Adaptive notch filtering for tracking multiple complex sinusoid signals

This thesis is related to the field of digital signal processing; where the aim of this research is to develop features of an infinite impulse response adaptive notch filter capable of tracking multiple complex sinusoid signals. Adaptive notch filters are commonly used in: Radar, Sonar, and Communication systems, and have the ability to track the frequencies of real or complex sinusoid signals; thus removing noise from an estimate, and enhancing the performance of a system. This research programme began by implementing four currently proposed adaptive notch structures. These structures were simulated and compared: for tracking between two and four signals; however, in their current form they are only capable of tracking real sinusoid signals. Next, one of these structures is developed further, to facilitate the ability to track complex sinusoid signals. This original structure gives superior performance over Regalia's comparable structure under certain conditions, which has been proven by simulations and results. Complex adaptive notch filter structures generally contain two parameters: the first tracks a target frequency, then the second controls the adaptive notch filter's bandwidth. This thesis develops the notch filter, so that the bandwidth parameter can be adapted via a method of steepest ascent; and also investigates tracking complex-valued chirp signals. Lastly, stochastic search methods are considered; and particle swarm optimisation has been applied to reinitialise an adaptive notch filter, when tracking two signals; thus more quickly locating an unknown frequency, after the frequency of the complex sinusoid signal jumps

Adaptive Interference Mitigation in GPS Receivers

Satellite navigation systems (GNSS) are among the most complex radio-navigation systems, providing positioning, navigation, and timing (PNT) information. A growing number of public sector and commercial applications rely on the GNSS PNT service to support business growth, technical development, and the day-to-day operation of technology and socioeconomic systems. As GNSS signals have inherent limitations, they are highly vulnerable to intentional and unintentional interference. GNSS signals have spectral power densities far below ambient thermal noise. Consequently, GNSS receivers must meet high standards of reliability and integrity to be used within a broad spectrum of applications. GNSS receivers must employ effective interference mitigation techniques to ensure robust, accurate, and reliable PNT service. This research aims to evaluate the effectiveness of the Adaptive Notch Filter (ANF), a precorrelation mitigation technique that can be used to excise Continuous Wave Interference (CWI), hop-frequency and chirp-type interferences from GPS L1 signals. To mitigate unwanted interference, state-of-the-art ANFs typically adjust a single parameter, the notch centre frequency, and zeros are constrained extremely close to unity. Because of this, the notch centre frequency converges slowly to the target frequency. During this slow converge period, interference leaks into the acquisition block, thus sabotaging the operation of the acquisition block. Furthermore, if the CWI continuously hops within the GPS L1 in-band region, the subsequent interference frequency is locked onto after a delay, which means constant interference occurs in the receiver throughout the delay period. This research contributes to the field of interference mitigation at GNSS's receiver end using adaptive signal processing, predominately for GPS. This research can be divided into three stages. I first designed, modelled and developed a Simulink-based GPS L1 signal simulator, providing a homogenous test signal for existing and proposed interference mitigation algorithms. Simulink-based GPS L1 signal simulator provided great flexibility to change various parameters to generate GPS L1 signal under different conditions, e.g. Doppler Shift, code phase delay and amount of propagation degradation. Furthermore, I modelled three acquisition schemes for GPS signals and tested GPS L1 signals acquisition via coherent and non-coherent integration methods. As a next step, I modelled different types of interference signals precisely and implemented and evaluated existing adaptive notch filters in MATLAB in terms of Carrier to Noise Density (\u1d436/\u1d4410), Signal to Noise Ratio (SNR), Peak Degradation Metric, and Mean Square Error (MSE) at the output of the acquisition module in order to create benchmarks. Finally, I designed, developed and implemented a novel algorithm that simultaneously adapts both coefficients in lattice-based ANF. Mathematically, I derived the full-gradient term for the notch's bandwidth parameter adaptation and developed a framework for simultaneously adapting both coefficients of a lattice-based adaptive notch filter. I evaluated the performance of existing and proposed interference mitigation techniques under different types of interference signals. Moreover, I critically analysed different internal signals within the ANF structure in order to develop a new threshold parameter that resets the notch bandwidth at the start of each subsequent interference frequency. As a result, I further reduce the complexity of the structural implementation of lattice-based ANF, allowing for efficient hardware realisation and lower computational costs. It is concluded from extensive simulation results that the proposed fully adaptive lattice-based provides better interference mitigation performance and superior convergence properties to target frequency compared to traditional ANF algorithms. It is demonstrated that by employing the proposed algorithm, a receiver is able to operate with a higher dynamic range of JNR than is possible with existing methods. This research also presents the design and MATLAB implementation of a parameterisable Complex Adaptive Notch Filer (CANF). Present analysis on higher order CANF for detecting and mitigating various types of interference for complex baseband GPS L1 signals. In the end, further research was conducted to suppress interference in the GPS L1 signal by exploiting autocorrelation properties and discarding some portion of the main lobe of the GPS L1 signal. It is shown that by removing 30% spectrum of the main lobe, either from left, right, or centre, the GPS L1 signal is still acquirable

Fir notch filter design: a review

Notch filters are invariably used in communication, control, instrumentation and bio-medical engineering, besides a host of other fields, to eliminate noise and power line interferences. Digital notch filters can be designed as infinite impulse response (IIR) as well as finite impulse response (FIR) structures. As compared to the latter, IIR filters have the advantage that they require lower orders for efficient approximation of a given set of specifications. However, IIR filters are potentially unstable and do not provide linear phase characteristics, in general. FIR filters, on the other hand, are unconditionally stable and can be designed to give exact linear phase characteristics. We, in this review paper, focus our attention to the recent design techniques proposed by us for FIR notch filters. Standard FIR filter design methods, such as windowing, frequency sampling and computer-aided/optimization may be used for designing FIR notch filters. However, most of these methods result in ripples in the passbands. In many situations, maximally at (MF) filters are preferred since they have maximum attenuation in the stopband and hence can yield the best signal-to-noise ratio. A number of methods are available in the literature for designing MF digital filters. We, in this paper, review the design techniques for computing the weights of MF FIR notch filters. A number of design methodologies have been highlighted that lead to either recursive or explicit formulas for the computation of weights of FIR notch filters. Procedures for the design of FIR notch filters with maximal flatness of the amplitude response (in the Butterworth sense) at ω = 0 and ω = p have been given. Empirical formulas for finding the filter length N have also been proposed. By relaxing the linear phase property, it is possible to reduce the filter order required for a given magnitude response specifications. An FIR filter (with non-linear phase) can be derived from a second order IIR notch filter prototype. Explicit mathematical formulas for computing the weights for such FIR notch filters have been given. Design approaches based on the use of (i) Bernstein polynomials, and (ii) lowpass filter design have also been exploited to obtain maximally at FIR notch filters

Interlaced Direct Adaptive Regulation Scheme Applied to a Benchmark Problem

International audienceDirect adaptive regulation schemes using Internal Model Principle and FIR Youla-Kučera controller parametriza-tion have been extensively used for attenuation of multiple unknown and time varying narrow band disturbances [10], [5], [2].This approach provides very good results but requires a very careful design of the central controller in order to keep the water bed effect on the output sensitivity function at a an acceptable level. To simplify the design of the central controller, an adaptive regulation scheme is proposed in this paper which will incorporate a particular adaptive IIR Youla-Kučera Filter, called ρ-notch structure (the denominator is a projection inside the unit circle of the poles of the model of the disturbance which has roots on the unit circle). The adaptive scheme estimates separately the numerator and denominator parameters of the IIR Youla-Kučera Filter. The use of this approach drastically simplify the design of the central controller and provides even better results than [2] with the advantage to use a single central controller independently of the number of narrow band disturbances. Real-time results obtained on an active vibration control system will illustrate the potential of this approach. Comparison with other approaches applied to the same system are also provided

Optimal control algorithm design for a prototype of active noise control system

High-level noise can represent a serious risk for the health, industrial operations often represent continuous exposure to noise, thus an important trouble to handle. An alternative of solution can be the use of passive mechanisms of noise reductions, nonetheless its application cannot diminish low-frequency noise. Active Noise Control (ANC) is the solution used for low-frequency noise, ANC systems work according to the superposition principle generating a secondary anti-noise signal to reduce both. Nevertheless, the generation of an anti-noise signal with same oppose characteristics of the original noise signal presupposes the utilization of special techniques such as adaptive algorithms. These algorithms involve computational costs. The present research present the optimization of a specific ANC algorithm in the step-size criteria. Delayed Filtered-x LMS (FxLMS) algorithm using an optimal step-size is evaluated in a prototype of ANC system.Tesi

An FPGA architecture design of a high performance adaptive notch filter

The occurrence of narrowband interference near frequencies carrying information is a common problem in modern control and signal processing applications. A very narrow notch filter is required in order to remove the unwanted signal while not compromising the integrity of the carrier signal. In many practical situations, the interference may wander within a frequency band, in which case a wider notch filter would be needed to guarantee its removal, which may also allow for the degradation of information being carried in nearby frequencies. If the interference frequency could be autonomously tracked, a narrow bandwidth notch filter could be successfully implemented for the particular frequency. Adaptive signal processing is a powerful technique that can be used in the tracking and elimination of such a signal. An application where an adaptive notch filter becomes necessary is in biomedical instrumentation, such as the electrocardiogram recorder. The recordings can become useless when in the presence of electromagnetic fields generated by power lines. Research was conducted to fully characterize the interference. Research on notch filter structures and adaptive filter algorithms has been carried out. The lattice form filter structure was chosen for its inherent stability and performance benefits. A new adaptive filter algorithm was developed targeting a hardware implementation. The algorithm used techniques from several other algorithms that were found to be beneficial. This work developed the hardware implementation of a lattice form adaptive notch filter to be used for the removal of power line interference from electrocardiogram signals. The various design tradeo s encountered were documented. The final design was targeted toward multiple field programmable gate arrays using multiple optimization efforts. Those results were then compared. The adaptive notch filter was able to successfully track and remove the interfering signal. The lattice form structure utilized by the proposed filter was verified to exhibit an inherently stable realization. The filter was subjected to various environments that modeled the different power line disturbances that could be present. The final filter design resulted in a 3 dB bandwidth of 15.8908 Hz, and a null depth of 54 dB. For the baseline test case, the algorithm achieved convergence after 270 iterations. The final hardware implementation was successfully verified against the MATLAB simulation results. A speedup of 3.8 was seen between the Xilinx Virtex-5 and Spartan-II device technologies. The final design used a small fraction of the available resources for each of the two devices that were characterized. This would allow the component to be more readily available to be added to existing projects, or further optimized by utilizing additional logic