Binary-valued Sensors Research Articles

Input Design in Worst-Case System Identification Using Binary Sensors

This technical note addresses system identification using binary-valued sensors in a worst-case set-membership setting. The main contribution is the solution of the optimal input design problem for identification of scalar gains, which is instrumental to the construction of suboptimal input signals for identification of FIR models of arbitrary order. Two different cost functions are considered for input design: the maximum parametric identification error and the relative uncertainty reduction with respect to the minimum achievable error. It is shown that in the latter case, the solution enjoys the property of being independent of the length of the identification experiment and as such it can be implemented as an optimal recursive procedure over a time interval of arbitrary length.

Signal estimation with binary-valued sensors

This paper introduces several algorithms for signal estimation using binary-valued output sensing. The main idea is derived from the empirical measure approach for quantized identification, which has been shown to be convergent and asymptotically efficient when the unknown parameters are constants. Signal estimation under binary-valued observations must take into consideration of time varying variables. Typical empirical measure based algorithms are modified with exponential weighting and threshold adaptation to accommodate time-varying natures of the signals. Without any information on signal generators, the authors establish estimation algorithms, interaction between noise reduction by averaging and signal tracking, convergence rates, and asymptotic efficiency. A threshold adaptation algorithm is introduced. Its convergence and convergence rates are analyzed by using the ODE method for stochastic approximation problems.

State Observers and Stabilization of Systems with Binary-Valued Observations

This paper introduces an observer for linear time invariant systems in continuous time whose outputs are measured only by binary-valued sensors. The traditional observers will fail in general, even if the system has a full-rank observability matrix. It is shown that by controlling the sensor threshold, it is always possible to cause the output to cross the sensor threshold within a designated time interval. Information on the time instants of threshold crossing is then used to develop state estimates. Convergence properties of the state observer are established. It is shown that by generating appropriate switching time sequences, state observers are convergent in the mean squares sense, with probability one, and exponentially. Combined with a state feedback using the state estimates, this state estimator leads to a stabilizing output feedback.

State reconstruction for linear time-invariant systems with binary-valued output observations

This paper focuses on state reconstruction problems for systems whose outputs are measured only by binary-valued sensors. A binary-valued sensor is characterized by its switching threshold or post-switching location and by its output that indicates only whether the system output is above or below the threshold. The traditional passive-type state reconstruction that does not require input design will fail in general, even if the system has a full-rank observability matrix. It is shown that under controllability conditions and bounded uncertainty on the initial state, it is always possible to construct a causal input that will cause the output to cross the sensor threshold in a designated time interval. Information on the time instants of threshold crossing is then used to reconstruct the initial state. It is proved that if the system is observable, such a reconstruction is always possible if the eigenvalues of the system are all real valued. If the eigenvalues of the system contain only purely imaginary and non-repeating values, it is sufficient that threshold crossing occurs within a relatively small time interval. In general without constraints on system eigenvalues, an input can always be randomized to ensure that the state can be reconstructed with probability one. These results lead to an active state reconstruction algorithm.

Identification of Wiener systems with binary-valued output observations

This work is concerned with identification of Wiener systems whose outputs are measured by binary-valued sensors. The system consists of a linear FIR (finite impulse response) subsystem of known order, followed by a nonlinear function with a known parametrization structure. The parameters of both linear and nonlinear parts are unknown. Input design, identification algorithms, and their essential properties are presented under the assumptions that the distribution function of the noise is known and the nonlinearity is continuous and invertible. It is shown that under scaled periodic inputs, identification of Wiener systems can be decomposed into a finite number of core identification problems. The concept of joint identifiability of the core problem is introduced to capture the essential conditions under which the Wiener system can be identified with binary-valued observations. Under scaled full-rank conditions and joint identifiability, a strongly convergent algorithm is constructed. The algorithm is shown to be asymptotically efficient for the core identification problem, hence achieving asymptotic optimality in its convergence rate. For computational simplicity, recursive algorithms are also developed.

System identification using binary sensors

System identification is investigated for plants that are equipped with only binary-valued sensors. Optimal identification errors, time complexity, optimal input design, and impact of disturbances and unmodeled dynamics on identification accuracy and complexity are examined in both stochastic and deterministic information frameworks. It is revealed that binary sensors impose fundamental limitations on identification accuracy and time complexity, and carry distinct features beyond identification with regular sensors. Comparisons between the stochastic and deterministic frameworks indicate a complementary nature in their utility in binary-sensor identification.