalman filter, and a fully-coupled extended Kalman filter. These filters are listed in the order of increasing computational complexity. All of the filters can track the target with some degree of accuracy. While the pure alpha-beta filter appreciably lags the other filters in performance for this problem, its augmented version is very competitive with the extended Kalman filter under benign conditions. Perhaps the most surprising result is that under all conditions examined, the decoupled (linear) Kalman filter, which is at least an order of magnitude less computationally complex, performs nearly identical to the coupled, extended Kalman filter. Four different filtering options are considered for the problem of tracking an exoatmospheric ballistic target with no maneuvers. The four filters are an alpha-beta filter, an augmented alpha-beta filter, a decoupled Kalman filter, and a fully-coupled extended Kalman filter. These filters are listed in the order of increasing computational complexity. All of the filters can track the target with some degree of accuracy. While the pure alpha-beta filter appreciably lags the other filters in performance for this problem, its augmented version is very competitive with the extended Kalman filter under benign conditions. Perhaps the most surprising result is that under all conditions examined, the decoupled (linear) Kalman filter, which is at least an order of magnitude less computationally complex, performs nearly identical to the coupled, extended Kalman filter.

For most tracking applications the Kalman filter is reliable and efficient, but it is limited to a relatively restricted class of linear Gaussian problems. To solve problems beyond this restricted class, particle filters are proving to be dependable methods for stochastic dynamic estimation. Packed with 867 equations, this cutting-edge book introduces the latest advances in particle filter theory, discusses their relevance to defense surveillance systems, and examines defense-related applications of particle filters to nonlinear and non-Gaussian problems. With this hands-on guide, you can develop more accurate and reliable nonlinear filter designs and more precisely predict the performance of these designs. You can also apply particle filters to tracking a ballistic object, detection and tracking of stealthy targets, tracking through the blind Doppler zone, bi-static radar tracking, passive ranging (bearings-only tracking) of maneuvering targets, range-only tracking, terrain-aided tracking of ground vehicles, and group and extended object tracking.

The efficient use of a search-surface radar or sonar, in which one or more targets appear on the screen intermittently usually demands a device for tracking the targets automatically. Such a device, called a track while scan system, must make an estimate of each target's instantaneous position from the sampled-data information provided by the radar. For this purpose, an alpha-beta filter and an optimal Kalman filter, that must track maneuvering targets, are analyzed here and compared in terms of tracking accuracy for tactical applications.