Energy Efficient GNSS Signal Acquisition Using Singular Value Decomposition (SVD)

Abstract

A significant challenge in global navigation satellite system (GNSS) signal processing is a requirement for a very high sampling rate. The recently-emerging compressed sensing (CS) theory makes processing GNSS signals at a low sampling rate possible if the signal has a sparse representation in a certain space. Based on CS and SVD theories, an algorithm for sampling GNSS signals at a rate much lower than the Nyquist rate and reconstructing the compressed signal is proposed in this research, which is validated after the output from that process still performs signal detection using the standard fast Fourier transform (FFT) parallel frequency space search acquisition. The sparse representation of the GNSS signal is the most important precondition for CS, by constructing a rectangular Toeplitz matrix (TZ) of the transmitted signal, calculating the left singular vectors using SVD from the TZ, to achieve sparse signal representation. Next, obtaining the M-dimensional observation vectors based on the left singular vectors of the SVD, which are equivalent to the sampler operator in standard compressive sensing theory, the signal can be sampled below the Nyquist rate, and can still be reconstructed via ℓ1 minimization with accuracy using convex optimization. As an added value, there is a GNSS signal acquisition enhancement effect by retaining the useful signal and filtering out noise by projecting the signal into the most significant proper orthogonal modes (PODs) which are the optimal distributions of signal power. The algorithm is validated with real recorded signals, and the results show that the proposed method is effective for sampling, reconstructing intermediate frequency (IF) GNSS signals in the time discrete domain.

A Survey on IoT Positioning Leveraging LPWAN, GNSS, and LEO-PNT

“…By getting rid of chipset constraints, the goal is to reduce device complexity by a factor 10 [43]. Furthermore, a Compressed Sensing (CS) technique requires a smaller number of samples, reducing the amount of memory needed [93].…”

Engineering Applications of Adaptive Kalman Filtering Based on Singular Value Decomposition (SVD)

“…More work can be done in future K-SVD adaptive applications by including the Joseph stabilized form instead of the conventional form of the Riccati equation to avoid the propagation of antisymmetric problems and fine-tuning the process noise covariance matrix Q k . We believe that the key points and principles derived here will find their way to applications in high-speed signal processing by combining K-SVD, K-SVD adaptive and SVD compressive sensing [25]. For future research, we intend to explore particular technology uses.…”