Academic literature on the topic 'Detection and estimation theory'

This thesis focuses on techniques for analyzing the performance of estimation and detection algorithms under conditions which could be encountered in wireless networks, with emphasis on wireless sensor networks. These include phenomena such as measurement losses, fading channels, measurement delays and power constraints.<br>We first look at the hidden Markov model (HMM) filter with random measurement losses. The loss process is governed by another Markov chain. In the two-state case we derive analytical expressions to compute the probability of error. In the multi-state case we derive approximations that are valid at high signal-to-noise ratio (SNR). Relationships between the error probability and parameters of the loss process are investigated.<br>We then consider the problem of detecting two-state Markov chains in noise, under the Neyman-Pearson formulation. Our measure of performance here is the error exponent, and we give methods for computing this, firstly when channels are time-invariant, and then for time-varying fading channels. We also characterize the behaviour of the error exponent at high SNR.<br>We will look at the fixed lag Kalman smoother with random measurement losses. We investigate both the notion of estimator stability via expectation of the error covariance, and a probabilistic constraint on the error covariance. A comparison with the Kalman filter where lost measurements are retransmitted is made.<br>Finally we consider the distributed estimation of scalar linear systems using multiple sensors under the analog forwarding scheme. We study the asymptotic behaviour of the steady state error covariance as the number of sensors increases. We formulate optimization problems to minimize the sum power subject to error covariance constraints, and to minimize the error covariance subject to sum power constraints. We compare between the performance of multi-access and orthogonal access schemes, and for fading channels the effects of various levels of channel state information (CSI).

The impact of false information injection is investigated for linear dynamic systems with multiple sensors. First, it is assumed that the system is unaware of the existence of false information and the adversary is trying to maximize the negative effect of the false information on Kalman filter's estimation performance under a power constraint. The false information attack under different conditions is mathematically characterized. For the adversary, many closed-form results for the optimal attack strategies that maximize the Kalman filter's estimation error are theoretically derived. It is shown that by choosing the optimal correlation coefficients among the false information and allocating power optimally among sensors, the adversary could significantly increase the Kalman filter's estimation errors. In order to detect the false information injected by an adversary, we investigate the strategies for the Bayesian estimator to detect the false information and defend itself from such attacks. We assume that the adversary attacks the system with certain probability, and that he/she adopts the worst possible strategy that maximizes the mean squared error (MSE) if the attack is undetected. An optimal Bayesian detector is designed which minimizes the average system estimation error instead of minimizing the probability of detection error, as a conventional Bayesian detector typically does. The case that the adversary attacks the system continuously is also studied. In this case, sparse attack strategies in multi-sensor dynamic systems are investigated from the adversary's point of view. It is assumed that the defender can perfectly detect and remove the sensors once they are corrupted by false information injected by an adversary. The adversary's goal is to maximize the covariance matrix of the system state estimate by the end of attack period under the constraint that the adversary can only attack the system a few times over the sensor and over the time, which leads to an integer programming problem. In order to overcome the prohibitive complexity of the exhaustive search, polynomial-time algorithms, such as greedy search and dynamic programming, are proposed to find the suboptimal attack strategies. As for greedy search, it starts with an empty set， and one sensor is added at each iteration, whose elimination will lead to the maximum system estimation error. The process terminates when the cardinality of the active set reaches to the sparsity constraint. Greedy search based approaches such as sequential forward selection (SFS), sequential backward selection (SBS), and simplex improved sequential forward selection (SFS-SS) are discussed and corresponding attack strategies are provided. Dynamic programming is also used in obtaining the sub-optimal attack strategy. The validity of dynamic programming lies on a straightforward but important nature of dynamic state estimation systems: the credibility of the state estimate at current step is in accordance with that at previous step. The problem of false information attack on and the Kalman filter's defense of state estimation in dynamic multi-sensor systems is also investigated from a game theoretic perspective. The relationship between the Kalman filter and the adversary can be regarded as a two-person zero-sum game. The condition under which both sides of the game will reach a Nash equilibrium is investigated.