Sequential state estimates subject to multiple equality constraints

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Typical probability-based sequential state estimators generate point estimates which, while mathematically optimal, may be physically impossible estimates of the system state. For example, if a state variable of a dynamic system can attain only a discrete set of values, it is probable that a probability-based estimate of that state variable will not attain one of the elements of the discrete set of values. While, in many problems, this may not greatly affect the overall design of a system in which the estimator is a component, there are many situations in which this result might produce unreliable results, including system instability. In this paper, a sequential estimator is discussed which generates state estimates for linear, time-invariant discrete-time dynamic systems in which the state is subject to an instantaneous equality constraint. That is, at each sample time the state is constrained to lie in a given region of the state space. For the example above, the point estimate of the state is constrained to attain one of the set of discrete values which the state variable must attain. It is shown that the solution of this problem, at each time instant, requires only the unconstrained linear sequential estimate at that instant and the instantaneous constraints which define the constraint region. If the linear estimate satisfies the constraints, then it is also the constrained estimate. If the unconstrained estimate does not satisfy the constraints, then the solution is generated from the solution of a set of static nonlinear equations.


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