Contents

### **Preface XI**


Preface

The content of this book brings together the research results on state-of-the-art Kalman fil‐ tering theory for advanced applications to real-world problems. In **Chapter 1**, the philoso‐ phy and the historical development of Kalman filter from ancient times to the present are followed by the connection between randomness, probability, statistics, random process, es‐ timation theory, and the Kalman filter. A reference recursive recipe (RRR) methodology is proposed, and the efficacy is demonstrated by its application to a simulated spring, mass and damper system, and a real airplane flight data having a larger number of unknown pa‐ rameters and statistics. In **Chapter 2**, a new structure of the forecast error covariance matrix is proposed to mitigate the problems with limited ensemble size and model error in an en‐ semble Kalman filter (EnKF). An adaptive procedure equipped with a second-order least squares method is applied to estimate the inflation factors of forecast and observational er‐ ror covariance matrices. The proposed method is tested on the well-known atmosphere like Lorenz-96 model with spatially correlated observational systems. In **Chapter 3**, state and pa‐ rameter estimation in vehicle dynamics utilizing the unscented Kalman filter is presented. The estimation runs in real time based on a detailed vehicle model and standard measure‐ ments taken within the car. The results are validated using a Volkswagen Golf GTE Plug-In Hybrid for various dynamic test maneuvers and a Genesys ADMA measurement unit for high precision measurements of the vehicle's states. In **Chapter 4**, a sensitivity-based adap‐ tive square-root unscented Kalman filter (SRUKF) is presented. This algorithm combines an unscented Kalman filter (UKF) and the Recursive Prediction Error Method to estimate sys‐ tem states, parameters, and covariances online. In **Chapter 5**, an adaptive Taylor Kalman filter with PSO tuning for tracking nonstationary signal parameters in a noisy environment with primary focus on time-varying power signals is presented. The proposed PSO-tuned Taylor Kalman filter exhibits robust tracking capabilities even under changing signal dy‐ namics, is immune to critical noise conditions and harmonic contaminations, and reveals ex‐ cellent convergence properties. In **Chapter 6**, the estimation of heart strain from noninvasive measurements, heart rate (HR), and chest skin temperature (ST), obtained "online" via wearable body sensors via Kalman filter, is investigated. The experiments are performed us‐ ing data from laboratory and outfield-based heart strain profiling studies in which subjects performed a high-intensity military foot march. In **Chapter 7**, a method of predicting finan‐ cial distress based on Kalman filtering is improved dynamically. Based on the state-space method, two models that are used to describe the dynamic process and discriminant rules of financial distress are established, respectively: a process model and a discriminant model. An empirical study for China's manufacturing industry is also conducted. In **Chapter 8**, an application of the Kalman filter to the navigation of mobile robots, specifically the time-tocontact problem, is presented. A monocular vision-based approach to detect potential obsta‐ cles and to follow them over time through their apparent size change is used. The approach

