Abstract
This paper presents a quantized Kalman filter implemented using unreliable memories. We consider that both the quantization and the unreliable memories introduce errors in the computations, and we develop an error propagation model that takes into account these two sources of errors. In addition to providing updated Kalman filter equations, the proposed error model accurately predicts the covariance of the estimation error and gives a relation between the performance of the filter and its energy consumption, depending on the noise level in the memories. Then, since memories are responsible for a large part of the energy consumption of embedded systems, optimization methods are introduced to minimize the memory energy consumption under the desired estimation performance of the filter. The first method computes the optimal energy levels allocated to each memory bank individually, and the second one optimizes the energy allocation per groups of memory banks. Simulations show a close match between the theoretical analysis and experimental results. Furthermore, they demonstrate an important reduction in energy consumption of more than 50%.
Highlights
Kalman filtering is a very common recursive estimation task in statistical signal processing [1], and it is often implemented on resource-limited hardware
We propose a methodology for minimizing the energy of the unreliable memories used in the Kalman filter, under a given performance constraint
We first evaluate the accuracy of the proposed theoretical analysis, and we provide solutions to the two considered optimization problems
Summary
Kalman filtering is a very common recursive estimation task in statistical signal processing [1], and it is often implemented on resource-limited hardware. Applications that require an embedded energy-efficient Kalman filter include air quality monitoring [2], biomedical wearable sensors [3], forest fire detection [4] and vehicle positioning [5]. Energy budgets for embedded systems show that memory access consumes about a hundred-times more energy than integer computations [6]. In this paper, we focus on optimizing the energy used by memories in Kalman filters. All memories used in integrated circuits exhibit a fundamental trade-off between data storage reliability and energy consumption that is related to the inability of perfectly controlling the fabrication process. The energy consumption of static random access memories (SRAMs) can be reduced by lowering its supply voltage; this increases the probability that some of the stored bits cannot be retrieved correctly [7]
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