Ambiguity function and accuracy of the hyperbolic chirp: comparison with the linear chirp

In this paper, we derive the Ambiguity Function (AF) of a narrowband and a wideband hyperbolic chirp. We calculate the second derivatives of the squared amplitude of the narrowband Complex Ambiguity Function (CAF) and use them to calculate the Fisher Information Matrix (FIM) of the estimators of the target range and velocity. The FIM is then used to calculate the Cramer-Rao Lower Bounds (CRLB) of the variance of the estimators and to ´ carry out an analysis of estimation performance and a comparison with the case of a liner chirp with a rectangular and a Gaussian amplitude modulation. The analysis and the calculations of the CRLB are also extended to a train of hyperbolic chirps. Results corroborate that at narrowband the hyperbolic chirp is less Doppler tolerant than the linear chirp and show that the hyperbolic chirp provides a comparable measurement accuracy to the linear chirp. Results at wideband corroborate the superior Doppler tolerance of the hyperbolic chirp with respect to that of the linear chirp

Measurements and analysis of multistatic and multimodal micro-Doppler signatures for automatic target classification

The purpose of this paper is to present an experimental trial carried out at the Defence Academy of the United Kingdom to measure simultaneous multistatic and multimodal micro-Doppler signatures of various targets, including humans and flying UAVs. ewline Signatures were gathered using a network of sensors consisting of a CW monostatic radar operating at 10 GHz (X-band) and an ultrasound radar with a monostatic and a bistatic channel operating at 45 kHz and 35 kHz, respectively. A preliminary analysis of automatic target classification performance and a comparison with the radar monostatic case is also presented

Baseband version of the bat-inspired spectrogram correlation and transformation receiver

Echolocating bats have evolved an excellent ability to detect and discriminate targets in highly challenging environments. They have had more than 50 million years of evolution to optimise their echolocation system with respect to their surrounding environment. Behavioural experiments have shown their exceptional ability to detect and classify targets even in highly cluttered surroundings. The way bats process signals is not exactly the same as in radar and hence it can be useful to investigate the differences. The Spectrogram Correlation And Transformation receiver (SCAT) is an existing model of the bat auditory system that takes into account the physiology and underlying neural organisation in bats which emit chirped signals. In this paper, we propose a baseband receiver equivalent to the SCAT. This will allow biologically inspired signal processing to be applied to radar baseband signals. It will also enable further theoretical analysis of the key concepts, advantages and limitations of the "bat signal processing" for the purpose of target detection, localisation and resolution. The equivalence is demonstrated by comparing the output of the original SCAT to that of our proposed baseband version using both simulated and experimental target echoes. Results show that the baseband receiver provides compatible frequency interference pattern for two closely located scatterers

Coordination of optimal guidance law and adaptive radiated waveform for interception and rendezvous problems

The authors present an algorithm that allows an interceptor aircraft equipped with an airborne radar to meet another air target (the intercepted) by developing a guidance law and automatically adapting and optimising the transmitted waveform on a pulse-to-pulse basis. The algorithm uses a Kalman filter to predict the relative position and speed of the interceptor with respect to the target. The transmitted waveform is automatically selected based on its ambiguity function and accuracy properties along the approaching path. For each pulse, the interceptor predicts its position and velocity with respect to the target, takes a measurement of range and radial velocity and, with the Kalman filter, refines the relative range and range rate estimates. These are fed into a linear quadratic Gaussian controller that ensures the interceptor reaches the target automatically and successfully with minimum error and with the minimum guidance energy consumption

Joint waveform and guidance control optimisation for target rendezvous

The algorithm developed in this paper jointly selects the optimal transmitted waveform and the control input so that a radar sensor on a moving platform with linear dynamics can reach a target by minimising a predefined cost. The cost proposed in this paper accounts for the energy of the transmitted radar signal, the energy of the platform control input and the relative position error between the platform and the target, which is a function of the waveform design and control input. Similarly to the Linear Quadratic Gaussian (LQG) control problem, we demonstrate that the optimal solution satisfies the separation principle between filtering and optimisation and, therefore, the optimum can be found analytically. The performance of the proposed solution is assessed with a set of simulations for a pulsed Doppler radar transmitting linearly frequency modulated chirps. Results show the effectiveness of the proposed approach for optimal waveform design and optimal guidance control

Extraction and analysis of micro-Doppler signatures by the Empirical Mode Decomposition

A set of experimental trials was conducted with a 10 GHz continuous wave radar to collect micro-Doppler signatures of a large single, double and triple bladed rotating fin and a sized miniature helicopter. We analysed the target micro-Doppler signatures and decomposed them using the Empirical Mode Decomposition (EMD) method in order to extract a series of Intrinsic Mode Functions (IMFs) which admit only an instantaneous frequency. The aim of this paper is to investigate what information is available in the target IMFs to help identify key features that can be used for improving target classification and identification. The experimental testing was complimented with a set of simulations to assist in the understanding of the results

Experimental analysis of multistatic multiband radar signatures of wind turbines

This study presents the analysis of recent experimental data acquired using two radar systems at S-band and X-band to measure simultaneous monostatic and bistatic signatures of operational wind turbines near Shrivenham, UK. Bistatic and multistatic radars are a potential approach to mitigate the adverse effects of wind farm clutter on the performance of radar systems, which is a well-known problem for air traffic control and air defence radar. This analysis compares the simultaneous monostatic and bistatic micro-Doppler signatures of two operational turbines and investigates the key differences at bistatic angles up to 23°. The variations of the signature with different polarisations, namely vertical transmitted and vertical received and horizontal transmitted and horizontal received, are also discussed

Measurements of the radar cross section of a nano-drone at K-band

Nano-drones, are insect-like sized drones with a threat capability of intrusion to provide intelligence and potentially violate secure establishments and public privacy rights. They are an existing technology which is becoming increasingly more available, portable, affordable and easy to operate. As such, they represent a plausible defence and security threat. In this paper, a setup is presented that is used to measure the 3-dimensional Radar Cross Section (RCS) of a nano-drone for three elevation planes with a 5-degree resolution step in azimuth and elevation. The results presented in this paper are unique because there has been very little work, if any, in the existing literature attempting to measure the RCS of such small drones. They are also key to inform further work investigating the development of nano-drone detection radar systems as well as nano-drone detection and classification signal processing solutions

Micro-doppler-based in-home aided and unaided walking recognition with multiple radar and sonar systems

Published in IET Radar, Sonar and Navigation. Online first 21/06/2016.The potential for using micro-Doppler signatures as a basis for distinguishing between aided and unaided gaits is considered in this study for the purpose of characterising normal elderly gait and assessment of patient recovery. In particular, five different classes of mobility are considered: normal unaided walking, walking with a limp, walking using a cane or tripod, walking with a walker, and using a wheelchair. This presents a challenging classification problem as the differences in micro-Doppler for these activities can be quite slight. Within this context, the performance of four different radar and sonar systems – a 40 kHz sonar, a 5.8 GHz wireless pulsed Doppler radar mote, a 10 GHz X-band continuous wave (CW) radar, and a 24 GHz CW radar – is evaluated using a broad range of features. Performance improvements using feature selection is addressed as well as the impact on performance of sensor placement and potential occlusion due to household objects. Results show that nearly 80% correct classification can be achieved with 10 s observations from the 24 GHz CW radar, whereas 86% performance can be achieved with 5 s observations of sonar

Multibeam radar based on linear frequency modulated waveform diversity

Multibeam radar (MBR) systems based on waveform diversity require a set of orthogonal waveforms in order to generate multiple channels in transmission and extract them efficiently at the receiver with digital signal processing. Linear frequency modulated (LFM) signals are extensively used in radar systems due to their pulse compression properties, Doppler tolerance, and ease of generation. Here, the authors investigate the level of isolation between MBR channels based on LFM chirps with rectangular and Gaussian amplitude envelopes. The orthogonal properties and the mathematical expressions of the isolation are derived as a function of the chirp design diversity, and specifically for diverse frequency slopes and frequency offsets. The analytical expressions are validated with a set of simulations as well as with experiments at C-band using a rotating target