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.

Abstract: An apparatus, system and method for producing a bid price for a service or a good. The apparatus is configured to determine market pricing of an offering derivable from a labor pricing model to estimate a cost of a service, or derivable from a bill of materials model to estimate a cost of a good; determine strategic pricing of the offering derivable from a likelihood of an action being taken and a magnitude of pricing change if that action occurs; determine a competitor evaluation of the offering capturing a view of a customer towards each competitive offering along factors that may incorporate factors beyond solely cost; and aggregate the market pricing, the strategic pricing, and the competitor evaluation to produce a bid price for the offering to win a competition within a confidence interval.

Abstract: A system and method for estimating a system state. The method includes constructing a first estimate of a system state at a first time including a first covariance matrix describing an accuracy of the first estimate. A second estimate of the state is constructed at a second time, after the first time, including a second covariance matrix. A value of a characteristic of the system state is measured at the second time and the second estimate of the system state and the second covariance matrix are adjusted based on the value of the characteristic. A third estimate of the system state is constructed at a third time, before the second time, including a third covariance matrix describing an accuracy of the third estimate. A fourth estimate of the system state is constructed at a fourth time being after the second time.