Method for multiple antenna joint time of arrival and angle of arrival estimation

A method for joint time of arrival and angle of arrival estimation for a signal, the method comprising:

• accessing a ranging signal transmitted from a transmitter and received at a set of antenna elements of a receiver, the ranging signal comprising a set of multiplexed sub-signals, each multiplexed sub-signal, in the set of multiplexed sub-signals, characterized by a frequency in a set of frequencies;
• for each antenna element in the set of antenna elements, recording a subset of time domain samples, in a set of time domain samples, representing the ranging signal received at the antenna element;
• generating a structured data representation of the set of time domain samples;
• generating a decomposed representation of the set of time domain samples by executing a matrix decomposition operation on the structured data representation of the set of time domain samples, the decomposed representation comprising a signal subspace matrix;
• generating a first set of matrices based on the decomposed representation, the first set of matrices comprising:
• a first matrix comprising a first subset of rows of the signal subspace matrix;
• and
• a second matrix comprising a second subset of rows of the signal subspace matrix;
• calculating a first set of generalized eigenvalues according to a first matrix pencil characterized by the first set of matrices;
• calculating a set of angle of arrival estimates for the ranging signal based on the first set of generalized eigenvalues;
• generating a shuffled matrix based on the decomposed representation and a shuffling matrix;
• generating a second set of matrices based on the shuffled matrix, the second set of matrices comprising:
• a third matrix comprising a third subset of rows of the shuffled matrix;
• and
• a fourth matrix comprising a fourth subset of rows of the shuffled matrix;
• calculating a second set of generalized eigenvalues according to a second matrix pencil characterized by the second set of matrices;
• calculating a set of time of arrival estimates for the ranging signal based on the second set of generalized eigenvalues;
• selecting a first time of arrival estimate, in the set of time of arrival estimates, as corresponding to a line of sight component of the ranging signal;
• and
• identifying a first angle of arrival estimate, in the set of angle of arrival estimates, corresponding to the first time of arrival estimate.

A method for joint time of arrival and angle of arrival estimation for a signal, the method comprising:

• accessing a ranging signal transmitted from a transmitter and received at a set of antenna elements of a receiver via a channel, the ranging signal comprising a set of multiplexed sub-signals, each multiplexed sub-signal, in the set of multiplexed sub-signals, characterized by a frequency in a set of frequencies;
• for each antenna element in the set of antenna elements:
• recording a subset of time domain samples, in a set of time domain samples, representing the ranging signal received at the antenna element;
• and
• accessing a steering matrix, in a set of steering matrices, characterized by:
• the set of frequencies;
• a set of time delay values;
• a set of phase angle values;
• and
• a distance between the antenna elements and a reference antenna element in the set of antenna elements;
• generating a structured data representation of the set of time domain samples characterized by the set of steering matrices and a set of channel coefficients;
• calculating a sparse representation of the channel by:
• executing a sparse recovery algorithm based on the structured data representation of the set of time domain samples;
• and
• isolating a subset of channel coefficients, in the set of channel coefficients, by executing L1-norm regularization based on the structured data representation of the set of time domain samples, the subset of channel coefficients corresponding to a subset of time delay values, in the set of time delay values, and a subset of phase angle values in the set of phase angle values;
• and
• calculating a time of arrival estimate based on the first time delay value and an angle of arrival estimate for the ranging signal received at the set of antenna elements based on the sparse representation of the channel by:
• calculating a set of candidate time of arrival estimates for the ranging signal received at the set of antenna elements based on the subset of time delay values, the set of candidate time of arrival estimates comprising the time of arrival estimate;
• and
• calculating a set of candidate angle of arrival estimates for the ranging signal received at the set of antenna elements based on the subset of phase angle values, the set of candidate angle of arrival estimates comprising the angle of arrival estimate.