Control of a physical system based on inferred state

1. A physical system comprising:

a sensor;

an actuator; and

processing hardware;

wherein:

operation of the actuator is controlled by the processing hardware based on a state of the physical system which is inferred from sensor data;

the processing hardware includes:

an input interface configured for accessing the sensor data from the sensor and representing sensor measurements associated with the state of the physical system;

an output interface to the actuator via which the processing hardware performs the control of the operation of the actuator; and

a processor subsystem configured to use the sensor data by:

obtaining a sensor measurement from the sensor data accessed via the input interface;

applying the sensor measurement obtained from the accessed sensor data to a mathematical prior knowledge-based state model that identifies an initial inference of the state of the physical system that corresponds to the sensor measurement;

applying the initial inference of the state of the physical system identified by the model and the sensor measurement obtained from the accessed sensor data to a recurrent neural network that the processor subsystem executed and that has been learned to minimize an error between initial inferences identified by the mathematical prior knowledge-based state model and a ground truth and to provide a final inference of the state of the physical system; and

performing the control of the operation of the actuator based on the final inference of the state of the physical system;

the execution, by the processor subsystem, of the recurrent neural network, to which the initial inference of the state of the physical system and the sensor measurement has been applied, includes performing an iterative refinement of the inference gradually from the initial inference of the state of the physical system to the final inference of the state of the physical system, the iterative refinement including performing a plurality of iterations that include:

a first iteration that operates on the sensor measurement applied to the mathematical prior knowledge-based model and on the initial inference of the state of the physical system obtained from the mathematical prior knowledge-based model;

a final iteration; and

at least one intermediate iteration between the first iteration and the final iteration;

each of the at least one intermediate iteration obtains as input, and processes, the sensor measurement that had been applied to the mathematical prior knowledge-based model, a respective modified inference of the state of the physical system that had been output by an immediately preceding one of the iterations, and a respective hidden state of the recurrent network that had been output by the immediately preceding one of the iterations, the processing by the respective intermediate iteration producing:

a further hidden state; and

a further modified inference of the state of the physical system by generating a correction value as a function of the input sensor measurement, the input respective modified inference of the state of the physical system, and the input respective hidden state and then modifying the input respective modified inference of the state of the physical system by the correction value; and

the final iteration obtains as input, and processes, the sensor measurement that had been applied to the mathematical prior knowledge-based model, the further modified inference of the state of the physical system that had been produced by an immediately preceding one of the at least one intermediate iteration, and the further hidden state that had been produced by the immediately preceding one of the at least one intermediate iteration, the processing by the final iteration producing the final inference of the state of the physical system by generating a further correction value as a function of the input sensor measurement, the input further modified inference of the state of the physical system, and the further hidden state that had been produced by the immediately preceding one of the at least one intermediate iteration, and then modifying the input further modified inference of the state of the physical system by the further correction value.

2. The system according to claim 1 , wherein the processor subsystem is configured to:

using the input interface, obtain a time-series of sensor measurements;

obtain the initial inference of the state by using the time-series of sensor measurements and a time-series of previous inferred states as input to the mathematical prior knowledge-based state model;

apply the recurrent neural network to the initial inference of the state and the time-series of sensor measurements to obtain a time-series of correction values; and

obtain the final inference of the state by combining the initial inference of the state with the time-series of correction values.

3. The system according to claim 1 , wherein the recurrent neural network includes a gated recurrent unit to establish recursion in the recurrent neural network.

4. The system according to claim 1 , wherein the mathematical prior knowledge-based state model provides a physics-based modelling of the state as a function of the sensor measurement and a previous inferred state.

5. The system according to claim 1 , wherein the mathematical prior knowledge-based state model includes a transitional model part which models a conditional probability of the state to be inferred given a previous inferred state, and a measurement model part which models a conditional probability of the sensor measurement given the state to be inferred.

6. The system according to claim 5 , wherein the processor subsystem is configured to iteratively infer the state by Kalman Filtering by assuming that probability distributions of the mathematical prior knowledge-based state model are linear and Gaussian.

7. The system according to claim 1 , wherein the actuator is a vehicle actuator or a robotics actuator.

8. The system according to claim 1 , wherein the system is configured to cause a sensory perceptible warning signal to be generated when the final inference of the state of the physical system indicates a failure of the physical system.

9. A method of a physical system that includes a sensor, an actuator, and processing hardware in which operation of the actuator is controlled by the processing hardware based on a state of the physical system which is inferred from sensor data, the method comprising the following steps:

using an input interface of the processing hardware, accessing the sensor data from the sensor and representing sensor measurements associated with the state of the physical system;

performing the following, by a processor subsystem of the processing hardware, using the sensor data:

obtaining a sensor measurement from the sensor data from the sensor accessed via the input interface;

applying the sensor measurement obtained from the accessed sensor data to a mathematical prior knowledge-based model that identifies an initial inference of the state of the physical system that corresponds to the sensor measurement;

applying the initial inference of the state of the physical system identified by the model and the sensor measurement obtained from the accessed sensor data to a recurrent neural network that is executed by the processor subsystem and that has been learned to minimize an error between initial inferences identified by the mathematical prior knowledge-based state model and a ground truth and to provide a final inference of the state of the physical system; and

performing the control of the operation of the actuator based on the final inference of the physical system;

wherein:

the execution, by the processor system of the recurrent neural network, to which the initial inference of the state of the physical system and the sensor measurement has been applied, includes performing an iterative refinement of the inference gradually from the initial inference of the state of the physical system to the final inference of the state of the physical system, the iterative refinement including performing a plurality of iterations that include:

a first iteration that operates on the sensor measurement applied to the mathematical prior knowledge-based model and on the initial inference of the state of the physical system obtained from the mathematical prior knowledge-based model;

a final iteration; and

at least one intermediate iteration between the first iteration and the final iteration;

each of the at least one intermediate iteration obtains as input, and processes, the sensor measurement that had been applied to the mathematical prior knowledge-based model, a respective modified inference of the state of the physical system that had been output by an immediately preceding one of the iterations, and a respective hidden state of the recurrent neural network that had been output by the immediately preceding one of the iterations, the processing by the respective intermediate iteration producing:

a further hidden state; and

a further modified inference of the state of the physical system by generating a correction value as a function of the input sensor measurement, the input respective modified inference of the state of the physical system, and the input respective hidden state and then modifying the input respective modified inference of the state of the physical system by the correction value; and

the final iteration obtains as input, and processes, the sensor measurement that had been applied to the mathematical prior knowledge-based model, the further modified inference of the state of the physical system that had been produced by an immediately preceding one of the at least one intermediate iteration, and the further hidden state that had been produced by the immediately preceding one of the at least one intermediate iteration, the processing by the final iteration producing the final inference of the state of the physical system by generating a further correction value as a function of the input sensor measurement, the input further modified inference of the state of the physical system, and the further hidden state that had been produced by the immediately preceding one of the at least one intermediate iteration, and then modifying the input further modified inference of the state of the physical system by the further correction value.