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An accelerometer can be constructed using a radioactive proof mass, the position of which can be determined on the basis of the difference between the mean number of emitted charged particles detected at opposite walls when the proof mass is not centered. If the emission rate is relatively small, however, the mean counting rate is very noisy; satisfactory operation requires optimum signal processing. The control system, designed by linear stochastic control theory, generates forces that tend to keep the proof mass centered between walls of the instrument and simultaneously produces an estimated acceleration output. The Poisson-type noise of the pickoff is approximated by Gaussian noise; the acceleration input is modeled as a random walk. It is found by simulation that for an instrument with 1.0 inch spacing between the walls, the proof mass excursion can be confined to a peak-to-peak amplitude of 0.36 inch in a severe acceleration environment. The accelerometer output tracks a constant input without error and, when the input acceleration has a random component, the rms error is of the order of ten percent of the random component.