A Study on the Performance Comparison of α-β-γ Filter and Kalman Filter for a Tracking Module on board High Dynamic Warships

Tracking refers to the estimation of the state of a target on motion with some degree of accuracy given at least one measurement. The measurement, which is the output obtained from sensors, contains system errors and errors resulting from the surrounding environment. Tracking filters play the key role of target state estimation after which the tracking system is updated. Therefore, the type of filter used in carrying out the estimations is crucial in determining the integrity and reliability of the updated value. This is especially true since different filters vary in their performance when subjected to different environments and initial conditions of motion dynamics. In addition, applications of different filter design methods have previously confirmed that filtering performance is a tradeoff between error reduction and a good transient response. Therefore, the criteria for selecting a particular filter for use in a tracking application depends on the given performance requirement. This study explores and investigates the operation of the Kalman filter and three α-β-γ tracking filter models that include Benedict-Bordner also known as the Simpson filter, Gray-Murray model and the fading memory α-β-γ filter. These filters are then compared based on the ability to reduce noise and follow a high dynamic target warship with minimum total lag error. The total lag error is the cumulative residual error computed from the difference between the true and the predicted positions, and the true and estimated positions for the given data samples. The results indicate that, although the Benedict-Bordner model performs poorly compared to the other filters in all aspects of performance comparison, the filter starts off sluggishly at the beginning of the tracking process as indicated by the overshooting on the trajectories, but stabilizes and picks up a good transient response as the tracking duration increases. The Gray-Murray model, on the other hand, demonstrates a better tracking ability as depicted by its higher accuracy and an even better response to a change in the target’s maneuver as compared to the Benedict-Bordner model. The Fading memory model out-performs the other two α-β-γ filters in terms of tracking and estimation error reduction, but based on sensitivity to target maneuvers and variance reduction ratio the Gray-Murray model demonstrates a slightly better performance. The Kalman filter, on the other hand, has a higher tracking accuracy compared to the α-β-γ filters which, however, have a higher sensitivity to target maneuvers and data stability as indicated by the steadier trajectories obtained. These results are a further proof that no one particular filter is perfect in all dimensions of selection criteria but it is rather a compromise that has to be made depending on the requirement of the physical system under consideration.Chapter 1 Introduction 1 1.1 Scope 1 1.2 Literature 2 1.2.1 Role of a Filter in a Physical System 2 1.2.2 Literature Review 3 1.3 Methodology and Contents 6 Chapter 2 Theory of Tracking Filters 8 2.1 Theory of α-β-γ Tracking Filter 8 2.1.1 Benedict-Bordner model 10 2.1.2 Gray-Murray model 10 2.1.3 The Fading memory model 11 2.2 Theory of the Kalman Filter 12 Chapter 3 Simulation 15 3.1 Initial Input of Target Dynamics 15 3.2 Input Motion Model of the Target Dynamics 15 3.3 Noise Modelling 16 3.4 α-β-γ Filter Weights Selection and Computation 17 3.4.1 Filter Gain Coefficient Selection Using Benedict-Bordner Model 17 3.4.2 Filter Gain Coefficient Selection Using Gray-Murray Model 18 3.4.3 Filter Gain Coefficient Selection Using Fading Memory Model 20 3.4.3.1 Fading memory model Optimization 22 3.4.3.1.1 Optimization by Position 23 3.4.3.1.2 Optimization by Velocity and Acceleration 28 3.5 Kalman Filter Tuning 31 3.5.1 Q Covariance Matrix Tuning 31 3.5.2 R Covariance Matrix Tuning 33 3.6 Result Analysis and Discussion 34 3.6.1 α-β-γ Filter Results and Remarks 34 3.6.2 Kalman Filter Results and Remarks 40 3.6.3 Kalman Filter vs. α-β-γ Filter 42 Chapter 4 Conclusion and Future Prospects 44 Reference 47 Acknowledgments 49Maste

Study of Multi-Modal and Non-Gaussian Probability Density Functions in Target Tracking with Applications to Dim Target Tracking

The majority of deployed target tracking systems use some variant of the Kalman filter for their state estimation algorithm. In order for a Kalman filter to be optimal, the measurement and state equations must be linear and the process and measurement noises must be Gaussian random variables (or vectors). One problem arises when the state or measurement function becomes a multi-modal Gaussian mixture. This typically occurs with the interactive multiple model (IMM) technique and its derivatives and also with probabilistic and joint probabilistic data association (PDA/JPDA) algorithms. Another common problem in target tracking is that the target\u27s signal-to-noise ratio (SNR) at the sensor is often low. This situation is often referred to as the dim target tracking or track-before-detect (TBD) scenario. When this occurs, the probability density function (PDF) of the measurement likelihood function becomes non-Gaussian and often has a Rayleigh or Ricean distribution. In this case, a Kalman filter variant may also perform poorly. The common solution to both of these problems is the particle filter (PF). A key drawback of PF algorithms, however, is that they are computationally expensive. This dissertation, thus, concentrates on developing PF algorithms that provide comparable performance to conventional PFs but at lower particle costs and presents the following four research efforts. 1. A multirate multiple model particle filter (MRMMPF) is presented in Section-3. The MRMMPF tracks a single, high signal-to-noise-ratio, maneuvering target in clutter. It coherently accumulates measurement information over multiple scans via discrete wavelet transforms (DWT) and multirate processing. This provides the MRMMPF with a much stronger data association capability than is possible with a single scan algorithm. In addition, its particle filter nature allows it to better handle multiple modes that arise from multiple target motion models. Consequently, the MRMMPF provides substantially better root-mean-square error (RMSE) tracking performance than either a full-rate or multirate Kalman filter tracker or full-rate multiple model particle filter (MMPF) with a same particle count. 2. A full-rate multiple model particle filter for track-before-detect (MMPF-TBD) and a multirate multiple model particle filter for track-before-detect (MRMMPF-TBD) are presented in Section-4. These algorithms extend the areas mentioned above and track low SNR targets which perform small maneuvers. The MRMMPF-TBD and MMPF-TBD both use a combined probabilistic data association (PDA) and maximum likelihood (ML) approach. The MRMMPF-TBD provides equivalent RMSE performance at substantially lower particle counts than a full-rate MMPF-TBD. In addition, the MRMMPF-TBD tracks very dim constant velocity targets that the MMPF-TBD cannot. 3. An extended spatial domain multiresolutional particle filter (E-SD-MRES-PF) is developed in Section-5. The E-SD-MRES-PF modifies and extends a recently developed spatial domain multiresolutional particle filter prototype. The prototype SD-MRES-PF was only demonstrated for one update cycle. In contrast, E-SD-MRES-PF functions over multiple update cycles and provides comparable RMSE performance at a reduced particle cost under a variety of PDF scenarios. 4. Two variants of a single-target Gaussian mixture model particle filter (GMMPF) are presented in Section-6. The GMMPF models the particle cloud as a Gaussian finite mixture model (FMM). MATLAB simulations show that the GMMPF provides performance comparable to a particle filter but at a lower particle cost