B.F. La Scala

Design of an extended Kalman filter frequency tracker

The design of an extended Kalman filter for tracking a time-varying frequency is discussed. Its principal modes of failure are explained. The design tradeoff between balancing noise rejection and tracking at a maximal slew rate is discussed. The performance penalties for overdesign and underdesign of noise covariances are examined, and theoretically supported design guidelines are suggested.

Integrated track splitting filter - efficient multi-scan single target tracking in clutter

A fully automatic tracking algorithm must be able to deal with an unknown number of targets, unknown target initiation and termination times, false measurements and possibly time-varying target trajectory behaviour. An efficient algorithm for tracking in this environment is presented here. This approach makes use of estimates of the probability of target existence, which is an integral part of the algorithm. This allows for the efficient generation and management of possible target hypotheses, yielding an algorithm with performance that matches what can be obtained by multiple hypothesis tracking-based approaches, but at a significantly lower computational cost. This paper considers only the single target case for clarity. The extension to multiple targets is easily incorporated into this framework. Simulation studies are given that show the effectiveness of this approach in the presence of heavy and nonuniform clutter when tracking a target in an environment of low probability of detection and in an environment where the target performs violent manoeuvres.

Multi-target tracking in clutter without measurement assignment

This paper presents a new approach for multitarget tracking in a cluttered environment. Optimal all neighbour multi-target tracking (MTT) in clutter enumerates all possible joint measurement-to-target assignments and calculates the a posteriori probabilities of each of these joint assignments, e.g. J(I)PDA and MHT. The numerical complexity of this process is exponential in the number of tracks and the number of measurements involved. Our approach starts with an all-neighbour single-target tracking (STT) filter which provides the a priori probabilities of measurement origin; e.g. IPDA, IMM-PDA, ITS. These probabilities are used to modify the clutter density at the location of the selected measurements. In effect, the STT filter is transformed into a MTT filter with a numerical complexity which is linear in the number of tracks and the number of measurements. Measurement features, such as amplitude, can also be incorporated. Simulations are used to verify the approach when tracking crossing targets in an environment of heavy and non-uniform clutter.

An extended Kalman filter frequency tracker for high-noise environments

The problem of constructing a frequency tracker for weak, narrowband signals with slowly varying frequency is considered. An extended Kalman filter is proposed that uses prior knowledge of the nature of the signal to overcome the difficulties presented by the inherent nonlinearity of the problem and the very low signal-to-noise ratios.

Optimal adaptive waveform selection for target detection

Modern phased array radars are able to adaptively modify their performance to the environment. To make full use of this capability, scheduling algorithms need to be designed. This paper poses the problem of adaptive waveform scheduling for detecting new targets in the context of finite horizon stochastic dynamic programming. The result is a scheduling algorithm that minimises the time taken to detect new targets, detecting these targets in accordance with importance, while minimising the use of radar resources.

MAP estimation of target manoeuvre sequence with the expectation-maximization algorithm

Two algorithms are derived for the problem of tracking a manoeuvring target based on a sequence of noisy measurements of the state. Manoeuvres are modeled as unknown input (acceleration) terms entering linearly into the state equation and chosen from a discrete set. The expectation maximization (EM) algorithm is first applied, resulting in a multi-pass estimator of the MAP sequence of inputs. The expectation step for each pass involves computation of state estimates in a bank of Kalman smoothers tuned to the possible manoeuvre sequences. The maximization computation is efficiently implemented using the Viterbi algorithm. A second, recursive estimator is then derived using a modified EM-type cost function. To obtain a dynamic programming recursion, the target state is assumed to satisfy a Markov property with respect to the manoeuvre sequence. This results in a recursive but suboptimal estimator implementable on a Viterbi trellis. The transition costs of the latter algorithm, which depend on filtered estimates of the state, are compared with the costs arising in a Viterbi-based manoeuvre estimator due to Averbuch, et al. (1991). It is shown that the two criteria differ only in the weighting matrix of the quadratic part of the cost function. Simulations are provided to demonstrate the performance of both the batch and recursive estimators compared with Averbuchs method and the interacting multiple model filter.

Optimal target tracking with restless bandits

Abstract This paper examines the problem of adaptive beam scheduling to minimise target tracking error with a phased array radar. It is shown that this can be posed in a framework that is similar to a particular type of dynamic programming problem known as the restless bandit problem. We will show that when the problem is put in this framework it has an indexable solution under certain circumstances.

Integrated track splitting suite of target tracking filters

This paper presents new algorithms for mulfi-scan, single target and multi target tracking in clutter. The algorithms from the Integrated Track Splif- ring (ITS) family offilters model each track as a set of components, where each component has a unique meas- uremenf history which consists ofzero or one measure- men1 received each scan. For each componenf, as well as for each track, the state estimate and the a-posferiori probability of component existence are computed recur- sively. Three algorithms are presenfed in fhis paper. The ITSfilfer is a single target tracking algorithm. The Joint ITS (JITS) filter is a multi target tracking algorithm which calculafes the a-posteriori probabilities of all pos- sible measurement-to-track assignmenfs, from which a- posteriori probabilities of component and track existence are computed. In each scan, fhe number of assignments grows exponentially in the number of trach and the num- ber of measuremenfs involved. The Linear Joint ITS (I-IITS) filter is anofher multi targef tracking algorifhm which decouples individual tracks in a mulfi-hack sifua- tion using the a-priori probabilities of possible measure- ment origins. In each scan, the LJlTSfilfer has a number of operations which is linear in the number offracks and the number of measurements involved.

Minimum Necessary Data Rates for Accurate Track Fusion

Advances in technology are making distributed networks of sensor platforms a reality for surveillance systems. Such networks provide many benefits including the ability to cover a broader area, to compute more accurate target estimates and provide a reduction in susceptibility to countermeasures. In spite of these advantages, many practical issues remain in the deployment of such networks. One such significant issue is bandwidth limitations on the communication channels between the sensor platforms. This paper examines the effect of bandwidth restrictions on a decentralised system architecture. In such a structure, each sensor tracks targets within its individual surveillance region and then transmits its track data to a global fusion centre. The minimum necessary data rates required to permit reconstruction of the global track estimates to a given level of accuracy are presented in the case when the track state can be represented by a Gauss-Markov system.

Differential Geometry Measures of Nonlinearity for Ground Moving Target Indicator (GMTI) Filtering

The ground moving target indicator (GMTI) radar is widely used to detect, geolocate, track, and classify ground-moving targets in all weather, day-night, and cluttered conditions. The measurements of a GMTI radar are slant range, azimuth, and range-rate or Doppler. These measurements are nonlinear functions of the target state. Until recently, a quantitative measure of the degree of nonlinearity (DoN) for nonlinear filtering problems was lacking. Recently, the DoN of a filtering problem with a nonlinear measurement model has been quantified using the differential geometry based measures of nonlinearity such as the parameter-effects curvature and intrinsic curvature. We calculate three types of parameter-effects curvature and intrinsic curvature for the nonlinear GMTI filtering problem for a variety of scenarios. We vary the distance between the target and the GMTI sensor in these scenarios using simulated data. We demonstrate that the state estimation mean square error (MSE) increases with increase in the DoN