System and method for state estimation in a noisy machine-learning environment

Abstract

A system and method for estimating a system state. The method includes making a first measurement and a second measurement of a value of a characteristic of a state of a system. The method includes constructing first filter measurement and time estimates after the second measurement coinciding with the first measurement including corresponding covariance matrices describing an accuracy of the first filter measurement and time estimates. The method includes constructing second filter measurement and time estimates coinciding with the second measurement including corresponding covariance matrices describing an accuracy of the second filter measurement and time estimates. The method includes constructing a smoothing estimate from the first and second filter measurement estimates. The method includes constructing a first prediction estimate that provides a forecast of a value of the characteristic of the state of the system including a first prediction covariance matrix describing an accuracy of the first prediction estimate.

1 . A method, comprising:
 making a first measurement of a value of a characteristic of a state of a system;   making a second measurement of a value of said characteristic of said state of said system after said first measurement;   constructing a first filter measurement estimate after said second measurement coinciding with said first measurement including a first filter measurement covariance matrix describing an accuracy of said first filter measurement estimate;   constructing a first filter time estimate after said first filter measurement estimate including a first filter time covariance matrix describing an accuracy of said first filter time estimate employing a dynamic model of said state of said system;   constructing a second filter measurement estimate after said first filter time estimate coinciding with said second measurement including a second filter measurement covariance matrix describing an accuracy of said second filter measurement estimate;   constructing a second filter time estimate after said second filter measurement estimate including a second filter time covariance matrix describing an accuracy of said second filter time estimate employing said dynamic model of said state of said system;   constructing a smoothing estimate from said first filter measurement estimate and said second filter measurement estimate; and   constructing a first prediction estimate after said smoothing estimate that provides a forecast of a value of said characteristic of said state of said system including a first prediction covariance matrix describing an accuracy of said first prediction estimate employing said dynamic model of said state of said system.   
     
     
         2 . The method as recited in  claim 1  further comprising constructing a second prediction estimate after said first prediction estimate that provides another forecast of a value of said characteristic of said state of said system including a second prediction covariance matrix describing an accuracy of said second prediction estimate employing said dynamic model of said state of said system. 
     
     
         3 . The method as recited in  claim 1  further comprising constructing a plurality of prediction estimates that provides a corresponding plurality of forecasts of a value of said characteristic of said state of said system including a corresponding plurality of prediction covariance matrices describing an accuracy of said plurality of prediction estimates employing said dynamic model of said state of said system. 
     
     
         4 . The method as recited in  claim 1  wherein constructing said smoothing estimate comprises sweeping backward recursively from said second filter measurement estimate to said first filter measurement estimate. 
     
     
         5 . The method as recited in  claim 1  further comprising altering said state of said system based on said first prediction estimate. 
     
     
         6 . The method as recited in  claim 1  wherein said constructing said first filter measurement estimate, said first filter time estimate, said second filter measurement estimate and said second filter time estimate are performed by a Kalman filter. 
     
     
         7 . The method as recited in  claim 1  further comprising reporting said state of said system based on said first prediction estimate. 
     
     
         8 . The method as recited in  claim 1  wherein said first measurement comprises a plurality of independent measurements characterized by a diagonal measurement covariance matrix. 
     
     
         9 . The method as recited in  claim 1  wherein said dynamic model comprises a linear dynamic model with constant coefficients. 
     
     
         10 . The method as recited in  claim 1  wherein said dynamic model comprises a matrix with coefficients that describes a temporal evolution of said state of said system. 
     
     
         11 . An apparatus operable to construct a state of a system, comprising:
 processing circuitry coupled to a memory, configured to:   make a first measurement of a value of a characteristic of said state of said system;   make a second measurement of a value of said characteristic of said state of said system after said first measurement;   construct a first filter measurement estimate after said second measurement coinciding with said first measurement including a first filter measurement covariance matrix describing an accuracy of said first filter measurement estimate;   construct a first filter time estimate after said first filter measurement estimate including a first filter time covariance matrix describing an accuracy of said first filter time estimate employing a dynamic model of said state of said system;   construct a second filter measurement estimate after said first filter time estimate coinciding with said second measurement including a second filter measurement covariance matrix describing an accuracy of said second filter measurement estimate;   construct a second filter time estimate after said second filter measurement estimate including a second filter time covariance matrix describing an accuracy of said second filter time estimate employing said dynamic model of said state of said system;   construct a smoothing estimate from said first filter measurement estimate and said second filter measurement estimate; and   construct a first prediction estimate after said smoothing estimate that provides a forecast of a value of said characteristic of said state of said system including a first prediction covariance matrix describing an accuracy of said first prediction estimate employing said dynamic model of said state of said system.   
     
     
         12 . The apparatus as recited in  claim 11  wherein said processing circuitry is further configured to construct a second prediction estimate after said first prediction estimate that provides another forecast of a value of said characteristic of said state of said system including a second prediction covariance matrix describing an accuracy of said second prediction estimate employing said dynamic model of said state of said system. 
     
     
         13 . The apparatus as recited in  claim 11  wherein said processing circuitry is further configured to construct a plurality of prediction estimates that provides a corresponding plurality of forecasts of a value of said characteristic of said state of said system including a corresponding plurality of prediction covariance matrices describing an accuracy of said plurality of prediction estimates employing said dynamic model of said state of said system. 
     
     
         14 . The apparatus as recited in  claim 11  wherein said processing circuitry is configured to construct said smoothing estimate by sweeping backward recursively from said second filter measurement estimate to said first filter measurement estimate. 
     
     
         15 . The apparatus as recited in  claim 11  wherein said processing circuitry is further configured to alter said state of said system based on said first prediction estimate. 
     
     
         16 . The apparatus as recited in  claim 11  wherein said processing circuitry is configured to construct said first filter measurement estimate, said first filter time estimate, said second filter measurement estimate and said second filter time estimate with a Kalman filter. 
     
     
         17 . The apparatus as recited in  claim 11  wherein said processing circuitry is further configured to report said state of said system based on said first prediction estimate. 
     
     
         18 . The apparatus as recited in  claim 11  wherein said first measurement comprises a plurality of independent measurements characterized by a diagonal measurement covariance matrix. 
     
     
         19 . The apparatus as recited in  claim 11  wherein said dynamic model comprises a linear dynamic model with constant coefficients. 
     
     
         20 . The apparatus as recited in  claim 11  wherein said dynamic model comprises a matrix with coefficients that describes a temporal evolution of said state of said system.