Kalman Filtering Techniques for Radar Tracking

K.V. Ramachandra

• Publisher: CRC Press
• Year: 2018
• Print ISBN: 9780824793227
• eBook ISBN: 9781351830775
• Topic: Technology & Engineering
• Subtopic: Electrical Engineering & Telecommunications
• Index: Technology & Engineering

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.

1

Kalman Filter

1.1 Introduction

1.2 Discrete-time kalman filter

1.3 Continuous-time kalman-bucy filter

1.4 Continuous-discrete-time kalman-bucy filter

1.5 Summary

References

1.1 INTRODUCTION

The Kalman filter has made a dramatic impact on linear estimation because of its adaptability for implementation on a digital computer for online estimation and usefulness of the state space approach. Today the Kalman filter is an established technique widely applied in the fields of navigation, guidance, attitude control, satellite orbit determination, aircraft and missiles tracking, radar, sonar and biomedical signal processing, reentry of space vehicles, etc. [1–11]. Many new applications of this powerful technique are being reported in various fields of engineering and technology.

The general discrete time formulation of the Kalman filter [1], the continuous time Kalman-Bucy filter [2], and the continuous discrete time Kalman-Bucy filter [2,6] are presented in this chapter.

1.2 DISCRETE-TIME KALMAN FILTER

The statistical model of the signal process is assumed to be described by the discrete, linear, vector matrix equation of the form [1–11]

(1.1)

X k + 1 = F k X k + G k W k

where

X _k = n-dimensional state vector at the k th stage

F _k = n × n transition matrix

G _k = n × r input distribution matrix

W _k = rdimensional random input vector

W _k is assumed to be white gaussian with the following properties:

(1.2)

E { W k } = 0 E { W j W k T } = Q δ jk

where Q is the r × r covariance matrix of the process noise W _k and δ _jk is the Dirac delta function.

The statistical model of the measurement process is described by

(1.3)

Z k = H k X k + V k

where Z _k is the mdimensional measurement vec...

Table of contents

• Cover
• Halftitle
• Title
• Copyright
• Contents
• Preface
• Acknowledgment
• 1 Kalman Filter
• 2 Discrete-time one-dimensional tracking filters
• 3 Discrete‐time two‐dimensional tracking filters
• 4 Discrete‐Time Three‐Dimensional Tracking Filters
• 5 Continuous‐time one‐dimensional tracking filters with position measurements
• 6 Continuous-discrete-time one-dimensional tracking filters with position measurements
• 7 Continuous-Discrete-Time One-Dimensional Tracking Filters with Position and Rate Measurements
• 8 Continuous‐Time One‐Dimensional Kalman Tracking Filters with Position and Velocity Measurements
• 9 Maneuvering target tracking
• 10 Tracking a maneuvering target in clutter
• 11 Introduction to Multitarget Tracking
• Index