Proc. SPIE. 5809, Signal Processing, Sensor Fusion, and Target Recognition XIV
KEYWORDS: Data compression, Image compression, Detection and tracking algorithms, Image processing, Fourier transforms, Signal processing, System identification, Target recognition, Algorithm development, Standards development
When processing a signal or an image using the Discrete Cosine Transform (DCT) or Discrete Sine Transform (DST), a typical approach is to extract a portion of the signal by windowing and then form the DCT or DST of the window contents. By shifting the window point by point over the signal, the entire signal may be processed. DCTs and DSTs are defined where the denominator in the transform kernel is either an odd or an even integer, resulting in transforms known as the even DCT (EDCT), even DST (EDST), odd DCT (ODCT) and odd DST (ODST). Each is available in types I to IV, for a total of 16 different transforms. The widely used transform commonly called the "DCT" is actually the EDCT-II. In this paper we extend our previous work using the EDCT-II and EDST-II, and show that a similar approach yields algorithms for the ODCT-II and ODST-II. We develop algorithms to "update" the ODCT-II and ODST-II simultaneously to reflect the modified window contents using less computation than directly evaluating the modified transform via standard Fast Transform algorithms. These algorithms are able to handle arbitrary step sizes up to the length of the transform, i.e. the algorithm simultaneously updates the ODCT-II and ODST-II to reflect inclusion of r, where 1 ≤ r ≤ N-1, additional data points and removal of r old points from the signal. Examples of applications where this algorithm would be useful include target recognition where time constraints may not permit the immediate processing of every incoming data point, adaptive system identification, etc.
We propose a new approach for laser guided weapon guidance that minimizes the total active laser target designation time. The weapon makes use of inertial or GPS guidance within a Kalman filtering framework, and maintains covariance information indicating the uncertainty of its knowledge of the weapon-to-target vector. At any time, the missile needs to be sure that it can navigate to any point within the area around the target that is described by this covariance. Therefore, at each moment during the flight, there exists a covariance threshold above which the weapon cannot guarantee its ability to navigate to the target. This threshold will decrease with time as the weapon-to-target distance decreases. In our proposed approach, when the threshold is exceeded, the weapon requests a brief laser designation of the target. The laser designation provides an accurate measurement of the bearing of the target with respect to the missile, and this is used to improve the estimate of the weapon-to-target vector. In turn, this can be fed back into the Kalman filter to improve the internal state estimate. By minimizing laser designation time, this approach reduces the chance of compromise of the designation agent, and of the fact that targeting is taking place. It also achieves the benefit of improving the accuracy of the underlying inertial or other navigational system, or alternatively the estimate of absolute target position.
KEYWORDS: Logic, Clocks, Detection and tracking algorithms, Fourier transforms, Field programmable gate arrays, Signal processing, Very large scale integration, Algorithm development, Data communications, Rapid manufacturing
An algorithm is developed in the companion paper, to update the existing DFT to represent the new data series that results when a new signal point is received. Updating the DFT in this way uses less computation than directly evaluating the DFT using the FFT algorithm, This reduces the computational order by a factor of log2 N. The algorithm is able to work in the presence of data window function, for use with rectangular window, the split triangular, Hanning, Hamming, and Blackman windows. In this paper, a hardware implementation of this algorithm, using FPGA technology, is outlined. Unlike traditional fully customized VLSI circuits, FPGAs represent a technical break through in the corresponding industry. The FPGA implements thousands of gates of logic in a single IC chip and it can be programmed by users at their site in a few seconds or less depending on the type of device used. The risk is low and the development time is short. The advantages have made FPGAs very popular for rapid prototyping of algorithms in the area of digital communication, digital signal processing, and image processing. Our paper addresses the related issues of implementation using hardware descriptive language in the development of the design and the subsequent downloading on the programmable hardware chip.
In many identification and target recognition applications, the incoming signal will have properties that render it amenable to analysis or processing in the Fourier domain. In such applications, however, it is usually essential that the identification or target recognition be performed in real time. An important constraint upon real-time processing in the Fourier domain is the time taken to perform the Discrete Fourier Transform (DFT). Ideally, a new Fourier transform should be obtained after the arrival of every new data point. However, the Fast Fourier Transform (FFT) algorithm requires on the order of N log<SUB>2</SUB> N operations, where N is the length of the transform, and this usually makes calculation of the transform for every new data point computationally prohibitive. In this paper, we develop an algorithm to update the existing DFT to represent the new data series that results when a new signal point is received. Updating the DFT in this way uses less computational order by a factor of log<SUB>2</SUB> N. The algorithm can be modified to work in the presence of data window functions. This is a considerable advantage, because windowing is often necessary to reduce edge effects that occur because the implicit periodicity of the Fourier transform is not exhibited by the real-world signal. Versions are developed in this paper for use with the boxcar window, the split triangular, Hanning, Hamming, and Blackman windows. Generalization of these results to 2D is also presented.