Method for model-based ranging and localization

A method comprising:

• during a first time period:
• accessing a first set of time-difference-of-arrival measurement data associated with a first signal transmitted by a first transmitter at a first time and received by a first pair of nodes in a first set of nodes arranged in a first geometry within a first environment;
• generating a first set of parameters of a first mixture model based on the first set of time-difference-of-arrival measurement data and a neural network;
• generating a first probability density function, in a first set of probability density functions, representing a first distribution of distances between the first transmitter and the first pair of nodes at the first time based on the first set of parameters and the first set of time-difference-of-arrival measurement data;
• accessing a first set of reference data representing a first known time-difference-of-arrival of the first signal for the first pair of nodes;
• calculating a first loss function, in a first set of loss functions, for the first probability density function based on the first set of reference data;
• calculating a first composite loss function based on an average of the first set of loss functions;
• and
• training the neural network based on backpropagation of the first set of loss functions and the first composite loss function;
• and
• during a second time period succeeding the first time period:
• accessing a second set of time-difference-of-arrival measurement data associated with a second signal transmitted by a second transmitter at a second time and received by a second pair of nodes in a second set of nodes arranged in a second geometry within a second environment;
• generating a second set of parameters of a second mixture model based on the second set of time-difference-of-arrival measurement data and the neural network;
• generating a second probability density function, in a second set of probability density functions, representing a second distribution of distances between the second transmitter and the second pair of nodes at the second time based on the second set of parameters and the second set of time-difference-of-arrival measurement data;
• generating a spatial probability density function based on the second set of probability density functions, the spatial probability density function representing likelihoods of positions of the second transmitter within the second environment at the second time;
• calculating a set of likelihoods of the second transmitter positioned at a set of grid points representing the second environment based on the spatial probability density function;
• and
• identifying a target grid point, in the set of grid points, exhibiting the highest likelihood in the set of likelihoods as an estimated position of the second transmitter at the second time.